/usr/include/deal.II/matrix_free/fe_evaluation.h is in libdeal.ii-dev 8.4.2-2+b1.
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//
// Copyright (C) 2011 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__matrix_free_fe_evaluation_h
#define dealii__matrix_free_fe_evaluation_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/template_constraints.h>
#include <deal.II/base/symmetric_tensor.h>
#include <deal.II/base/vectorization.h>
#include <deal.II/base/smartpointer.h>
#include <deal.II/matrix_free/matrix_free.h>
#include <deal.II/matrix_free/shape_info.h>
#include <deal.II/matrix_free/mapping_data_on_the_fly.h>
DEAL_II_NAMESPACE_OPEN
// forward declarations
namespace parallel
{
namespace distributed
{
template <typename> class Vector;
}
}
namespace internal
{
DeclException0 (ExcAccessToUninitializedField);
}
template <int dim, int fe_degree, int n_q_points_1d = fe_degree+1,
int n_components_ = 1, typename Number = double > class FEEvaluation;
/**
* This is the base class for the FEEvaluation classes. This class is a base
* class and needs usually not be called in user code. It does not have any
* public constructor. The usage is through the class FEEvaluation instead. It
* implements a reinit method that is used to set pointers so that operations
* on quadrature points can be performed quickly, access functions to vectors
* for the @p read_dof_values, @p set_dof_values, and @p
* distributed_local_to_global functions, as well as methods to access values
* and gradients of finite element functions.
*
* This class has three template arguments:
*
* @param dim Dimension in which this class is to be used
*
* @param n_components Number of vector components when solving a system of
* PDEs. If the same operation is applied to several components of a PDE (e.g.
* a vector Laplace equation), they can be applied simultaneously with one
* call (and often more efficiently)
*
* @param Number Number format, usually @p double or @p float
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011
*/
template <int dim, int n_components_, typename Number>
class FEEvaluationBase
{
public:
typedef Number number_type;
typedef Tensor<1,n_components_,VectorizedArray<Number> > value_type;
typedef Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > > gradient_type;
static const unsigned int dimension = dim;
static const unsigned int n_components = n_components_;
/**
* @name 1: General operations
*/
//@{
/**
* Initializes the operation pointer to the current cell. Unlike the reinit
* functions taking a cell iterator as argument below and the
* FEValues::reinit() methods, where the information related to a particular
* cell is generated in the reinit call, this function is very cheap since
* all data is pre-computed in @p matrix_free, and only a few indices have
* to be set appropriately.
*/
void reinit (const unsigned int cell);
/**
* Initialize the data to the current cell using a TriaIterator object as
* usual in FEValues. The argument is either of type
* DoFHandler::active_cell_iterator or DoFHandler::level_cell_iterator. This
* option is only available if the FEEvaluation object was created with a
* finite element, quadrature formula and correct update flags and
* <b>without</b> a MatrixFree object. This initialization method loses the
* ability to use vectorization, see also the description of the
* FEEvaluation class. When this reinit method is used, FEEvaluation can
* also read from vectors (but less efficient than with data coming from
* MatrixFree).
*/
template <typename DoFHandlerType, bool level_dof_access>
void reinit (const TriaIterator<DoFCellAccessor<DoFHandlerType,level_dof_access> > &cell);
/**
* Initialize the data to the current cell using a TriaIterator object as
* usual in FEValues. This option is only available if the FEEvaluation
* object was created with a finite element, quadrature formula and correct
* update flags and <b>without</b> a MatrixFree object. This initialization
* method loses the ability to use vectorization, see also the description
* of the FEEvaluation class. When this reinit method is used, FEEvaluation
* can <b>not</b> read from vectors because no DoFHandler information is
* available.
*/
void reinit (const typename Triangulation<dim>::cell_iterator &cell);
/**
* For the transformation information stored in MappingInfo, this function
* returns the index which belongs to the current cell as specified in @p
* reinit. Note that MappingInfo has different fields for Cartesian cells,
* cells with affine mapping and with general mappings, so in order to
* access the correct data, this interface must be used together with
* get_cell_type.
*/
unsigned int get_cell_data_number() const;
/**
* Returns the type of the cell the @p reinit function has been called for.
* Valid values are @p cartesian for Cartesian cells (which allows for
* considerable data compression), @p affine for cells with affine mappings,
* and @p general for general cells without any compressed storage applied.
*/
internal::MatrixFreeFunctions::CellType get_cell_type() const;
/**
* Returns a reference to the ShapeInfo object currently in use.
*/
const internal::MatrixFreeFunctions::ShapeInfo<Number> &
get_shape_info() const;
/**
* Fills the JxW values currently used.
*/
void
fill_JxW_values(AlignedVector<VectorizedArray<Number> > &JxW_values) const;
//@}
/**
* @name 2: Reading from and writing to vectors
*/
//@{
/**
* For the vector @p src, read out the values on the degrees of freedom of
* the current cell, and store them internally. Similar functionality as the
* function DoFAccessor::get_interpolated_dof_values when no constraints are
* present, but it also includes constraints from hanging nodes, so one can
* see it as a similar function to ConstraintMatrix::read_dof_values as
* well. Note that if vectorization is enabled, the DoF values for several
* cells are set.
*
* If some constraints on the vector are inhomogeneous, use the function
* read_dof_values_plain instead and provide the vector with useful data
* also in constrained positions by calling ConstraintMatrix::distribute.
* When accessing vector entries during the solution of linear systems, the
* temporary solution should always have homogeneous constraints and this
* method is the correct one.
*
* If this class was constructed without a MatrixFree object and the
* information is acquired on the fly through a
* DoFHandler<dim>::cell_iterator, only one single cell is used by this
* class and this function extracts the values of the underlying components
* on the given cell. This call is slower than the ones done through a
* MatrixFree object and lead to a structure that does not effectively use
* vectorization in the evaluate routines based on these values (instead,
* VectorizedArray::n_array_elements same copies are worked on).
*/
template <typename VectorType>
void read_dof_values (const VectorType &src);
/**
* For a collection of several vector @p src, read out the values on the
* degrees of freedom of the current cell for @p n_components (template
* argument), starting at @p first_index, and store them internally. Similar
* functionality as the function ConstraintMatrix::read_dof_values. Note
* that if vectorization is enabled, the DoF values for several cells are
* set.
*/
template <typename VectorType>
void read_dof_values (const std::vector<VectorType> &src,
const unsigned int first_index=0);
/**
* Reads data from several vectors. Same as other function with std::vector,
* but accepts a vector of pointers to vectors.
*/
template <typename VectorType>
void read_dof_values (const std::vector<VectorType *> &src,
const unsigned int first_index=0);
/**
* For the vector @p src, read out the values on the degrees of freedom of
* the current cell, and store them internally. Similar functionality as the
* function DoFAccessor::get_interpolated_dof_values. As opposed to the
* read_dof_values function, this function reads out the plain entries from
* vectors, without taking stored constraints into account. This way of
* access is appropriate when the constraints have been distributed on the
* vector by a call to ConstraintMatrix::distribute previously. This
* function is also necessary when inhomogeneous constraints are to be used,
* as MatrixFree can only handle homogeneous constraints. Note that if
* vectorization is enabled, the DoF values for several cells are set.
*
* If this class was constructed without a MatrixFree object and the
* information is acquired on the fly through a
* DoFHandler<dim>::cell_iterator, only one single cell is used by this
* class and this function extracts the values of the underlying components
* on the given cell. This call is slower than the ones done through a
* MatrixFree object and lead to a structure that does not effectively use
* vectorization in the evaluate routines based on these values (instead,
* VectorizedArray::n_array_elements same copies are worked on).
*/
template <typename VectorType>
void read_dof_values_plain (const VectorType &src);
/**
* For a collection of several vector @p src, read out the values on the
* degrees of freedom of the current cell for @p n_components (template
* argument), starting at @p first_index, and store them internally. Similar
* functionality as the function DoFAccessor::read_dof_values. Note that if
* vectorization is enabled, the DoF values for several cells are set.
*/
template <typename VectorType>
void read_dof_values_plain (const std::vector<VectorType> &src,
const unsigned int first_index=0);
/**
* Reads data from several vectors without resolving constraints. Same as
* other function with std::vector, but accepts a vector of pointers to
* vectors.
*/
template <typename VectorType>
void read_dof_values_plain (const std::vector<VectorType *> &src,
const unsigned int first_index=0);
/**
* Takes the values stored internally on dof values of the current cell and
* sums them into the vector @p dst. The function also applies constraints
* during the write operation. The functionality is hence similar to the
* function ConstraintMatrix::distribute_local_to_global. If vectorization
* is enabled, the DoF values for several cells are used.
*
* If this class was constructed without a MatrixFree object and the
* information is acquired on the fly through a
* DoFHandler<dim>::cell_iterator, only one single cell is used by this
* class and this function extracts the values of the underlying components
* on the given cell. This call is slower than the ones done through a
* MatrixFree object and lead to a structure that does not effectively use
* vectorization in the evaluate routines based on these values (instead,
* VectorizedArray::n_array_elements same copies are worked on).
*/
template<typename VectorType>
void distribute_local_to_global (VectorType &dst) const;
/**
* Takes the values stored internally on dof values of the current cell for
* a vector-valued problem consisting of @p n_components (template argument)
* and sums them into the collection of vectors vector @p dst, starting at
* index @p first_index. The function also applies constraints during the
* write operation. The functionality is hence similar to the function
* ConstraintMatrix::distribute_local_to_global. If vectorization is
* enabled, the DoF values for several cells are used.
*/
template<typename VectorType>
void distribute_local_to_global (std::vector<VectorType> &dst,
const unsigned int first_index=0) const;
/**
* Writes data to several vectors. Same as other function with std::vector,
* but accepts a vector of pointers to vectors.
*/
template<typename VectorType>
void distribute_local_to_global (std::vector<VectorType *> &dst,
const unsigned int first_index=0) const;
/**
* Takes the values stored internally on dof values of the current cell and
* sums them into the vector @p dst. The function also applies constraints
* during the write operation. The functionality is hence similar to the
* function ConstraintMatrix::distribute_local_to_global. Note that if
* vectorization is enabled, the DoF values for several cells are used.
*
* If this class was constructed without a MatrixFree object and the
* information is acquired on the fly through a
* DoFHandler<dim>::cell_iterator, only one single cell is used by this
* class and this function extracts the values of the underlying components
* on the given cell. This call is slower than the ones done through a
* MatrixFree object and lead to a structure that does not effectively use
* vectorization in the evaluate routines based on these values (instead,
* VectorizedArray::n_array_elements same copies are worked on).
*/
template<typename VectorType>
void set_dof_values (VectorType &dst) const;
/**
* Takes the values stored internally on dof values of the current cell for
* a vector-valued problem consisting of @p n_components (template argument)
* and sums them into the collection of vectors vector @p dst, starting at
* index @p first_index. The function also applies constraints during the
* write operation. The functionality is hence similar to the function
* ConstraintMatrix::distribute_local_to_global. Note that if vectorization
* is enabled, the DoF values for several cells are used.
*/
template<typename VectorType>
void set_dof_values (std::vector<VectorType> &dst,
const unsigned int first_index=0) const;
/**
* Writes data to several vectors. Same as other function with std::vector,
* but accepts a vector of pointers to vectors.
*/
template<typename VectorType>
void set_dof_values (std::vector<VectorType *> &dst,
const unsigned int first_index=0) const;
//@}
/**
* @name 3: Data access
*/
//@{
/**
* Returns the value stored for the local degree of freedom with index @p
* dof. If the object is vector-valued, a vector-valued return argument is
* given. Note that when vectorization is enabled, values from several cells
* are grouped together. If @p set_dof_values was called last, the value
* corresponds to the one set there. If @p integrate was called last, it
* instead corresponds to the value of the integrated function with the test
* function of the given index.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
value_type get_dof_value (const unsigned int dof) const;
/**
* Write a value to the field containing the degrees of freedom with
* component @p dof. Writes to the same field as is accessed through @p
* get_dof_value. Therefore, the original data that was read from a vector
* is overwritten as soon as a value is submitted.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
void submit_dof_value (const value_type val_in,
const unsigned int dof);
/**
* Returns the value of a finite element function at quadrature point number
* @p q_point after a call to @p evaluate(true,...), or the value that has
* been stored there with a call to @p submit_value. If the object is
* vector-valued, a vector-valued return argument is given. Note that when
* vectorization is enabled, values from several cells are grouped together.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
value_type get_value (const unsigned int q_point) const;
/**
* Write a value to the field containing the values on quadrature points
* with component @p q_point. Access to the same field as through @p
* get_value. If applied before the function @p integrate(true,...) is
* called, this specifies the value which is tested by all basis function on
* the current cell and integrated over.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
void submit_value (const value_type val_in,
const unsigned int q_point);
/**
* Returns the gradient of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true,...), or the value
* that has been stored there with a call to @p submit_gradient.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
gradient_type get_gradient (const unsigned int q_point) const;
/**
* Write a contribution that is tested by the gradient to the field
* containing the values on quadrature points with component @p q_point.
* Access to the same field as through @p get_gradient. If applied before
* the function @p integrate(...,true) is called, this specifies what is
* tested by all basis function gradients on the current cell and integrated
* over.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
void submit_gradient(const gradient_type grad_in,
const unsigned int q_point);
/**
* Returns the Hessian of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true). If only the
* diagonal or even the trace of the Hessian, the Laplacian, is needed, use
* the other functions below.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
Tensor<1,n_components_,Tensor<2,dim,VectorizedArray<Number> > >
get_hessian (const unsigned int q_point) const;
/**
* Returns the diagonal of the Hessian of a finite element function at
* quadrature point number @p q_point after a call to @p evaluate(...,true).
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
gradient_type get_hessian_diagonal (const unsigned int q_point) const;
/**
* Returns the Laplacian (i.e., the trace of the Hessian) of a finite
* element function at quadrature point number @p q_point after a call to @p
* evaluate(...,true). Compared to the case when computing the full Hessian,
* some operations can be saved when only the Laplacian is requested.
*
* Note that the derived class FEEvaluationAccess overloads this operation
* with specializations for the scalar case (n_components == 1) and for the
* vector-valued case (n_components == dim).
*/
value_type get_laplacian (const unsigned int q_point) const;
/**
* Takes values on quadrature points, multiplies by the Jacobian determinant
* and quadrature weights (JxW) and sums the values for all quadrature
* points on the cell. The result is a scalar, representing the integral
* over the function over the cell. If a vector-element is used, the
* resulting components are still separated. Moreover, if vectorization is
* enabled, the integral values of several cells are represented together.
*/
value_type integrate_value () const;
//@}
/**
* @name 4: Access to internal data
*/
//@{
/**
* Returns a read-only pointer to the first field of the dof values. This is
* the data field the read_dof_values() functions write into. First come the
* the dof values for the first component, then all values for the second
* component, and so on. This is related to the internal data structures
* used in this class. In general, it is safer to use the get_dof_value()
* function instead.
*/
const VectorizedArray<Number> *begin_dof_values () const;
/**
* Returns a read and write pointer to the first field of the dof values.
* This is the data field the read_dof_values() functions write into. First
* come the the dof values for the first component, then all values for the
* second component, and so on. This is related to the internal data
* structures used in this class. In general, it is safer to use the
* get_dof_value() function instead.
*/
VectorizedArray<Number> *begin_dof_values ();
/**
* Returns a read-only pointer to the first field of function values on
* quadrature points. First come the function values on all quadrature
* points for the first component, then all values for the second component,
* and so on. This is related to the internal data structures used in this
* class. The raw data after a call to @p evaluate only contains unit cell
* operations, so possible transformations, quadrature weights etc. must be
* applied manually. In general, it is safer to use the get_value() function
* instead, which does all the transformation internally.
*/
const VectorizedArray<Number> *begin_values () const;
/**
* Returns a read and write pointer to the first field of function values on
* quadrature points. First come the function values on all quadrature
* points for the first component, then all values for the second component,
* and so on. This is related to the internal data structures used in this
* class. The raw data after a call to @p evaluate only contains unit cell
* operations, so possible transformations, quadrature weights etc. must be
* applied manually. In general, it is safer to use the get_value() function
* instead, which does all the transformation internally.
*/
VectorizedArray<Number> *begin_values ();
/**
* Returns a read-only pointer to the first field of function gradients on
* quadrature points. First comes the x-component of the gradient for the
* first component on all quadrature points, then the y-component, and so
* on. Next comes the x-component of the second component, and so on. This
* is related to the internal data structures used in this class. The raw
* data after a call to @p evaluate only contains unit cell operations, so
* possible transformations, quadrature weights etc. must be applied
* manually. In general, it is safer to use the get_gradient() function
* instead, which does all the transformation internally.
*/
const VectorizedArray<Number> *begin_gradients () const;
/**
* Returns a read and write pointer to the first field of function gradients
* on quadrature points. First comes the x-component of the gradient for the
* first component on all quadrature points, then the y-component, and so
* on. Next comes the x-component of the second component, and so on. This
* is related to the internal data structures used in this class. The raw
* data after a call to @p evaluate only contains unit cell operations, so
* possible transformations, quadrature weights etc. must be applied
* manually. In general, it is safer to use the get_gradient() function
* instead, which does all the transformation internally.
*/
VectorizedArray<Number> *begin_gradients ();
/**
* Returns a read-only pointer to the first field of function hessians on
* quadrature points. First comes the xx-component of the hessian for the
* first component on all quadrature points, then the yy-component, zz-
* component in (3D), then the xy-component, and so on. Next comes the xx-
* component of the second component, and so on. This is related to the
* internal data structures used in this class. The raw data after a call to
* @p evaluate only contains unit cell operations, so possible
* transformations, quadrature weights etc. must be applied manually. In
* general, it is safer to use the get_laplacian() or get_hessian()
* functions instead, which does all the transformation internally.
*/
const VectorizedArray<Number> *begin_hessians () const;
/**
* Returns a read and write pointer to the first field of function hessians
* on quadrature points. First comes the xx-component of the hessian for the
* first component on all quadrature points, then the yy-component, zz-
* component in (3D), then the xy-component, and so on. Next comes the xx-
* component of the second component, and so on. This is related to the
* internal data structures used in this class. The raw data after a call to
* @p evaluate only contains unit cell operations, so possible
* transformations, quadrature weights etc. must be applied manually. In
* general, it is safer to use the get_laplacian() or get_hessian()
* functions instead, which does all the transformation internally.
*/
VectorizedArray<Number> *begin_hessians ();
/**
* Returns the numbering of local degrees of freedom within the evaluation
* routines of FEEvaluation in terms of the standard numbering on finite
* elements.
*/
const std::vector<unsigned int> &
get_internal_dof_numbering() const;
//@}
protected:
/**
* Constructor. Made protected to prevent users from directly using this
* class. Takes all data stored in MatrixFree. If applied to problems with
* more than one finite element or more than one quadrature formula selected
* during construction of @p matrix_free, @p fe_no and @p quad_no allow to
* select the appropriate components.
*/
FEEvaluationBase (const MatrixFree<dim,Number> &matrix_free,
const unsigned int fe_no,
const unsigned int quad_no,
const unsigned int fe_degree,
const unsigned int n_q_points);
/**
* Constructor that comes with reduced functionality and works similar as
* FEValues. The arguments are similar to the ones passed to the constructor
* of FEValues, with the notable difference that FEEvaluation expects a one-
* dimensional quadrature formula, Quadrature<1>, instead of a @p dim
* dimensional one. The finite element can be both scalar or vector valued,
* but this method always only selects a scalar base element at a time (with
* @p n_components copies as specified by the class template argument). For
* vector-valued elements, the optional argument @p first_selected_component
* allows to specify the index of the base element to be used for
* evaluation. Note that the internal data structures always assume that the
* base element is primitive, non-primitive are not supported currently.
*
* As known from FEValues, a call to the reinit method with a
* Triangulation::cell_iterator is necessary to make the geometry and
* degrees of freedom of the current class known. If the iterator includes
* DoFHandler information (i.e., it is a DoFHandler::cell_iterator or
* similar), the initialization allows to also read from or write to vectors
* in the standard way for DoFHandler::active_cell_iterator types for one
* cell at a time. However, this approach is much slower than the path with
* MatrixFree with MPI since index translation has to be done. As only one
* cell at a time is used, this method does not vectorize over several
* elements (which is most efficient for vector operations), but only
* possibly within the element if the evaluate/integrate routines are
* combined inside user code (e.g. for computing cell matrices).
*
* The optional FEEvaluationBase object allows several FEEvaluation objects
* to share the geometry evaluation, i.e., the underlying mapping and
* quadrature points do only need to be evaluated once. This only works if
* the quadrature formulas are the same. Otherwise, a new evaluation object
* is created. Make sure to not pass an optional object around when you
* intend to use the FEEvaluation object in %parallel with another one
* because otherwise the intended sharing may create race conditions.
*/
template <int n_components_other>
FEEvaluationBase (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other);
/**
* Copy constructor. If FEEvaluationBase was constructed from a mapping, fe,
* quadrature, and update flags, the underlying geometry evaluation based on
* FEValues will be deep-copied in order to allow for using in parallel with
* threads.
*/
FEEvaluationBase (const FEEvaluationBase &other);
/**
* A unified function to read from and write into vectors based on the given
* template operation. It can perform the operation for @p read_dof_values,
* @p distribute_local_to_global, and @p set_dof_values. It performs the
* operation for several vectors at a time.
*/
template<typename VectorType, typename VectorOperation>
void read_write_operation (const VectorOperation &operation,
VectorType *vectors[]) const;
/**
* For a collection of several vector @p src, read out the values on the
* degrees of freedom of the current cell for @p n_components (template
* argument), and store them internally. Similar functionality as the
* function DoFAccessor::read_dof_values. Note that if vectorization is
* enabled, the DoF values for several cells are set.
*/
template<typename VectorType>
void read_dof_values_plain (const VectorType *src_data[]);
/**
* Internal data fields that store the values. Derived classes will know the
* length of all arrays at compile time and allocate the memory on the
* stack. This makes it possible to cheaply set up a FEEvaluation object and
* write thread-safe programs by letting each thread own a private object of
* this type. In this base class, only pointers to the actual data are
* stored.
*
* This field stores the values for local degrees of freedom (e.g. after
* reading out from a vector but before applying unit cell transformations
* or before distributing them into a result vector). The methods
* get_dof_value() and submit_dof_value() read from or write to this field.
*/
VectorizedArray<Number> *values_dofs[n_components];
/**
* This field stores the values of the finite element function on quadrature
* points after applying unit cell transformations or before integrating.
* The methods get_value() and submit_value() access this field.
*/
VectorizedArray<Number> *values_quad[n_components];
/**
* This field stores the gradients of the finite element function on
* quadrature points after applying unit cell transformations or before
* integrating. The methods get_gradient() and submit_gradient() (as well as
* some specializations like get_symmetric_gradient() or get_divergence())
* access this field.
*/
VectorizedArray<Number> *gradients_quad[n_components][dim];
/**
* This field stores the Hessians of the finite element function on
* quadrature points after applying unit cell transformations. The methods
* get_hessian(), get_laplacian(), get_hessian_diagonal() access this field.
*/
VectorizedArray<Number> *hessians_quad[n_components][(dim*(dim+1))/2];
/**
* Stores the number of the quadrature formula of the present cell.
*/
const unsigned int quad_no;
/**
* Stores the number of components in the finite element as detected in the
* MatrixFree storage class for comparison with the template argument.
*/
const unsigned int n_fe_components;
/**
* Stores the active fe index for this class for efficient indexing in the
* hp case.
*/
const unsigned int active_fe_index;
/**
* Stores the active quadrature index for this class for efficient indexing
* in the hp case.
*/
const unsigned int active_quad_index;
/**
* Stores a pointer to the underlying data.
*/
const MatrixFree<dim,Number> *matrix_info;
/**
* Stores a pointer to the underlying DoF indices and constraint description
* for the component specified at construction. Also contained in
* matrix_info, but it simplifies code if we store a reference to it.
*/
const internal::MatrixFreeFunctions::DoFInfo *dof_info;
/**
* Stores a pointer to the underlying transformation data from unit to real
* cells for the given quadrature formula specified at construction. Also
* contained in matrix_info, but it simplifies code if we store a reference
* to it.
*/
const internal::MatrixFreeFunctions::MappingInfo<dim,Number> *mapping_info;
/**
* In case the class is initialized from MappingFEEvaluation instead of
* MatrixFree, this data structure holds the evaluated shape data.
*/
std_cxx11::shared_ptr<internal::MatrixFreeFunctions::ShapeInfo<Number> > stored_shape_info;
/**
* Stores a pointer to the unit cell shape data, i.e., values, gradients and
* Hessians in 1D at the quadrature points that constitute the tensor
* product. Also contained in matrix_info, but it simplifies code if we
* store a reference to it.
*/
const internal::MatrixFreeFunctions::ShapeInfo<Number> *data;
/**
* A pointer to the Cartesian Jacobian information of the present cell. Only
* set to a useful value if on a Cartesian cell, otherwise zero.
*/
const Tensor<1,dim,VectorizedArray<Number> > *cartesian_data;
/**
* A pointer to the Jacobian information of the present cell. Only set to a
* useful value if on a non-Cartesian cell.
*/
const Tensor<2,dim,VectorizedArray<Number> > *jacobian;
/**
* A pointer to the Jacobian determinant of the present cell. If on a
* Cartesian cell or on a cell with constant Jacobian, this is just the
* Jacobian determinant, otherwise the Jacobian determinant times the
* quadrature weight.
*/
const VectorizedArray<Number> *J_value;
/**
* A pointer to the quadrature weights of the underlying quadrature formula.
*/
const VectorizedArray<Number> *quadrature_weights;
/**
* A pointer to the quadrature points on the present cell.
*/
const Point<dim,VectorizedArray<Number> > *quadrature_points;
/**
* A pointer to the diagonal part of the Jacobian gradient on the present
* cell. Only set to a useful value if on a general cell with non-constant
* Jacobian.
*/
const Tensor<2,dim,VectorizedArray<Number> > *jacobian_grad;
/**
* A pointer to the upper diagonal part of the Jacobian gradient on the
* present cell. Only set to a useful value if on a general cell with non-
* constant Jacobian.
*/
const Tensor<1,(dim>1?dim*(dim-1)/2:1),Tensor<1,dim,VectorizedArray<Number> > > * jacobian_grad_upper;
/**
* After a call to reinit(), stores the number of the cell we are currently
* working with.
*/
unsigned int cell;
/**
* Stores the type of the cell we are currently working with after a call to
* reinit(). Valid values are @p cartesian, @p affine and @p general, which
* have different implications on how the Jacobian transformations are
* stored internally in MappingInfo.
*/
internal::MatrixFreeFunctions::CellType cell_type;
/**
* The stride to access the correct data in MappingInfo.
*/
unsigned int cell_data_number;
/**
* Debug information to track whether dof values have been initialized
* before accessed. Used to control exceptions when uninitialized data is
* used.
*/
bool dof_values_initialized;
/**
* Debug information to track whether values on quadrature points have been
* initialized before accessed. Used to control exceptions when
* uninitialized data is used.
*/
bool values_quad_initialized;
/**
* Debug information to track whether gradients on quadrature points have
* been initialized before accessed. Used to control exceptions when
* uninitialized data is used.
*/
bool gradients_quad_initialized;
/**
* Debug information to track whether Hessians on quadrature points have
* been initialized before accessed. Used to control exceptions when
* uninitialized data is used.
*/
bool hessians_quad_initialized;
/**
* Debug information to track whether values on quadrature points have been
* submitted for integration before the integration is actually stared. Used
* to control exceptions when uninitialized data is used.
*/
bool values_quad_submitted;
/**
* Debug information to track whether gradients on quadrature points have
* been submitted for integration before the integration is actually stared.
* Used to control exceptions when uninitialized data is used.
*/
bool gradients_quad_submitted;
/**
* Geometry data that can be generated FEValues on the fly with the
* respective constructor.
*/
std_cxx1x::shared_ptr<internal::MatrixFreeFunctions::MappingDataOnTheFly<dim,Number> > mapped_geometry;
/**
* For use with on-the-fly evaluation, provide a data structure to store the
* global dof indices on the current cell from a reinit call.
*/
std::vector<types::global_dof_index> old_style_dof_indices;
/**
* For a FiniteElement with more than one finite element, select at which
* component this data structure should start.
*/
const unsigned int first_selected_component;
/**
* A temporary data structure necessary to read degrees of freedom when no
* MatrixFree object was given at initialization.
*/
mutable std::vector<types::global_dof_index> local_dof_indices;
/**
* Make other FEEvaluationBase as well as FEEvaluation objects friends.
*/
template <int, int, typename> friend class FEEvaluationBase;
template <int, int, int, int, typename> friend class FEEvaluation;
};
/**
* This class provides access to the data fields of the FEEvaluation classes.
* Generic access is achieved through the base class, and specializations for
* scalar and vector-valued elements are defined separately.
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011
*/
template <int dim, int n_components_, typename Number>
class FEEvaluationAccess : public FEEvaluationBase<dim,n_components_,Number>
{
public:
typedef Number number_type;
typedef Tensor<1,n_components_,VectorizedArray<Number> > value_type;
typedef Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > > gradient_type;
static const unsigned int dimension = dim;
static const unsigned int n_components = n_components_;
typedef FEEvaluationBase<dim,n_components_, Number> BaseClass;
protected:
/**
* Constructor. Made protected to prevent initialization in user code. Takes
* all data stored in MatrixFree. If applied to problems with more than one
* finite element or more than one quadrature formula selected during
* construction of @p matrix_free, @p fe_no and @p quad_no allow to select
* the appropriate components.
*/
FEEvaluationAccess (const MatrixFree<dim,Number> &matrix_free,
const unsigned int fe_no,
const unsigned int quad_no,
const unsigned int fe_degree,
const unsigned int n_q_points);
/**
* Constructor with reduced functionality for similar usage of FEEvaluation
* as FEValues, including matrix assembly.
*/
template <int n_components_other>
FEEvaluationAccess (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other);
/**
* Copy constructor
*/
FEEvaluationAccess (const FEEvaluationAccess &other);
};
/**
* This class provides access to the data fields of the FEEvaluation classes.
* Partial specialization for scalar fields that defines access with simple
* data fields, i.e., scalars for the values and Tensor<1,dim> for the
* gradients.
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011
*/
template <int dim, typename Number>
class FEEvaluationAccess<dim,1,Number> : public FEEvaluationBase<dim,1,Number>
{
public:
typedef Number number_type;
typedef VectorizedArray<Number> value_type;
typedef Tensor<1,dim,VectorizedArray<Number> > gradient_type;
static const unsigned int dimension = dim;
typedef FEEvaluationBase<dim,1,Number> BaseClass;
/**
* Returns the value stored for the local degree of freedom with index @p
* dof. If the object is vector-valued, a vector-valued return argument is
* given. Note that when vectorization is enabled, values from several cells
* are grouped together. If @p set_dof_values was called last, the value
* corresponds to the one set there. If @p integrate was called last, it
* instead corresponds to the value of the integrated function with the test
* function of the given index.
*/
value_type get_dof_value (const unsigned int dof) const;
/**
* Write a value to the field containing the degrees of freedom with
* component @p dof. Access to the same field as through @p get_dof_value.
*/
void submit_dof_value (const value_type val_in,
const unsigned int dof);
/**
* Returns the value of a finite element function at quadrature point number
* @p q_point after a call to @p evaluate(true,...), or the value that has
* been stored there with a call to @p submit_value. If the object is
* vector-valued, a vector-valued return argument is given. Note that when
* vectorization is enabled, values from several cells are grouped together.
*/
value_type get_value (const unsigned int q_point) const;
/**
* Write a value to the field containing the values on quadrature points
* with component @p q_point. Access to the same field as through @p
* get_value. If applied before the function @p integrate(true,...) is
* called, this specifies the value which is tested by all basis function on
* the current cell and integrated over.
*/
void submit_value (const value_type val_in,
const unsigned int q_point);
/**
* Returns the gradient of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true,...), or the value
* that has been stored there with a call to @p submit_gradient.
*/
gradient_type get_gradient (const unsigned int q_point) const;
/**
* Write a contribution that is tested by the gradient to the field
* containing the values on quadrature points with component @p q_point.
* Access to the same field as through @p get_gradient. If applied before
* the function @p integrate(...,true) is called, this specifies what is
* tested by all basis function gradients on the current cell and integrated
* over.
*/
void submit_gradient(const gradient_type grad_in,
const unsigned int q_point);
/**
* Returns the Hessian of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true). If only the
* diagonal part of the Hessian or its trace, the Laplacian, are needed, use
* the respective functions below.
*/
Tensor<2,dim,VectorizedArray<Number> >
get_hessian (unsigned int q_point) const;
/**
* Returns the diagonal of the Hessian of a finite element function at
* quadrature point number @p q_point after a call to @p evaluate(...,true).
*/
gradient_type get_hessian_diagonal (const unsigned int q_point) const;
/**
* Returns the Laplacian of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true).
*/
value_type get_laplacian (const unsigned int q_point) const;
/**
* Takes values on quadrature points, multiplies by the Jacobian determinant
* and quadrature weights (JxW) and sums the values for all quadrature
* points on the cell. The result is a scalar, representing the integral
* over the function over the cell. If a vector-element is used, the
* resulting components are still separated. Moreover, if vectorization is
* enabled, the integral values of several cells are represented together.
*/
value_type integrate_value () const;
protected:
/**
* Constructor. Made protected to avoid initialization in user code. Takes
* all data stored in MatrixFree. If applied to problems with more than one
* finite element or more than one quadrature formula selected during
* construction of @p matrix_free, @p fe_no and @p quad_no allow to select
* the appropriate components.
*/
FEEvaluationAccess (const MatrixFree<dim,Number> &matrix_free,
const unsigned int fe_no,
const unsigned int quad_no,
const unsigned int fe_degree,
const unsigned int n_q_points);
/**
* Constructor with reduced functionality for similar usage of FEEvaluation
* as FEValues, including matrix assembly.
*/
template <int n_components_other>
FEEvaluationAccess (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other);
/**
* Copy constructor
*/
FEEvaluationAccess (const FEEvaluationAccess &other);
};
/**
* This class provides access to the data fields of the FEEvaluation classes.
* Partial specialization for fields with as many components as the underlying
* space dimension, i.e., values are of type Tensor<1,dim> and gradients of
* type Tensor<2,dim>. Provides some additional functions for access, like the
* symmetric gradient and divergence.
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011
*/
template <int dim, typename Number>
class FEEvaluationAccess<dim,dim,Number> : public FEEvaluationBase<dim,dim,Number>
{
public:
typedef Number number_type;
typedef Tensor<1,dim,VectorizedArray<Number> > value_type;
typedef Tensor<2,dim,VectorizedArray<Number> > gradient_type;
static const unsigned int dimension = dim;
static const unsigned int n_components = dim;
typedef FEEvaluationBase<dim,dim,Number> BaseClass;
/**
* Returns the gradient of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true,...).
*/
gradient_type get_gradient (const unsigned int q_point) const;
/**
* Returns the divergence of a vector-valued finite element at quadrature
* point number @p q_point after a call to @p evaluate(...,true,...).
*/
VectorizedArray<Number> get_divergence (const unsigned int q_point) const;
/**
* Returns the symmetric gradient of a vector-valued finite element at
* quadrature point number @p q_point after a call to @p
* evaluate(...,true,...). It corresponds to <tt>0.5
* (grad+grad<sup>T</sup>)</tt>.
*/
SymmetricTensor<2,dim,VectorizedArray<Number> >
get_symmetric_gradient (const unsigned int q_point) const;
/**
* Returns the curl of the vector field, $nabla \times v$ after a call to @p
* evaluate(...,true,...).
*/
Tensor<1,(dim==2?1:dim),VectorizedArray<Number> >
get_curl (const unsigned int q_point) const;
/**
* Returns the Hessian of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true). If only the
* diagonal of the Hessian or its trace, the Laplacian, is needed, use the
* respective functions.
*/
Tensor<3,dim,VectorizedArray<Number> >
get_hessian (const unsigned int q_point) const;
/**
* Returns the diagonal of the Hessian of a finite element function at
* quadrature point number @p q_point after a call to @p evaluate(...,true).
*/
gradient_type get_hessian_diagonal (const unsigned int q_point) const;
/**
* Write a contribution that is tested by the gradient to the field
* containing the values on quadrature points with component @p q_point.
* Access to the same field as through @p get_gradient. If applied before
* the function @p integrate(...,true) is called, this specifies what is
* tested by all basis function gradients on the current cell and integrated
* over.
*/
void submit_gradient(const gradient_type grad_in,
const unsigned int q_point);
/**
* Write a contribution that is tested by the gradient to the field
* containing the values on quadrature points with component @p q_point.
* This function is an alternative to the other submit_gradient function
* when using a system of fixed number of equations which happens to
* coincide with the dimension for some dimensions, but not all. To allow
* for dimension-independent programming, this function can be used instead.
*/
void submit_gradient(const Tensor<1,dim,Tensor<1,dim,VectorizedArray<Number> > > grad_in,
const unsigned int q_point);
/**
* Write a contribution that is tested by the divergence to the field
* containing the values on quadrature points with component @p q_point.
* Access to the same field as through @p get_gradient. If applied before
* the function @p integrate(...,true) is called, this specifies what is
* tested by all basis function gradients on the current cell and integrated
* over.
*/
void submit_divergence (const VectorizedArray<Number> div_in,
const unsigned int q_point);
/**
* Write a contribution that is tested by the gradient to the field
* containing the values on quadrature points with component @p q_point.
* Access to the same field as through @p get_gradient. If applied before
* the function @p integrate(...,true) is called, this specifies the
* gradient which is tested by all basis function gradients on the current
* cell and integrated over.
*/
void submit_symmetric_gradient(const SymmetricTensor<2,dim,VectorizedArray<Number> > grad_in,
const unsigned int q_point);
/**
* Write the components of a curl containing the values on quadrature point
* @p q_point. Access to the same data field as through @p get_gradient.
*/
void submit_curl (const Tensor<1,dim==2?1:dim,VectorizedArray<Number> > curl_in,
const unsigned int q_point);
protected:
/**
* Constructor. Made protected to avoid initialization in user code. Takes
* all data stored in MatrixFree. If applied to problems with more than one
* finite element or more than one quadrature formula selected during
* construction of @p matrix_free, @p fe_no and @p quad_no allow to select
* the appropriate components.
*/
FEEvaluationAccess (const MatrixFree<dim,Number> &matrix_free,
const unsigned int fe_no,
const unsigned int quad_no,
const unsigned int dofs_per_cell,
const unsigned int n_q_points);
/**
* Constructor with reduced functionality for similar usage of FEEvaluation
* as FEValues, including matrix assembly.
*/
template <int n_components_other>
FEEvaluationAccess (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other);
/**
* Copy constructor
*/
FEEvaluationAccess (const FEEvaluationAccess &other);
};
/**
* This class provides access to the data fields of the FEEvaluation classes.
* Partial specialization for scalar fields in 1d that defines access with
* simple data fields, i.e., scalars for the values and Tensor<1,1> for the
* gradients.
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011, Shiva
* Rudraraju, 2014
*/
template <typename Number>
class FEEvaluationAccess<1,1,Number> : public FEEvaluationBase<1,1,Number>
{
public:
typedef Number number_type;
typedef VectorizedArray<Number> value_type;
typedef Tensor<1,1,VectorizedArray<Number> > gradient_type;
static const unsigned int dimension = 1;
typedef FEEvaluationBase<1,1,Number> BaseClass;
/**
* Returns the value stored for the local degree of freedom with index @p
* dof. If the object is vector-valued, a vector-valued return argument is
* given. Note that when vectorization is enabled, values from several cells
* are grouped together. If @p set_dof_values was called last, the value
* corresponds to the one set there. If @p integrate was called last, it
* instead corresponds to the value of the integrated function with the test
* function of the given index.
*/
value_type get_dof_value (const unsigned int dof) const;
/**
* Write a value to the field containing the degrees of freedom with
* component @p dof. Access to the same field as through @p get_dof_value.
*/
void submit_dof_value (const value_type val_in,
const unsigned int dof);
/**
* Returns the value of a finite element function at quadrature point number
* @p q_point after a call to @p evaluate(true,...), or the value that has
* been stored there with a call to @p submit_value. If the object is
* vector-valued, a vector-valued return argument is given. Note that when
* vectorization is enabled, values from several cells are grouped together.
*/
value_type get_value (const unsigned int q_point) const;
/**
* Write a value to the field containing the values on quadrature points
* with component @p q_point. Access to the same field as through @p
* get_value. If applied before the function @p integrate(true,...) is
* called, this specifies the value which is tested by all basis function on
* the current cell and integrated over.
*/
void submit_value (const value_type val_in,
const unsigned int q_point);
/**
* Returns the gradient of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true,...), or the value
* that has been stored there with a call to @p submit_gradient.
*/
gradient_type get_gradient (const unsigned int q_point) const;
/**
* Write a contribution that is tested by the gradient to the field
* containing the values on quadrature points with component @p q_point.
* Access to the same field as through @p get_gradient. If applied before
* the function @p integrate(...,true) is called, this specifies what is
* tested by all basis function gradients on the current cell and integrated
* over.
*/
void submit_gradient(const gradient_type grad_in,
const unsigned int q_point);
/**
* Returns the Hessian of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true). If only the
* diagonal part of the Hessian or its trace, the Laplacian, are needed, use
* the respective functions below.
*/
Tensor<2,1,VectorizedArray<Number> >
get_hessian (unsigned int q_point) const;
/**
* Returns the diagonal of the Hessian of a finite element function at
* quadrature point number @p q_point after a call to @p evaluate(...,true).
*/
gradient_type get_hessian_diagonal (const unsigned int q_point) const;
/**
* Returns the Laplacian of a finite element function at quadrature point
* number @p q_point after a call to @p evaluate(...,true).
*/
value_type get_laplacian (const unsigned int q_point) const;
/**
* Takes values on quadrature points, multiplies by the Jacobian determinant
* and quadrature weights (JxW) and sums the values for all quadrature
* points on the cell. The result is a scalar, representing the integral
* over the function over the cell. If a vector-element is used, the
* resulting components are still separated. Moreover, if vectorization is
* enabled, the integral values of several cells are represented together.
*/
value_type integrate_value () const;
protected:
/**
* Constructor. Made protected to avoid initialization in user code. Takes
* all data stored in MatrixFree. If applied to problems with more than one
* finite element or more than one quadrature formula selected during
* construction of @p matrix_free, @p fe_no and @p quad_no allow to select
* the appropriate components.
*/
FEEvaluationAccess (const MatrixFree<1,Number> &matrix_free,
const unsigned int fe_no,
const unsigned int quad_no,
const unsigned int fe_degree,
const unsigned int n_q_points);
/**
* Constructor with reduced functionality for similar usage of FEEvaluation
* as FEValues, including matrix assembly.
*/
template <int n_components_other>
FEEvaluationAccess (const Mapping<1> &mapping,
const FiniteElement<1> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<1,n_components_other,Number> *other);
/**
* Copy constructor
*/
FEEvaluationAccess (const FEEvaluationAccess &other);
};
/**
* The class that provides all functions necessary to evaluate functions at
* quadrature points and cell integrations. In functionality, this class is
* similar to FEValues<dim>, however, it includes a lot of specialized
* functions that make it much faster (between 5 and 500, depending on the
* polynomial order).
*
* <h3>Usage and initialization</h3>
*
* <h4>Fast usage in combination with MatrixFree</h4>
*
* The first and foremost way of usage is to initialize this class from a
* MatrixFree object that caches everything related to the degrees of freedom
* and the mapping information. This way, it is possible to use vectorization
* for applying a vector operation for several cells at once. This setting is
* explained in the step-37 and step-48 tutorial programs. For vector-valued
* problems, the deal.II test suite includes a few additional examples as
* well, e.g. the Stokes operator found at
* https://github.com/dealii/dealii/blob/master/tests/matrix_free/matrix_vector_stokes_noflux.cc
*
* For most operator evaluation tasks, this path provides the most efficient
* solution by combining pre-computed data for the mapping (Jacobian
* transformations for the geometry description) with on-the-fly evaluation of
* basis functions. In other words, the framework provides a trade-off between
* memory usage and initialization of objects that is suitable for matrix-free
* operator evaluation.
*
* <h4>Usage without pre-initialized MatrixFree object</h4>
*
* The second form of usage is to initialize FEEvaluation from geometry
* information generated by FEValues. This allows to apply the integration
* loops on the fly without prior initialization of MatrixFree objects. This
* can be useful when the memory and initialization cost of MatrixFree is not
* acceptable, e.g. when a different number of quadrature points should be
* used for one single evaluation in error computation. Also, when using the
* routines of this class to assemble matrices the trade-off implied by the
* MatrixFree class may not be desired. In such a case, the cost to initialize
* the necessary geometry data on the fly is comparably low and thus avoiding
* a global object MatrixFree can be useful. When used in this way, reinit
* methods reminiscent from FEValues with a cell iterator are to be used.
* However, note that this model results in working on a single cell at a
* time, with geometry data duplicated in all components of the vectorized
* array. Thus, vectorization is only useful when it can apply the same
* operation on different data, e.g. when performing matrix assembly.
*
* As an example, consider the following code to assemble the contributions to
* the Laplace matrix:
*
* @code
* FEEvaluation<dim,fe_degree> fe_eval (mapping, finite_element,
* QGauss<1>(fe_degree+1), flags);
* for (cell = dof_handler.begin_active();
* cell != dof_handler.end();
* ++cell)
* {
* fe_eval.reinit(cell);
* for (unsigned int i=0; i<dofs_per_cell;
* i += VectorizedArray<double>::n_array_elements)
* {
* const unsigned int n_items =
* i+VectorizedArray<double>::n_array_elements > dofs_per_cell ?
* (dofs_per_cell - i) : VectorizedArray<double>::n_array_elements;
*
* // Set n_items unit vectors
* for (unsigned int j=0; j<dofs_per_cell; ++j)
* fe_eval.begin_dof_values()[j] = VectorizedArray<double>();
* for (unsigned int v=0; v<n_items; ++v)
* fe_eval.begin_dof_values()[i+v][v] = 1.;
*
* // Apply operator on unit vector
* fe_eval.evaluate(true, true);
* for (unsigned int q=0; q<n_q_points; ++q)
* {
* fe_eval.submit_value(10.*fe_eval.get_value(q), q);
* fe_eval.submit_gradient(fe_eval.get_gradient(q), q);
* }
* fe_eval.integrate(true, true);
*
* // Insert computed entries in matrix
* for (unsigned int v=0; v<n_items; ++v)
* for (unsigned int j=0; j<dofs_per_cell; ++j)
* cell_matrix(fe_eval.get_internal_dof_numbering()[j],
* fe_eval.get_internal_dof_numbering()[i+v])
* = fe_eval.begin_dof_values()[j][v];
* }
* ...
* }
* @endcode
*
* This code generates the columns of the cell matrix with the loop over @p i
* above. The way this is done is the following: FEEvaluation's routines focus
* on the evaluation of finite element operators, so the way to get a cell
* matrix out of an operator evaluation is to apply it to all the unit vectors
* on the cell. This might seem inefficient but the evaluation routines used
* here are so quick that they still work much faster than what is possible
* with FEValues.
*
* Due to vectorization, we can actually generate matrix data for several unit
* vectors at a time (e.g. 4). The variable @p n_items make sure that we do
* the last iteration where the number of cell dofs is not divisible by the
* vectorization length correctly. Also note that we need to get the internal
* dof numbering applied by fe_eval because FEEvaluation internally uses a
* lexicographic numbering of degrees of freedom. This is necessary to
* efficiently work with tensor products where all degrees of freedom along a
* dimension must be laid out in a regular way.
*
* <h3>Description of evaluation routines</h3>
*
* This class contains specialized evaluation routines for several elements
* based on tensor-product quadrature formulas and tensor-product-like shape
* functions, including standard FE_Q or FE_DGQ elements and quadrature points
* symmetric around 0.5 (like Gauss quadrature), FE_DGP elements based on
* truncated tensor products as well as the faster case of Gauss-Lobatto
* elements with Gauss-Lobatto quadrature which give diagonal mass matrices
* and quicker evaluation internally. The main benefit of this class is the
* evaluation of all shape functions in all quadrature or integration over all
* shape functions in <code>dim (fe_degree+1)<sup>dim+1</sup> </code>
* operations instead of the slower <code>
* (fe_degree+1)<sup>2*dim</sup></code> complexity in the evaluation routines
* of FEValues.
*
* Note that many of the operations available through this class are inherited
* from the base class FEEvaluationBase, in particular reading from and
* writing to vectors. Also, the class inherits from FEEvaluationAccess that
* implements access to values, gradients and Hessians of the finite element
* function on quadrature points.
*
* This class assumes that shape functions of the FiniteElement under
* consideration do <em>not</em> depend on the actual shape of the cells in
* real space. Currently, other finite elements cannot be treated with the
* matrix-free concept.
*
* This class has five template arguments:
*
* @param dim Dimension in which this class is to be used
*
* @param fe_degree Degree of the tensor product finite element with
* fe_degree+1 degrees of freedom per coordinate direction
*
* @param n_q_points_1d Number of points in the quadrature formula in 1D,
* defaults to fe_degree+1
*
* @param n_components Number of vector components when solving a system of
* PDEs. If the same operation is applied to several components of a PDE (e.g.
* a vector Laplace equation), they can be applied simultaneously with one
* call (and often more efficiently). Defaults to 1.
*
* @param Number Number format, usually @p double or @p float. Defaults to @p
* double
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011
*/
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number >
class FEEvaluation : public FEEvaluationAccess<dim,n_components_,Number>
{
public:
typedef FEEvaluationAccess<dim,n_components_,Number> BaseClass;
typedef Number number_type;
typedef typename BaseClass::value_type value_type;
typedef typename BaseClass::gradient_type gradient_type;
static const unsigned int dimension = dim;
static const unsigned int n_components = n_components_;
static const unsigned int n_q_points = Utilities::fixed_int_power<n_q_points_1d,dim>::value;
static const unsigned int tensor_dofs_per_cell = Utilities::fixed_int_power<fe_degree+1,dim>::value;
/**
* Constructor. Takes all data stored in MatrixFree. If applied to problems
* with more than one finite element or more than one quadrature formula
* selected during construction of @p matrix_free, @p fe_no and @p quad_no
* allow to select the appropriate components.
*/
FEEvaluation (const MatrixFree<dim,Number> &matrix_free,
const unsigned int fe_no = 0,
const unsigned int quad_no = 0);
/**
* Constructor that comes with reduced functionality and works similar as
* FEValues. The arguments are similar to the ones passed to the constructor
* of FEValues, with the notable difference that FEEvaluation expects a one-
* dimensional quadrature formula, Quadrature<1>, instead of a @p dim
* dimensional one. The finite element can be both scalar or vector valued,
* but this method always only selects a scalar base element at a time (with
* @p n_components copies as specified by the class template). For vector-
* valued elements, the optional argument @p first_selected_component allows
* to specify the index of the base element to be used for evaluation. Note
* that the internal data structures always assume that the base element is
* primitive, non-primitive are not supported currently.
*
* As known from FEValues, a call to the reinit method with a
* Triangulation<dim>::cell_iterator is necessary to make the geometry and
* degrees of freedom of the current class known. If the iterator includes
* DoFHandler information (i.e., it is a DoFHandler<dim>::cell_iterator or
* similar), the initialization allows to also read from or write to vectors
* in the standard way for DoFHandler<dim>::active_cell_iterator types for
* one cell at a time. However, this approach is much slower than the path
* with MatrixFree with MPI since index translation has to be done. As only
* one cell at a time is used, this method does not vectorize over several
* elements (which is most efficient for vector operations), but only
* possibly within the element if the evaluate/integrate routines are
* combined inside user code (e.g. for computing cell matrices).
*/
FEEvaluation (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component = 0);
/**
* Constructor for the reduced functionality. This constructor is equivalent
* to the other one except that it makes the object use a $Q_1$ mapping
* (i.e., an object of type MappingQGeneric(1)) implicitly.
*/
FEEvaluation (const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component = 0);
/**
* Constructor for the reduced functionality. Similar to the other
* constructor with FiniteElement argument but using another
* FEEvaluationBase object to provide info about the geometry. This allows
* several FEEvaluation objects to share the geometry evaluation, i.e., the
* underlying mapping and quadrature points do only need to be evaluated
* once. Make sure to not pass an optional object around when you intend to
* use the FEEvaluation object in %parallel to the given one because
* otherwise the intended sharing may create race conditions.
*/
template <int n_components_other>
FEEvaluation (const FiniteElement<dim> &fe,
const FEEvaluationBase<dim,n_components_other,Number> &other,
const unsigned int first_selected_component = 0);
/**
* Copy constructor. If FEEvaluationBase was constructed from a mapping, fe,
* quadrature, and update flags, the underlying geometry evaluation based on
* FEValues will be deep-copied in order to allow for using in parallel with
* threads.
*/
FEEvaluation (const FEEvaluation &other);
/**
* Evaluates the function values, the gradients, and the Laplacians of the
* FE function given at the DoF values in the input vector at the quadrature
* points on the unit cell. The function arguments specify which parts
* shall actually be computed. Needs to be called before the functions @p
* get_value(), @p get_gradient() or @p get_laplacian give useful
* information (unless these values have been set manually).
*/
void evaluate (const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_hess = false);
/**
* This function takes the values and/or gradients that are stored on
* quadrature points, tests them by all the basis functions/gradients on the
* cell and performs the cell integration. The two function arguments @p
* integrate_val and @p integrate_grad are used to enable/disable some of
* values or gradients.
*/
void integrate (const bool integrate_val,
const bool integrate_grad);
/**
* Returns the q-th quadrature point stored in MappingInfo.
*/
Point<dim,VectorizedArray<Number> >
quadrature_point (const unsigned int q_point) const;
/**
* The number of scalar degrees of freedom on the cell. Usually close to
* tensor_dofs_per_cell, but depends on the actual element selected and is
* thus not static.
*/
const unsigned int dofs_per_cell;
private:
/**
* Internally stored variables for the different data fields.
*/
VectorizedArray<Number> my_data_array[n_components*(tensor_dofs_per_cell+1+(dim*dim+2*dim+1)*n_q_points)];
/**
* Checks if the template arguments regarding degree of the element
* corresponds to the actual element used at initialization.
*/
void check_template_arguments(const unsigned int fe_no);
/**
* Sets the pointers of the base class to my_data_array.
*/
void set_data_pointers();
/**
* Function pointer for the evaluate function
*/
void (*evaluate_funct) (const internal::MatrixFreeFunctions::ShapeInfo<Number> &,
VectorizedArray<Number> *values_dofs_actual[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
VectorizedArray<Number> *hessians_quad[][(dim*(dim+1))/2],
const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl);
/**
* Function pointer for the integrate function
*/
void (*integrate_funct)(const internal::MatrixFreeFunctions::ShapeInfo<Number> &,
VectorizedArray<Number> *values_dofs_actual[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
const bool evaluate_val,
const bool evaluate_grad);
};
namespace internal
{
namespace MatrixFreeFunctions
{
// a helper function to compute the number of DoFs of a DGP element at compile
// time, depending on the degree
template <int dim, int degree>
struct DGP_dofs_per_cell
{
// this division is always without remainder
static const unsigned int value =
(DGP_dofs_per_cell<dim-1,degree>::value * (degree+dim)) / dim;
};
// base specialization: 1d elements have 'degree+1' degrees of freedom
template <int degree>
struct DGP_dofs_per_cell<1,degree>
{
static const unsigned int value = degree+1;
};
}
}
/*----------------------- Inline functions ----------------------------------*/
#ifndef DOXYGEN
/*----------------------- FEEvaluationBase ----------------------------------*/
template <int dim, int n_components_, typename Number>
inline
FEEvaluationBase<dim,n_components_,Number>
::FEEvaluationBase (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no_in,
const unsigned int quad_no_in,
const unsigned int fe_degree,
const unsigned int n_q_points)
:
quad_no (quad_no_in),
n_fe_components (data_in.get_dof_info(fe_no_in).n_components),
active_fe_index (data_in.get_dof_info(fe_no_in).fe_index_from_degree
(fe_degree)),
active_quad_index (data_in.get_mapping_info().
mapping_data_gen[quad_no_in].
quad_index_from_n_q_points(n_q_points)),
matrix_info (&data_in),
dof_info (&data_in.get_dof_info(fe_no_in)),
mapping_info (&data_in.get_mapping_info()),
data (&data_in.get_shape_info
(fe_no_in, quad_no_in, active_fe_index,
active_quad_index)),
cartesian_data (0),
jacobian (0),
J_value (0),
quadrature_weights (mapping_info->mapping_data_gen[quad_no].
quadrature_weights[active_quad_index].begin()),
quadrature_points (0),
jacobian_grad (0),
jacobian_grad_upper(0),
cell (numbers::invalid_unsigned_int),
cell_type (internal::MatrixFreeFunctions::undefined),
cell_data_number (0),
first_selected_component (0)
{
for (unsigned int c=0; c<n_components_; ++c)
{
values_dofs[c] = 0;
values_quad[c] = 0;
for (unsigned int d=0; d<dim; ++d)
gradients_quad[c][d] = 0;
for (unsigned int d=0; d<(dim*dim+dim)/2; ++d)
hessians_quad[c][d] = 0;
}
Assert (matrix_info->mapping_initialized() == true,
ExcNotInitialized());
AssertDimension (matrix_info->get_size_info().vectorization_length,
VectorizedArray<Number>::n_array_elements);
AssertDimension (data->dofs_per_cell,
dof_info->dofs_per_cell[active_fe_index]/n_fe_components);
AssertDimension (data->n_q_points,
mapping_info->mapping_data_gen[quad_no].n_q_points[active_quad_index]);
Assert (n_fe_components == 1 ||
n_components == 1 ||
n_components == n_fe_components,
ExcMessage ("The underlying FE is vector-valued. In this case, the "
"template argument n_components must be a the same "
"as the number of underlying vector components."));
// do not check for correct dimensions of data fields here, should be done
// in derived classes
}
template <int dim, int n_components_, typename Number>
template <int n_components_other>
inline
FEEvaluationBase<dim,n_components_,Number>
::FEEvaluationBase (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other)
:
quad_no (-1),
n_fe_components (n_components_),
active_fe_index (-1),
active_quad_index (-1),
matrix_info (0),
dof_info (0),
mapping_info (0),
// select the correct base element from the given FE component
stored_shape_info (new internal::MatrixFreeFunctions::ShapeInfo<Number>(quadrature, fe, fe.component_to_base_index(first_selected_component).first)),
data (stored_shape_info.get()),
cartesian_data (0),
jacobian (0),
J_value (0),
quadrature_weights (0),
quadrature_points (0),
jacobian_grad (0),
jacobian_grad_upper(0),
cell (0),
cell_type (internal::MatrixFreeFunctions::general),
cell_data_number (0),
// keep the number of the selected component within the current base element
// for reading dof values
first_selected_component (fe.component_to_base_index(first_selected_component).second)
{
const unsigned int base_element_number =
fe.component_to_base_index(first_selected_component).first;
for (unsigned int c=0; c<n_components_; ++c)
{
values_dofs[c] = 0;
values_quad[c] = 0;
for (unsigned int d=0; d<dim; ++d)
gradients_quad[c][d] = 0;
for (unsigned int d=0; d<(dim*dim+dim)/2; ++d)
hessians_quad[c][d] = 0;
}
Assert(other == 0 || other->mapped_geometry.get() != 0, ExcInternalError());
if (other != 0 &&
other->mapped_geometry->get_quadrature() == quadrature)
mapped_geometry = other->mapped_geometry;
else
mapped_geometry.reset(new internal::MatrixFreeFunctions::
MappingDataOnTheFly<dim,Number>(mapping, quadrature,
update_flags));
jacobian = mapped_geometry->get_inverse_jacobians().begin();
J_value = mapped_geometry->get_JxW_values().begin();
quadrature_points = mapped_geometry->get_quadrature_points().begin();
Assert(fe.element_multiplicity(base_element_number) == 1 ||
fe.element_multiplicity(base_element_number)-first_selected_component >= n_components_,
ExcMessage("The underlying element must at least contain as many "
"components as requested by this class"));
}
template <int dim, int n_components_, typename Number>
inline
FEEvaluationBase<dim,n_components_,Number>
::FEEvaluationBase (const FEEvaluationBase<dim,n_components_,Number> &other)
:
quad_no (other.quad_no),
n_fe_components (other.n_fe_components),
active_fe_index (other.active_fe_index),
active_quad_index (other.active_quad_index),
matrix_info (other.matrix_info),
dof_info (other.dof_info),
mapping_info (other.mapping_info),
stored_shape_info (other.stored_shape_info),
data (other.data),
cartesian_data (other.cartesian_data),
jacobian (other.jacobian),
J_value (other.J_value),
quadrature_weights (other.quadrature_weights),
quadrature_points (other.quadrature_points),
jacobian_grad (other.jacobian_grad),
jacobian_grad_upper(other.jacobian_grad_upper),
cell (other.cell),
cell_type (other.cell_type),
cell_data_number (other.cell_data_number),
first_selected_component (other.first_selected_component)
{
for (unsigned int c=0; c<n_components_; ++c)
{
values_dofs[c] = 0;
values_quad[c] = 0;
for (unsigned int d=0; d<dim; ++d)
gradients_quad[c][d] = 0;
for (unsigned int d=0; d<(dim*dim+dim)/2; ++d)
hessians_quad[c][d] = 0;
}
// Create deep copy of mapped geometry for use in parallel...
if (other.mapped_geometry.get() != 0)
{
mapped_geometry.reset
(new internal::MatrixFreeFunctions::
MappingDataOnTheFly<dim,Number>(other.mapped_geometry->get_fe_values().get_mapping(),
other.mapped_geometry->get_quadrature(),
other.mapped_geometry->get_fe_values().get_update_flags()));
jacobian = mapped_geometry->get_inverse_jacobians().begin();
J_value = mapped_geometry->get_JxW_values().begin();
quadrature_points = mapped_geometry->get_quadrature_points().begin();
}
}
template <int dim, int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,n_components_,Number>::reinit (const unsigned int cell_in)
{
Assert (mapped_geometry == 0,
ExcMessage("FEEvaluation was initialized without a matrix-free object."
" Integer indexing is not possible"));
if (mapped_geometry != 0)
return;
Assert (dof_info != 0, ExcNotInitialized());
Assert (mapping_info != 0, ExcNotInitialized());
AssertIndexRange (cell_in, dof_info->row_starts.size()-1);
AssertDimension (((dof_info->cell_active_fe_index.size() > 0) ?
dof_info->cell_active_fe_index[cell_in] : 0),
active_fe_index);
cell = cell_in;
cell_type = mapping_info->get_cell_type(cell);
cell_data_number = mapping_info->get_cell_data_index(cell);
if (mapping_info->quadrature_points_initialized == true)
{
AssertIndexRange (cell_data_number, mapping_info->
mapping_data_gen[quad_no].rowstart_q_points.size());
const unsigned int index = mapping_info->mapping_data_gen[quad_no].
rowstart_q_points[cell];
AssertIndexRange (index, mapping_info->mapping_data_gen[quad_no].
quadrature_points.size());
quadrature_points =
&mapping_info->mapping_data_gen[quad_no].quadrature_points[index];
}
if (cell_type == internal::MatrixFreeFunctions::cartesian)
{
cartesian_data = &mapping_info->cartesian_data[cell_data_number].first;
J_value = &mapping_info->cartesian_data[cell_data_number].second;
}
else if (cell_type == internal::MatrixFreeFunctions::affine)
{
jacobian = &mapping_info->affine_data[cell_data_number].first;
J_value = &mapping_info->affine_data[cell_data_number].second;
}
else
{
const unsigned int rowstart = mapping_info->
mapping_data_gen[quad_no].rowstart_jacobians[cell_data_number];
AssertIndexRange (rowstart, mapping_info->
mapping_data_gen[quad_no].jacobians.size());
jacobian =
&mapping_info->mapping_data_gen[quad_no].jacobians[rowstart];
if (mapping_info->JxW_values_initialized == true)
{
AssertIndexRange (rowstart, mapping_info->
mapping_data_gen[quad_no].JxW_values.size());
J_value = &(mapping_info->mapping_data_gen[quad_no].
JxW_values[rowstart]);
}
if (mapping_info->second_derivatives_initialized == true)
{
AssertIndexRange(rowstart, mapping_info->
mapping_data_gen[quad_no].jacobians_grad_diag.size());
jacobian_grad = &mapping_info->mapping_data_gen[quad_no].
jacobians_grad_diag[rowstart];
AssertIndexRange(rowstart, mapping_info->
mapping_data_gen[quad_no].jacobians_grad_upper.size());
jacobian_grad_upper = &mapping_info->mapping_data_gen[quad_no].
jacobians_grad_upper[rowstart];
}
}
#ifdef DEBUG
dof_values_initialized = false;
values_quad_initialized = false;
gradients_quad_initialized = false;
hessians_quad_initialized = false;
#endif
}
template <int dim, int n_components_, typename Number>
template <typename DoFHandlerType, bool level_dof_access>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::reinit (const TriaIterator<DoFCellAccessor<DoFHandlerType,level_dof_access> > &cell)
{
Assert(matrix_info == 0,
ExcMessage("Cannot use initialization from cell iterator if "
"initialized from MatrixFree object. Use variant for "
"on the fly computation with arguments as for FEValues "
"instead"));
Assert(mapped_geometry.get() != 0, ExcNotInitialized());
mapped_geometry->reinit(static_cast<typename Triangulation<dim>::cell_iterator>(cell));
local_dof_indices.resize(cell->get_fe().dofs_per_cell);
if (level_dof_access)
cell->get_mg_dof_indices(local_dof_indices);
else
cell->get_dof_indices(local_dof_indices);
}
template <int dim, int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::reinit (const typename Triangulation<dim>::cell_iterator &cell)
{
Assert(matrix_info == 0,
ExcMessage("Cannot use initialization from cell iterator if "
"initialized from MatrixFree object. Use variant for "
"on the fly computation with arguments as for FEValues "
"instead"));
Assert(mapped_geometry.get() != 0, ExcNotInitialized());
mapped_geometry->reinit(cell);
}
template <int dim, int n_components_, typename Number>
inline
unsigned int
FEEvaluationBase<dim,n_components_,Number>
::get_cell_data_number () const
{
Assert (cell != numbers::invalid_unsigned_int, ExcNotInitialized());
return cell_data_number;
}
template <int dim, int n_components_, typename Number>
inline
internal::MatrixFreeFunctions::CellType
FEEvaluationBase<dim,n_components_,Number>::get_cell_type () const
{
Assert (cell != numbers::invalid_unsigned_int, ExcNotInitialized());
return cell_type;
}
template <int dim, int n_components_, typename Number>
inline
const internal::MatrixFreeFunctions::ShapeInfo<Number> &
FEEvaluationBase<dim,n_components_,Number>::get_shape_info() const
{
Assert(data != 0, ExcInternalError());
return *data;
}
template <int dim, int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::fill_JxW_values(AlignedVector<VectorizedArray<Number> > &JxW_values) const
{
AssertDimension(JxW_values.size(), data->n_q_points);
Assert (this->J_value != 0, ExcNotImplemented());
if (this->cell_type == internal::MatrixFreeFunctions::cartesian ||
this->cell_type == internal::MatrixFreeFunctions::affine)
{
Assert (this->mapping_info != 0, ExcNotImplemented());
VectorizedArray<Number> J = this->J_value[0];
for (unsigned int q=0; q<this->data->n_q_points; ++q)
JxW_values[q] = J * this->quadrature_weights[q];
}
else
for (unsigned int q=0; q<data->n_q_points; ++q)
JxW_values[q] = this->J_value[q];
}
namespace internal
{
// write access to generic vectors that have operator ().
template <typename VectorType>
inline
typename VectorType::value_type &
vector_access (VectorType &vec,
const unsigned int entry)
{
return vec(entry);
}
// read access to generic vectors that have operator ().
template <typename VectorType>
inline
typename VectorType::value_type
vector_access (const VectorType &vec,
const unsigned int entry)
{
return vec(entry);
}
// write access to distributed MPI vectors that have a local_element(uint)
// method to access data in local index space, which is what we use in
// DoFInfo and hence in read_dof_values etc.
template <typename Number>
inline
Number &
vector_access (parallel::distributed::Vector<Number> &vec,
const unsigned int entry)
{
return vec.local_element(entry);
}
// read access to distributed MPI vectors that have a local_element(uint)
// method to access data in local index space, which is what we use in
// DoFInfo and hence in read_dof_values etc.
template <typename Number>
inline
Number
vector_access (const parallel::distributed::Vector<Number> &vec,
const unsigned int entry)
{
return vec.local_element(entry);
}
// this is to make sure that the parallel partitioning in the
// parallel::distributed::Vector is really the same as stored in MatrixFree
template <typename VectorType>
inline
void check_vector_compatibility (const VectorType &vec,
const internal::MatrixFreeFunctions::DoFInfo &dof_info)
{
AssertDimension (vec.size(),
dof_info.vector_partitioner->size());
}
template <typename Number>
inline
void check_vector_compatibility (const parallel::distributed::Vector<Number> &vec,
const internal::MatrixFreeFunctions::DoFInfo &dof_info)
{
Assert (vec.partitioners_are_compatible(*dof_info.vector_partitioner),
ExcMessage("The parallel layout of the given vector is not "
"compatible with the parallel partitioning in MatrixFree. "
"Use MatrixFree::initialize_dof_vector to get a "
"compatible vector."));
}
// A class to use the same code to read from and write to vector
template <typename Number>
struct VectorReader
{
template <typename VectorType>
void process_dof (const unsigned int index,
VectorType &vec,
Number &res) const
{
res = vector_access (const_cast<const VectorType &>(vec), index);
}
template <typename VectorType>
void process_dof_global (const types::global_dof_index index,
VectorType &vec,
Number &res) const
{
res = const_cast<const VectorType &>(vec)(index);
}
void pre_constraints (const Number &,
Number &res) const
{
res = Number();
}
template <typename VectorType>
void process_constraint (const unsigned int index,
const Number weight,
VectorType &vec,
Number &res) const
{
res += weight * vector_access (const_cast<const VectorType &>(vec), index);
}
void post_constraints (const Number &sum,
Number &write_pos) const
{
write_pos = sum;
}
void process_empty (Number &res) const
{
res = Number();
}
};
// A class to use the same code to read from and write to vector
template <typename Number>
struct VectorDistributorLocalToGlobal
{
template <typename VectorType>
void process_dof (const unsigned int index,
VectorType &vec,
Number &res) const
{
vector_access (vec, index) += res;
}
template <typename VectorType>
void process_dof_global (const types::global_dof_index index,
VectorType &vec,
Number &res) const
{
vec(index) += res;
}
void pre_constraints (const Number &input,
Number &res) const
{
res = input;
}
template <typename VectorType>
void process_constraint (const unsigned int index,
const Number weight,
VectorType &vec,
Number &res) const
{
vector_access (vec, index) += weight * res;
}
void post_constraints (const Number &,
Number &) const
{
}
void process_empty (Number &) const
{
}
};
// A class to use the same code to read from and write to vector
template <typename Number>
struct VectorSetter
{
template <typename VectorType>
void process_dof (const unsigned int index,
VectorType &vec,
Number &res) const
{
vector_access (vec, index) = res;
}
template <typename VectorType>
void process_dof_global (const types::global_dof_index index,
VectorType &vec,
Number &res) const
{
vec(index) = res;
}
void pre_constraints (const Number &,
Number &) const
{
}
template <typename VectorType>
void process_constraint (const unsigned int,
const Number,
VectorType &,
Number &) const
{
}
void post_constraints (const Number &,
Number &) const
{
}
void process_empty (Number &) const
{
}
};
// allows to select between block vectors and non-block vectors, which
// allows to use a unified interface for extracting blocks on block vectors
// and doing nothing on usual vectors
template <typename VectorType, bool>
struct BlockVectorSelector {};
template <typename VectorType>
struct BlockVectorSelector<VectorType,true>
{
typedef typename VectorType::BlockType BaseVectorType;
static BaseVectorType *get_vector_component (VectorType &vec,
const unsigned int component)
{
AssertIndexRange (component, vec.n_blocks());
return &vec.block(component);
}
};
template <typename VectorType>
struct BlockVectorSelector<VectorType,false>
{
typedef VectorType BaseVectorType;
static BaseVectorType *get_vector_component (VectorType &vec,
const unsigned int)
{
return &vec;
}
};
}
template <int dim, int n_components_, typename Number>
template<typename VectorType, typename VectorOperation>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_write_operation (const VectorOperation &operation,
VectorType *src[]) const
{
// This functions processes all the functions read_dof_values,
// distribute_local_to_global, and set_dof_values with the same code. The
// distinction between these three cases is made by the input
// VectorOperation that either reads values from a vector and puts the data
// into the local data field or write local data into the vector. Certain
// operations are no-ops for the given use case.
// Case 1: No MatrixFree object given, simple case because we do not need to
// process constraints and need not care about vectorization
if (matrix_info == 0)
{
Assert (!local_dof_indices.empty(), ExcNotInitialized());
unsigned int index = first_selected_component * this->data->dofs_per_cell;
for (unsigned int comp = 0; comp<n_components; ++comp)
{
for (unsigned int i=0; i<this->data->dofs_per_cell; ++i, ++index)
{
operation.process_dof_global(local_dof_indices[this->data->lexicographic_numbering[index]],
*src[0], values_dofs[comp][i][0]);
for (unsigned int v=1; v<VectorizedArray<Number>::n_array_elements; ++v)
operation.process_empty(values_dofs[comp][i][v]);
}
}
return;
}
Assert (dof_info != 0, ExcNotInitialized());
Assert (matrix_info->indices_initialized() == true,
ExcNotInitialized());
Assert (cell != numbers::invalid_unsigned_int, ExcNotInitialized());
// loop over all local dofs. ind_local holds local number on cell, index
// iterates over the elements of index_local_to_global and dof_indices
// points to the global indices stored in index_local_to_global
const unsigned int *dof_indices = dof_info->begin_indices(cell);
const std::pair<unsigned short,unsigned short> *indicators =
dof_info->begin_indicators(cell);
const std::pair<unsigned short,unsigned short> *indicators_end =
dof_info->end_indicators(cell);
unsigned int ind_local = 0;
const unsigned int dofs_per_cell = this->data->dofs_per_cell;
const unsigned int n_irreg_components_filled = dof_info->row_starts[cell][2];
const bool at_irregular_cell = n_irreg_components_filled > 0;
// scalar case (or case when all components have the same degrees of freedom
// and sit on a different vector each)
if (n_fe_components == 1)
{
const unsigned int n_local_dofs =
VectorizedArray<Number>::n_array_elements * dofs_per_cell;
for (unsigned int comp=0; comp<n_components; ++comp)
internal::check_vector_compatibility (*src[comp], *dof_info);
Number *local_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
local_data[comp] =
const_cast<Number *>(&values_dofs[comp][0][0]);
// standard case where there are sufficiently many cells to fill all
// vectors
if (at_irregular_cell == false)
{
// check whether there is any constraint on the current cell
if (indicators != indicators_end)
{
for ( ; indicators != indicators_end; ++indicators)
{
// run through values up to next constraint
for (unsigned int j=0; j<indicators->first; ++j)
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_dof (dof_indices[j], *src[comp],
local_data[comp][ind_local+j]);
ind_local += indicators->first;
dof_indices += indicators->first;
// constrained case: build the local value as a linear
// combination of the global value according to constraints
Number value [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
operation.pre_constraints (local_data[comp][ind_local],
value[comp]);
const Number *data_val =
matrix_info->constraint_pool_begin(indicators->second);
const Number *end_pool =
matrix_info->constraint_pool_end(indicators->second);
for ( ; data_val != end_pool; ++data_val, ++dof_indices)
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_constraint (*dof_indices, *data_val,
*src[comp], value[comp]);
for (unsigned int comp=0; comp<n_components; ++comp)
operation.post_constraints (value[comp],
local_data[comp][ind_local]);
ind_local++;
}
// get the dof values past the last constraint
for (; ind_local < n_local_dofs; ++dof_indices, ++ind_local)
{
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_dof (*dof_indices, *src[comp],
local_data[comp][ind_local]);
}
}
else
{
// no constraint at all: compiler can unroll at least the
// vectorization loop
AssertDimension (dof_info->end_indices(cell)-dof_indices,
static_cast<int>(n_local_dofs));
for (unsigned int j=0; j<n_local_dofs; j+=VectorizedArray<Number>::n_array_elements)
for (unsigned int v=0; v<VectorizedArray<Number>::n_array_elements; ++v)
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_dof (dof_indices[j+v], *src[comp],
local_data[comp][j+v]);
}
}
// non-standard case: need to fill in zeros for those components that
// are not present (a bit more expensive), but there is not more than
// one such cell
else
{
Assert (n_irreg_components_filled > 0, ExcInternalError());
for ( ; indicators != indicators_end; ++indicators)
{
for (unsigned int j=0; j<indicators->first; ++j)
{
// non-constrained case: copy the data from the global
// vector, src, to the local one, local_src.
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_dof (dof_indices[j], *src[comp],
local_data[comp][ind_local]);
// here we jump over all the components that are artificial
++ind_local;
while (ind_local % VectorizedArray<Number>::n_array_elements
>= n_irreg_components_filled)
{
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_empty (local_data[comp][ind_local]);
++ind_local;
}
}
dof_indices += indicators->first;
// constrained case: build the local value as a linear
// combination of the global value according to constraint
Number value [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
operation.pre_constraints (local_data[comp][ind_local],
value[comp]);
const Number *data_val =
matrix_info->constraint_pool_begin(indicators->second);
const Number *end_pool =
matrix_info->constraint_pool_end(indicators->second);
for ( ; data_val != end_pool; ++data_val, ++dof_indices)
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_constraint (*dof_indices, *data_val,
*src[comp], value[comp]);
for (unsigned int comp=0; comp<n_components; ++comp)
operation.post_constraints (value[comp],
local_data[comp][ind_local]);
ind_local++;
while (ind_local % VectorizedArray<Number>::n_array_elements
>= n_irreg_components_filled)
{
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_empty (local_data[comp][ind_local]);
++ind_local;
}
}
for (; ind_local<n_local_dofs; ++dof_indices)
{
Assert (dof_indices != dof_info->end_indices(cell),
ExcInternalError());
// non-constrained case: copy the data from the global vector,
// src, to the local one, local_dst.
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_dof (*dof_indices, *src[comp],
local_data[comp][ind_local]);
++ind_local;
while (ind_local % VectorizedArray<Number>::n_array_elements
>= n_irreg_components_filled)
{
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_empty(local_data[comp][ind_local]);
++ind_local;
}
}
}
}
else
// case with vector-valued finite elements where all components are
// included in one single vector. Assumption: first come all entries to
// the first component, then all entries to the second one, and so
// on. This is ensured by the way MatrixFree reads out the indices.
{
internal::check_vector_compatibility (*src[0], *dof_info);
Assert (n_fe_components == n_components_, ExcNotImplemented());
const unsigned int n_local_dofs =
dofs_per_cell*VectorizedArray<Number>::n_array_elements * n_components;
Number *local_data =
const_cast<Number *>(&values_dofs[0][0][0]);
if (at_irregular_cell == false)
{
// check whether there is any constraint on the current cell
if (indicators != indicators_end)
{
for ( ; indicators != indicators_end; ++indicators)
{
// run through values up to next constraint
for (unsigned int j=0; j<indicators->first; ++j)
operation.process_dof (dof_indices[j], *src[0],
local_data[ind_local+j]);
ind_local += indicators->first;
dof_indices += indicators->first;
// constrained case: build the local value as a linear
// combination of the global value according to constraints
Number value;
operation.pre_constraints (local_data[ind_local], value);
const Number *data_val =
matrix_info->constraint_pool_begin(indicators->second);
const Number *end_pool =
matrix_info->constraint_pool_end(indicators->second);
for ( ; data_val != end_pool; ++data_val, ++dof_indices)
operation.process_constraint (*dof_indices, *data_val,
*src[0], value);
operation.post_constraints (value, local_data[ind_local]);
ind_local++;
}
// get the dof values past the last constraint
for (; ind_local<n_local_dofs; ++dof_indices, ++ind_local)
operation.process_dof (*dof_indices, *src[0],
local_data[ind_local]);
Assert (dof_indices == dof_info->end_indices(cell),
ExcInternalError());
}
else
{
// no constraint at all: compiler can unroll at least the
// vectorization loop
AssertDimension (dof_info->end_indices(cell)-dof_indices,
static_cast<int>(n_local_dofs));
for (unsigned int j=0; j<n_local_dofs; j+=VectorizedArray<Number>::n_array_elements)
for (unsigned int v=0; v<VectorizedArray<Number>::n_array_elements; ++v)
operation.process_dof (dof_indices[j+v], *src[0],
local_data[j+v]);
}
}
// non-standard case: need to fill in zeros for those components that
// are not present (a bit more expensive), but there is not more than
// one such cell
else
{
Assert (n_irreg_components_filled > 0, ExcInternalError());
for ( ; indicators != indicators_end; ++indicators)
{
for (unsigned int j=0; j<indicators->first; ++j)
{
// non-constrained case: copy the data from the global
// vector, src, to the local one, local_src.
operation.process_dof (dof_indices[j], *src[0],
local_data[ind_local]);
// here we jump over all the components that are artificial
++ind_local;
while (ind_local % VectorizedArray<Number>::n_array_elements
>= n_irreg_components_filled)
{
operation.process_empty (local_data[ind_local]);
++ind_local;
}
}
dof_indices += indicators->first;
// constrained case: build the local value as a linear
// combination of the global value according to constraint
Number value;
operation.pre_constraints (local_data[ind_local], value);
const Number *data_val =
matrix_info->constraint_pool_begin(indicators->second);
const Number *end_pool =
matrix_info->constraint_pool_end(indicators->second);
for ( ; data_val != end_pool; ++data_val, ++dof_indices)
operation.process_constraint (*dof_indices, *data_val,
*src[0], value);
operation.post_constraints (value, local_data[ind_local]);
ind_local++;
while (ind_local % VectorizedArray<Number>::n_array_elements
>= n_irreg_components_filled)
{
operation.process_empty (local_data[ind_local]);
++ind_local;
}
}
for (; ind_local<n_local_dofs; ++dof_indices)
{
Assert (dof_indices != dof_info->end_indices(cell),
ExcInternalError());
// non-constrained case: copy the data from the global vector,
// src, to the local one, local_dst.
operation.process_dof (*dof_indices, *src[0],
local_data[ind_local]);
++ind_local;
while (ind_local % VectorizedArray<Number>::n_array_elements
>= n_irreg_components_filled)
{
operation.process_empty (local_data[ind_local]);
++ind_local;
}
}
}
}
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_dof_values (const VectorType &src)
{
// select between block vectors and non-block vectors. Note that the number
// of components is checked in the internal data
typename internal::BlockVectorSelector<VectorType,
IsBlockVector<VectorType>::value>::BaseVectorType *src_data[n_components];
for (unsigned int d=0; d<n_components; ++d)
src_data[d] = internal::BlockVectorSelector<VectorType, IsBlockVector<VectorType>::value>::get_vector_component(const_cast<VectorType &>(src), d);
internal::VectorReader<Number> reader;
read_write_operation (reader, src_data);
#ifdef DEBUG
dof_values_initialized = true;
#endif
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_dof_values (const std::vector<VectorType> &src,
const unsigned int first_index)
{
AssertIndexRange (first_index, src.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= src.size()) : true),
ExcIndexRange (first_index + n_components_, 0, src.size()));
VectorType *src_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
src_data[comp] = const_cast<VectorType *>(&src[comp+first_index]);
internal::VectorReader<Number> reader;
read_write_operation (reader, src_data);
#ifdef DEBUG
dof_values_initialized = true;
#endif
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_dof_values (const std::vector<VectorType *> &src,
const unsigned int first_index)
{
AssertIndexRange (first_index, src.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= src.size()) : true),
ExcIndexRange (first_index + n_components_, 0, src.size()));
const VectorType *src_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
src_data[comp] = const_cast<VectorType *>(src[comp+first_index]);
internal::VectorReader<Number> reader;
read_write_operation (reader, src_data);
#ifdef DEBUG
dof_values_initialized = true;
#endif
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_dof_values_plain (const VectorType &src)
{
// select between block vectors and non-block vectors. Note that the number
// of components is checked in the internal data
const typename internal::BlockVectorSelector<VectorType,
IsBlockVector<VectorType>::value>::BaseVectorType *src_data[n_components];
for (unsigned int d=0; d<n_components; ++d)
src_data[d] = internal::BlockVectorSelector<VectorType, IsBlockVector<VectorType>::value>::get_vector_component(const_cast<VectorType &>(src), d);
read_dof_values_plain (src_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_dof_values_plain (const std::vector<VectorType> &src,
const unsigned int first_index)
{
AssertIndexRange (first_index, src.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= src.size()) : true),
ExcIndexRange (first_index + n_components_, 0, src.size()));
const VectorType *src_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
src_data[comp] = &src[comp+first_index];
read_dof_values_plain (src_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_dof_values_plain (const std::vector<VectorType *> &src,
const unsigned int first_index)
{
AssertIndexRange (first_index, src.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= src.size()) : true),
ExcIndexRange (first_index + n_components_, 0, src.size()));
const VectorType *src_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
src_data[comp] = src[comp+first_index];
read_dof_values_plain (src_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::distribute_local_to_global (VectorType &dst) const
{
Assert (dof_values_initialized==true,
internal::ExcAccessToUninitializedField());
// select between block vectors and non-block vectors. Note that the number
// of components is checked in the internal data
typename internal::BlockVectorSelector<VectorType,
IsBlockVector<VectorType>::value>::BaseVectorType *dst_data[n_components];
for (unsigned int d=0; d<n_components; ++d)
dst_data[d] = internal::BlockVectorSelector<VectorType, IsBlockVector<VectorType>::value>::get_vector_component(dst, d);
internal::VectorDistributorLocalToGlobal<Number> distributor;
read_write_operation (distributor, dst_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::distribute_local_to_global (std::vector<VectorType> &dst,
const unsigned int first_index) const
{
AssertIndexRange (first_index, dst.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= dst.size()) : true),
ExcIndexRange (first_index + n_components_, 0, dst.size()));
Assert (dof_values_initialized==true,
internal::ExcAccessToUninitializedField());
VectorType *dst_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
dst_data[comp] = &dst[comp+first_index];
internal::VectorDistributorLocalToGlobal<Number> distributor;
read_write_operation (distributor, dst_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::distribute_local_to_global (std::vector<VectorType *> &dst,
const unsigned int first_index) const
{
AssertIndexRange (first_index, dst.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= dst.size()) : true),
ExcIndexRange (first_index + n_components_, 0, dst.size()));
Assert (dof_values_initialized==true,
internal::ExcAccessToUninitializedField());
VectorType *dst_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
dst_data[comp] = dst[comp+first_index];
internal::VectorDistributorLocalToGlobal<Number> distributor;
read_write_operation (distributor, dst_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::set_dof_values (VectorType &dst) const
{
Assert (dof_values_initialized==true,
internal::ExcAccessToUninitializedField());
// select between block vectors and non-block vectors. Note that the number
// of components is checked in the internal data
typename internal::BlockVectorSelector<VectorType,
IsBlockVector<VectorType>::value>::BaseVectorType *dst_data[n_components];
for (unsigned int d=0; d<n_components; ++d)
dst_data[d] = internal::BlockVectorSelector<VectorType, IsBlockVector<VectorType>::value>::get_vector_component(dst, d);
internal::VectorSetter<Number> setter;
read_write_operation (setter, dst_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::set_dof_values (std::vector<VectorType> &dst,
const unsigned int first_index) const
{
AssertIndexRange (first_index, dst.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= dst.size()) : true),
ExcIndexRange (first_index + n_components_, 0, dst.size()));
Assert (dof_values_initialized==true,
internal::ExcAccessToUninitializedField());
VectorType *dst_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
dst_data[comp] = &dst[comp+first_index];
internal::VectorSetter<Number> setter;
read_write_operation (setter, dst_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::set_dof_values (std::vector<VectorType *> &dst,
const unsigned int first_index) const
{
AssertIndexRange (first_index, dst.size());
Assert (n_fe_components == 1, ExcNotImplemented());
Assert ((n_fe_components == 1 ?
(first_index+n_components <= dst.size()) : true),
ExcIndexRange (first_index + n_components_, 0, dst.size()));
Assert (dof_values_initialized==true,
internal::ExcAccessToUninitializedField());
VectorType *dst_data [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
dst_data[comp] = dst[comp+first_index];
internal::VectorSetter<Number> setter;
read_write_operation (setter, dst_data);
}
template <int dim, int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::read_dof_values_plain (const VectorType *src[])
{
// Case without MatrixFree initialization object
if (matrix_info == 0)
{
internal::VectorReader<Number> reader;
read_write_operation (reader, src);
return;
}
// this is different from the other three operations because we do not use
// constraints here, so this is a separate function.
Assert (dof_info != 0, ExcNotInitialized());
Assert (matrix_info->indices_initialized() == true,
ExcNotInitialized());
Assert (cell != numbers::invalid_unsigned_int, ExcNotInitialized());
Assert (dof_info->store_plain_indices == true, ExcNotInitialized());
// loop over all local dofs. ind_local holds local number on cell, index
// iterates over the elements of index_local_to_global and dof_indices
// points to the global indices stored in index_local_to_global
const unsigned int *dof_indices = dof_info->begin_indices_plain(cell);
const unsigned int dofs_per_cell = this->data->dofs_per_cell;
const unsigned int n_irreg_components_filled = dof_info->row_starts[cell][2];
const bool at_irregular_cell = n_irreg_components_filled > 0;
// scalar case (or case when all components have the same degrees of freedom
// and sit on a different vector each)
if (n_fe_components == 1)
{
const unsigned int n_local_dofs =
VectorizedArray<Number>::n_array_elements * dofs_per_cell;
for (unsigned int comp=0; comp<n_components; ++comp)
internal::check_vector_compatibility (*src[comp], *dof_info);
Number *local_src_number [n_components];
for (unsigned int comp=0; comp<n_components; ++comp)
local_src_number[comp] = &values_dofs[comp][0][0];
// standard case where there are sufficiently many cells to fill all
// vectors
if (at_irregular_cell == false)
{
for (unsigned int j=0; j<n_local_dofs; ++j)
for (unsigned int comp=0; comp<n_components; ++comp)
local_src_number[comp][j] =
internal::vector_access (*src[comp], dof_indices[j]);
}
// non-standard case: need to fill in zeros for those components that
// are not present (a bit more expensive), but there is not more than
// one such cell
else
{
Assert (n_irreg_components_filled > 0, ExcInternalError());
for (unsigned int ind_local=0; ind_local<n_local_dofs;
++dof_indices)
{
// non-constrained case: copy the data from the global vector,
// src, to the local one, local_dst.
for (unsigned int comp=0; comp<n_components; ++comp)
local_src_number[comp][ind_local] =
internal::vector_access (*src[comp], *dof_indices);
++ind_local;
while (ind_local % VectorizedArray<Number>::n_array_elements >= n_irreg_components_filled)
{
for (unsigned int comp=0; comp<n_components; ++comp)
local_src_number[comp][ind_local] = 0.;
++ind_local;
}
}
}
}
else
// case with vector-valued finite elements where all components are
// included in one single vector. Assumption: first come all entries to
// the first component, then all entries to the second one, and so
// on. This is ensured by the way MatrixFree reads out the indices.
{
internal::check_vector_compatibility (*src[0], *dof_info);
Assert (n_fe_components == n_components_, ExcNotImplemented());
const unsigned int n_local_dofs =
dofs_per_cell * VectorizedArray<Number>::n_array_elements * n_components;
Number *local_src_number = &values_dofs[0][0][0];
if (at_irregular_cell == false)
{
for (unsigned int j=0; j<n_local_dofs; ++j)
local_src_number[j] =
internal::vector_access (*src[0], dof_indices[j]);
}
// non-standard case: need to fill in zeros for those components that
// are not present (a bit more expensive), but there is not more than
// one such cell
else
{
Assert (n_irreg_components_filled > 0, ExcInternalError());
for (unsigned int ind_local=0; ind_local<n_local_dofs; ++dof_indices)
{
// non-constrained case: copy the data from the global vector,
// src, to the local one, local_dst.
local_src_number[ind_local] =
internal::vector_access (*src[0], *dof_indices);
++ind_local;
while (ind_local % VectorizedArray<Number>::n_array_elements >= n_irreg_components_filled)
{
local_src_number[ind_local] = 0.;
++ind_local;
}
}
}
}
#ifdef DEBUG
dof_values_initialized = true;
#endif
}
/*------------------------------ access to data fields ----------------------*/
template <int dim, int n_components, typename Number>
inline
const std::vector<unsigned int> &
FEEvaluationBase<dim,n_components,Number>::
get_internal_dof_numbering() const
{
return data->lexicographic_numbering;
}
template <int dim, int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_dof_values () const
{
return &values_dofs[0][0];
}
template <int dim, int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_dof_values ()
{
#ifdef DEBUG
dof_values_initialized = true;
#endif
return &values_dofs[0][0];
}
template <int dim, int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_values () const
{
Assert (values_quad_initialized || values_quad_submitted,
ExcNotInitialized());
return &values_quad[0][0];
}
template <int dim, int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_values ()
{
#ifdef DEBUG
values_quad_submitted = true;
#endif
return &values_quad[0][0];
}
template <int dim, int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_gradients () const
{
Assert (gradients_quad_initialized || gradients_quad_submitted,
ExcNotInitialized());
return &gradients_quad[0][0][0];
}
template <int dim, int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_gradients ()
{
#ifdef DEBUG
gradients_quad_submitted = true;
#endif
return &gradients_quad[0][0][0];
}
template <int dim, int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_hessians () const
{
Assert (hessians_quad_initialized, ExcNotInitialized());
return &hessians_quad[0][0][0];
}
template <int dim, int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,n_components,Number>::
begin_hessians ()
{
return &hessians_quad[0][0][0];
}
template <int dim, int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,n_components_,Number>
::get_dof_value (const unsigned int dof) const
{
AssertIndexRange (dof, this->data->dofs_per_cell);
Tensor<1,n_components_,VectorizedArray<Number> > return_value;
for (unsigned int comp=0; comp<n_components; comp++)
return_value[comp] = this->values_dofs[comp][dof];
return return_value;
}
template <int dim, int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,n_components_,Number>
::get_value (const unsigned int q_point) const
{
Assert (this->values_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
Tensor<1,n_components_,VectorizedArray<Number> > return_value;
for (unsigned int comp=0; comp<n_components; comp++)
return_value[comp] = this->values_quad[comp][q_point];
return return_value;
}
template <int dim, int n_components_, typename Number>
inline
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > >
FEEvaluationBase<dim,n_components_,Number>
::get_gradient (const unsigned int q_point) const
{
Assert (this->gradients_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > > grad_out;
// Cartesian cell
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
for (unsigned int comp=0; comp<n_components; comp++)
for (unsigned int d=0; d<dim; ++d)
grad_out[comp][d] = (this->gradients_quad[comp][d][q_point] *
cartesian_data[0][d]);
}
// cell with general/affine Jacobian
else
{
const Tensor<2,dim,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
jacobian[q_point] : jacobian[0];
for (unsigned int comp=0; comp<n_components; comp++)
{
for (unsigned int d=0; d<dim; ++d)
{
grad_out[comp][d] = (jac[d][0] *
this->gradients_quad[comp][0][q_point]);
for (unsigned int e=1; e<dim; ++e)
grad_out[comp][d] += (jac[d][e] *
this->gradients_quad[comp][e][q_point]);
}
}
}
return grad_out;
}
namespace internal
{
// compute tmp = hess_unit(u) * J^T. do this manually because we do not
// store the lower diagonal because of symmetry
template <typename Number>
inline
void
hessian_unit_times_jac (const Tensor<2,1,VectorizedArray<Number> > &jac,
const VectorizedArray<Number> *const hessians_quad[1],
const unsigned int q_point,
VectorizedArray<Number> (&tmp)[1][1])
{
tmp[0][0] = jac[0][0] * hessians_quad[0][q_point];
}
template <typename Number>
inline
void
hessian_unit_times_jac (const Tensor<2,2,VectorizedArray<Number> > &jac,
const VectorizedArray<Number> *const hessians_quad[3],
const unsigned int q_point,
VectorizedArray<Number> (&tmp)[2][2])
{
for (unsigned int d=0; d<2; ++d)
{
tmp[0][d] = (jac[d][0] * hessians_quad[0][q_point] +
jac[d][1] * hessians_quad[2][q_point]);
tmp[1][d] = (jac[d][0] * hessians_quad[2][q_point] +
jac[d][1] * hessians_quad[1][q_point]);
}
}
template <typename Number>
inline
void
hessian_unit_times_jac (const Tensor<2,3,VectorizedArray<Number> > &jac,
const VectorizedArray<Number> *const hessians_quad[6],
const unsigned int q_point,
VectorizedArray<Number> (&tmp)[3][3])
{
for (unsigned int d=0; d<3; ++d)
{
tmp[0][d] = (jac[d][0] * hessians_quad[0][q_point] +
jac[d][1] * hessians_quad[3][q_point] +
jac[d][2] * hessians_quad[4][q_point]);
tmp[1][d] = (jac[d][0] * hessians_quad[3][q_point] +
jac[d][1] * hessians_quad[1][q_point] +
jac[d][2] * hessians_quad[5][q_point]);
tmp[2][d] = (jac[d][0] * hessians_quad[4][q_point] +
jac[d][1] * hessians_quad[5][q_point] +
jac[d][2] * hessians_quad[2][q_point]);
}
}
}
template <int dim, int n_components_, typename Number>
inline
Tensor<1,n_components_,Tensor<2,dim,VectorizedArray<Number> > >
FEEvaluationBase<dim,n_components_,Number>
::get_hessian (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
Tensor<2,dim,VectorizedArray<Number> > hessian_out [n_components];
// Cartesian cell
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
const Tensor<1,dim,VectorizedArray<Number> > &jac = cartesian_data[0];
for (unsigned int comp=0; comp<n_components; comp++)
for (unsigned int d=0; d<dim; ++d)
{
hessian_out[comp][d][d] = (this->hessians_quad[comp][d][q_point] *
jac[d] * jac[d]);
switch (dim)
{
case 1:
break;
case 2:
hessian_out[comp][0][1] = (this->hessians_quad[comp][2][q_point] *
jac[0] * jac[1]);
break;
case 3:
hessian_out[comp][0][1] = (this->hessians_quad[comp][3][q_point] *
jac[0] * jac[1]);
hessian_out[comp][0][2] = (this->hessians_quad[comp][4][q_point] *
jac[0] * jac[2]);
hessian_out[comp][1][2] = (this->hessians_quad[comp][5][q_point] *
jac[1] * jac[2]);
break;
default:
Assert (false, ExcNotImplemented());
}
for (unsigned int e=d+1; e<dim; ++e)
hessian_out[comp][e][d] = hessian_out[comp][d][e];
}
}
// cell with general Jacobian
else if (this->cell_type == internal::MatrixFreeFunctions::general)
{
Assert (this->mapping_info->second_derivatives_initialized == true,
ExcNotInitialized());
const Tensor<2,dim,VectorizedArray<Number> > &jac = jacobian[q_point];
const Tensor<2,dim,VectorizedArray<Number> > &jac_grad = jacobian_grad[q_point];
const Tensor<1,(dim>1?dim*(dim-1)/2:1),
Tensor<1,dim,VectorizedArray<Number> > >
& jac_grad_UT = jacobian_grad_upper[q_point];
for (unsigned int comp=0; comp<n_components; comp++)
{
// compute laplacian before the gradient because it needs to access
// unscaled gradient data
VectorizedArray<Number> tmp[dim][dim];
internal::hessian_unit_times_jac (jac, this->hessians_quad[comp],
q_point, tmp);
// compute first part of hessian, J * tmp = J * hess_unit(u) * J^T
for (unsigned int d=0; d<dim; ++d)
for (unsigned int e=d; e<dim; ++e)
{
hessian_out[comp][d][e] = jac[d][0] * tmp[0][e];
for (unsigned int f=1; f<dim; ++f)
hessian_out[comp][d][e] += jac[d][f] * tmp[f][e];
}
// add diagonal part of J' * grad(u)
for (unsigned int d=0; d<dim; ++d)
for (unsigned int e=0; e<dim; ++e)
hessian_out[comp][d][d] += (jac_grad[d][e] *
this->gradients_quad[comp][e][q_point]);
// add off-diagonal part of J' * grad(u)
for (unsigned int d=0, count=0; d<dim; ++d)
for (unsigned int e=d+1; e<dim; ++e, ++count)
for (unsigned int f=0; f<dim; ++f)
hessian_out[comp][d][e] += (jac_grad_UT[count][f] *
this->gradients_quad[comp][f][q_point]);
// take symmetric part
for (unsigned int d=0; d<dim; ++d)
for (unsigned int e=d+1; e<dim; ++e)
hessian_out[comp][e][d] = hessian_out[comp][d][e];
}
}
// cell with general Jacobian, but constant within the cell
else // if (this->cell_type == internal::MatrixFreeFunctions::affine)
{
const Tensor<2,dim,VectorizedArray<Number> > &jac = jacobian[0];
for (unsigned int comp=0; comp<n_components; comp++)
{
// compute laplacian before the gradient because it needs to access
// unscaled gradient data
VectorizedArray<Number> tmp[dim][dim];
internal::hessian_unit_times_jac (jac, this->hessians_quad[comp],
q_point, tmp);
// compute first part of hessian, J * tmp = J * hess_unit(u) * J^T
for (unsigned int d=0; d<dim; ++d)
for (unsigned int e=d; e<dim; ++e)
{
hessian_out[comp][d][e] = jac[d][0] * tmp[0][e];
for (unsigned int f=1; f<dim; ++f)
hessian_out[comp][d][e] += jac[d][f] * tmp[f][e];
}
// no J' * grad(u) part here because the Jacobian is constant
// throughout the cell and hence, its derivative is zero
// take symmetric part
for (unsigned int d=0; d<dim; ++d)
for (unsigned int e=d+1; e<dim; ++e)
hessian_out[comp][e][d] = hessian_out[comp][d][e];
}
}
return Tensor<1,n_components_,Tensor<2,dim,VectorizedArray<Number> > >(hessian_out);
}
template <int dim, int n_components_, typename Number>
inline
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > >
FEEvaluationBase<dim,n_components_,Number>
::get_hessian_diagonal (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > > hessian_out;
// Cartesian cell
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
const Tensor<1,dim,VectorizedArray<Number> > &jac = cartesian_data[0];
for (unsigned int comp=0; comp<n_components; comp++)
for (unsigned int d=0; d<dim; ++d)
hessian_out[comp][d] = (this->hessians_quad[comp][d][q_point] *
jac[d] * jac[d]);
}
// cell with general Jacobian
else if (this->cell_type == internal::MatrixFreeFunctions::general)
{
Assert (this->mapping_info->second_derivatives_initialized == true,
ExcNotInitialized());
const Tensor<2,dim,VectorizedArray<Number> > &jac = jacobian[q_point];
const Tensor<2,dim,VectorizedArray<Number> > &jac_grad = jacobian_grad[q_point];
for (unsigned int comp=0; comp<n_components; comp++)
{
// compute laplacian before the gradient because it needs to access
// unscaled gradient data
VectorizedArray<Number> tmp[dim][dim];
internal::hessian_unit_times_jac (jac, this->hessians_quad[comp],
q_point, tmp);
// compute only the trace part of hessian, J * tmp = J *
// hess_unit(u) * J^T
for (unsigned int d=0; d<dim; ++d)
{
hessian_out[comp][d] = jac[d][0] * tmp[0][d];
for (unsigned int f=1; f<dim; ++f)
hessian_out[comp][d] += jac[d][f] * tmp[f][d];
}
for (unsigned int d=0; d<dim; ++d)
for (unsigned int e=0; e<dim; ++e)
hessian_out[comp][d] += (jac_grad[d][e] *
this->gradients_quad[comp][e][q_point]);
}
}
// cell with general Jacobian, but constant within the cell
else // if (this->cell_type == internal::MatrixFreeFunctions::affine)
{
const Tensor<2,dim,VectorizedArray<Number> > &jac = jacobian[0];
for (unsigned int comp=0; comp<n_components; comp++)
{
// compute laplacian before the gradient because it needs to access
// unscaled gradient data
VectorizedArray<Number> tmp[dim][dim];
internal::hessian_unit_times_jac (jac, this->hessians_quad[comp],
q_point, tmp);
// compute only the trace part of hessian, J * tmp = J *
// hess_unit(u) * J^T
for (unsigned int d=0; d<dim; ++d)
{
hessian_out[comp][d] = jac[d][0] * tmp[0][d];
for (unsigned int f=1; f<dim; ++f)
hessian_out[comp][d] += jac[d][f] * tmp[f][d];
}
}
}
return hessian_out;
}
template <int dim, int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,n_components_,Number>
::get_laplacian (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
Tensor<1,n_components_,VectorizedArray<Number> > laplacian_out;
const Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > > hess_diag
= get_hessian_diagonal(q_point);
for (unsigned int comp=0; comp<n_components; ++comp)
{
laplacian_out[comp] = hess_diag[comp][0];
for (unsigned int d=1; d<dim; ++d)
laplacian_out[comp] += hess_diag[comp][d];
}
return laplacian_out;
}
template <int dim, int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::submit_dof_value (const Tensor<1,n_components_,VectorizedArray<Number> > val_in,
const unsigned int dof)
{
#ifdef DEBUG
this->dof_values_initialized = true;
#endif
AssertIndexRange (dof, this->data->dofs_per_cell);
for (unsigned int comp=0; comp<n_components; comp++)
this->values_dofs[comp][dof] = val_in[comp];
}
template <int dim, int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::submit_value (const Tensor<1,n_components_,VectorizedArray<Number> > val_in,
const unsigned int q_point)
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->values_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::general)
{
const VectorizedArray<Number> JxW = J_value[q_point];
for (unsigned int comp=0; comp<n_components; ++comp)
this->values_quad[comp][q_point] = val_in[comp] * JxW;
}
else //if (this->cell_type < internal::MatrixFreeFunctions::general)
{
const VectorizedArray<Number> JxW = J_value[0] * quadrature_weights[q_point];
for (unsigned int comp=0; comp<n_components; ++comp)
this->values_quad[comp][q_point] = val_in[comp] * JxW;
}
}
template <int dim, int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,n_components_,Number>
::submit_gradient (const Tensor<1,n_components_,
Tensor<1,dim,VectorizedArray<Number> > >grad_in,
const unsigned int q_point)
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->gradients_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
const VectorizedArray<Number> JxW = J_value[0] * quadrature_weights[q_point];
for (unsigned int comp=0; comp<n_components; comp++)
for (unsigned int d=0; d<dim; ++d)
this->gradients_quad[comp][d][q_point] = (grad_in[comp][d] *
cartesian_data[0][d] * JxW);
}
else
{
const Tensor<2,dim,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
jacobian[q_point] : jacobian[0];
const VectorizedArray<Number> JxW =
this->cell_type == internal::MatrixFreeFunctions::general ?
J_value[q_point] : J_value[0] * quadrature_weights[q_point];
for (unsigned int comp=0; comp<n_components; ++comp)
for (unsigned int d=0; d<dim; ++d)
{
VectorizedArray<Number> new_val = jac[0][d] * grad_in[comp][0];
for (unsigned int e=1; e<dim; ++e)
new_val += (jac[e][d] * grad_in[comp][e]);
this->gradients_quad[comp][d][q_point] = new_val * JxW;
}
}
}
template <int dim, int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,n_components_,Number>
::integrate_value () const
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
Assert (this->values_quad_submitted == true,
internal::ExcAccessToUninitializedField());
#endif
Tensor<1,n_components_,VectorizedArray<Number> > return_value;
for (unsigned int comp=0; comp<n_components; ++comp)
return_value[comp] = this->values_quad[comp][0];
const unsigned int n_q_points = this->data->n_q_points;
for (unsigned int q=1; q<n_q_points; ++q)
for (unsigned int comp=0; comp<n_components; ++comp)
return_value[comp] += this->values_quad[comp][q];
return (return_value);
}
/*----------------------- FEEvaluationAccess --------------------------------*/
template <int dim, int n_components_, typename Number>
inline
FEEvaluationAccess<dim,n_components_,Number>
::FEEvaluationAccess (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no_in,
const unsigned int fe_degree,
const unsigned int n_q_points)
:
FEEvaluationBase <dim,n_components_,Number>
(data_in, fe_no, quad_no_in, fe_degree, n_q_points)
{}
template <int dim, int n_components_, typename Number>
template <int n_components_other>
inline
FEEvaluationAccess<dim,n_components_,Number>
::FEEvaluationAccess (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other)
:
FEEvaluationBase <dim,n_components_,Number>(mapping, fe, quadrature, update_flags,
first_selected_component, other)
{}
template <int dim, int n_components_, typename Number>
inline
FEEvaluationAccess<dim,n_components_,Number>
::FEEvaluationAccess (const FEEvaluationAccess<dim,n_components_,Number> &other)
:
FEEvaluationBase <dim,n_components_,Number>(other)
{}
/*-------------------- FEEvaluationAccess scalar ----------------------------*/
template <int dim, typename Number>
inline
FEEvaluationAccess<dim,1,Number>
::FEEvaluationAccess (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no_in,
const unsigned int fe_degree,
const unsigned int n_q_points)
:
FEEvaluationBase <dim,1,Number>
(data_in, fe_no, quad_no_in, fe_degree, n_q_points)
{}
template <int dim, typename Number>
template <int n_components_other>
inline
FEEvaluationAccess<dim,1,Number>
::FEEvaluationAccess (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other)
:
FEEvaluationBase <dim,1,Number> (mapping, fe, quadrature, update_flags,
first_selected_component, other)
{}
template <int dim, typename Number>
inline
FEEvaluationAccess<dim,1,Number>
::FEEvaluationAccess (const FEEvaluationAccess<dim,1,Number> &other)
:
FEEvaluationBase <dim,1,Number>(other)
{}
template <int dim, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,1,Number>
::get_dof_value (const unsigned int dof) const
{
AssertIndexRange (dof, this->data->dofs_per_cell);
return this->values_dofs[0][dof];
}
template <int dim, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,1,Number>
::get_value (const unsigned int q_point) const
{
Assert (this->values_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
return this->values_quad[0][q_point];
}
template <int dim, typename Number>
inline
Tensor<1,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,1,Number>
::get_gradient (const unsigned int q_point) const
{
// could use the base class gradient, but that involves too many inefficient
// initialization operations on tensors
Assert (this->gradients_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
Tensor<1,dim,VectorizedArray<Number> > grad_out;
// Cartesian cell
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
for (unsigned int d=0; d<dim; ++d)
grad_out[d] = (this->gradients_quad[0][d][q_point] *
this->cartesian_data[0][d]);
}
// cell with general/constant Jacobian
else
{
const Tensor<2,dim,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->jacobian[q_point] : this->jacobian[0];
for (unsigned int d=0; d<dim; ++d)
{
grad_out[d] = (jac[d][0] * this->gradients_quad[0][0][q_point]);
for (unsigned int e=1; e<dim; ++e)
grad_out[d] += (jac[d][e] * this->gradients_quad[0][e][q_point]);
}
}
return grad_out;
}
template <int dim, typename Number>
inline
Tensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,1,Number>
::get_hessian (const unsigned int q_point) const
{
return BaseClass::get_hessian(q_point)[0];
}
template <int dim, typename Number>
inline
Tensor<1,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,1,Number>
::get_hessian_diagonal (const unsigned int q_point) const
{
return BaseClass::get_hessian_diagonal(q_point)[0];
}
template <int dim, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,1,Number>
::get_laplacian (const unsigned int q_point) const
{
return BaseClass::get_laplacian(q_point)[0];
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,1,Number>
::submit_dof_value (const VectorizedArray<Number> val_in,
const unsigned int dof)
{
#ifdef DEBUG
this->dof_values_initialized = true;
AssertIndexRange (dof, this->data->dofs_per_cell);
#endif
this->values_dofs[0][dof] = val_in;
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,1,Number>
::submit_value (const VectorizedArray<Number> val_in,
const unsigned int q_point)
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->values_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::general)
{
const VectorizedArray<Number> JxW = this->J_value[q_point];
this->values_quad[0][q_point] = val_in * JxW;
}
else //if (this->cell_type < internal::MatrixFreeFunctions::general)
{
const VectorizedArray<Number> JxW = this->J_value[0] * this->quadrature_weights[q_point];
this->values_quad[0][q_point] = val_in * JxW;
}
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,1,Number>
::submit_gradient (const Tensor<1,dim,VectorizedArray<Number> > grad_in,
const unsigned int q_point)
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->gradients_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
const VectorizedArray<Number> JxW = this->J_value[0] * this->quadrature_weights[q_point];
for (unsigned int d=0; d<dim; ++d)
this->gradients_quad[0][d][q_point] = (grad_in[d] *
this->cartesian_data[0][d] *
JxW);
}
// general/affine cell type
else
{
const Tensor<2,dim,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->jacobian[q_point] : this->jacobian[0];
const VectorizedArray<Number> JxW =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->J_value[q_point] : this->J_value[0] * this->quadrature_weights[q_point];
for (unsigned int d=0; d<dim; ++d)
{
VectorizedArray<Number> new_val = jac[0][d] * grad_in[0];
for (unsigned int e=1; e<dim; ++e)
new_val += jac[e][d] * grad_in[e];
this->gradients_quad[0][d][q_point] = new_val * JxW;
}
}
}
template <int dim, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,1,Number>
::integrate_value () const
{
return BaseClass::integrate_value()[0];
}
/*----------------- FEEvaluationAccess vector-valued ------------------------*/
template <int dim, typename Number>
inline
FEEvaluationAccess<dim,dim,Number>
::FEEvaluationAccess (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no_in,
const unsigned int fe_degree,
const unsigned int n_q_points)
:
FEEvaluationBase <dim,dim,Number>
(data_in, fe_no, quad_no_in, fe_degree, n_q_points)
{}
template <int dim, typename Number>
template <int n_components_other>
inline
FEEvaluationAccess<dim,dim,Number>
::FEEvaluationAccess (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<dim,n_components_other,Number> *other)
:
FEEvaluationBase <dim,dim,Number> (mapping, fe, quadrature, update_flags,
first_selected_component, other)
{}
template <int dim, typename Number>
inline
FEEvaluationAccess<dim,dim,Number>
::FEEvaluationAccess (const FEEvaluationAccess<dim,dim,Number> &other)
:
FEEvaluationBase <dim,dim,Number>(other)
{}
template <int dim, typename Number>
inline
Tensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dim,Number>
::get_gradient (const unsigned int q_point) const
{
return BaseClass::get_gradient (q_point);
}
template <int dim, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,dim,Number>
::get_divergence (const unsigned int q_point) const
{
Assert (this->gradients_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
VectorizedArray<Number> divergence;
// Cartesian cell
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
divergence = (this->gradients_quad[0][0][q_point] *
this->cartesian_data[0][0]);
for (unsigned int d=1; d<dim; ++d)
divergence += (this->gradients_quad[d][d][q_point] *
this->cartesian_data[0][d]);
}
// cell with general/constant Jacobian
else
{
const Tensor<2,dim,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->jacobian[q_point] : this->jacobian[0];
divergence = (jac[0][0] * this->gradients_quad[0][0][q_point]);
for (unsigned int e=1; e<dim; ++e)
divergence += (jac[0][e] * this->gradients_quad[0][e][q_point]);
for (unsigned int d=1; d<dim; ++d)
for (unsigned int e=0; e<dim; ++e)
divergence += (jac[d][e] * this->gradients_quad[d][e][q_point]);
}
return divergence;
}
template <int dim, typename Number>
inline
SymmetricTensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dim,Number>
::get_symmetric_gradient (const unsigned int q_point) const
{
// copy from generic function into dim-specialization function
const Tensor<2,dim,VectorizedArray<Number> > grad = get_gradient(q_point);
VectorizedArray<Number> symmetrized [(dim*dim+dim)/2];
VectorizedArray<Number> half = make_vectorized_array (0.5);
for (unsigned int d=0; d<dim; ++d)
symmetrized[d] = grad[d][d];
switch (dim)
{
case 1:
break;
case 2:
symmetrized[2] = grad[0][1] + grad[1][0];
symmetrized[2] *= half;
break;
case 3:
symmetrized[3] = grad[0][1] + grad[1][0];
symmetrized[3] *= half;
symmetrized[4] = grad[0][2] + grad[2][0];
symmetrized[4] *= half;
symmetrized[5] = grad[1][2] + grad[2][1];
symmetrized[5] *= half;
break;
default:
Assert (false, ExcNotImplemented());
}
return SymmetricTensor<2,dim,VectorizedArray<Number> > (symmetrized);
}
template <int dim, typename Number>
inline
Tensor<1,(dim==2?1:dim),VectorizedArray<Number> >
FEEvaluationAccess<dim,dim,Number>
::get_curl (const unsigned int q_point) const
{
// copy from generic function into dim-specialization function
const Tensor<2,dim,VectorizedArray<Number> > grad = get_gradient(q_point);
Tensor<1,(dim==2?1:dim),VectorizedArray<Number> > curl;
switch (dim)
{
case 1:
Assert (false,
ExcMessage("Computing the curl in 1d is not a useful operation"));
break;
case 2:
curl[0] = grad[1][0] - grad[0][1];
break;
case 3:
curl[0] = grad[2][1] - grad[1][2];
curl[1] = grad[0][2] - grad[2][0];
curl[2] = grad[1][0] - grad[0][1];
break;
default:
Assert (false, ExcNotImplemented());
}
return curl;
}
template <int dim, typename Number>
inline
Tensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dim,Number>
::get_hessian_diagonal (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
return BaseClass::get_hessian_diagonal (q_point);
}
template <int dim, typename Number>
inline
Tensor<3,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dim,Number>
::get_hessian (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
return BaseClass::get_hessian(q_point);
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,dim,Number>
::submit_gradient (const Tensor<2,dim,VectorizedArray<Number> > grad_in,
const unsigned int q_point)
{
BaseClass::submit_gradient (grad_in, q_point);
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,dim,Number>
::submit_gradient (const Tensor<1,dim,Tensor<1,dim,VectorizedArray<Number> > >
grad_in,
const unsigned int q_point)
{
BaseClass::submit_gradient(grad_in, q_point);
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,dim,Number>
::submit_divergence (const VectorizedArray<Number> div_in,
const unsigned int q_point)
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->gradients_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
const VectorizedArray<Number> fac = this->J_value[0] *
this->quadrature_weights[q_point] * div_in;
for (unsigned int d=0; d<dim; ++d)
{
this->gradients_quad[d][d][q_point] = (fac *
this->cartesian_data[0][d]);
for (unsigned int e=d+1; e<dim; ++e)
{
this->gradients_quad[d][e][q_point] = VectorizedArray<Number>();
this->gradients_quad[e][d][q_point] = VectorizedArray<Number>();
}
}
}
else
{
const Tensor<2,dim,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->jacobian[q_point] : this->jacobian[0];
const VectorizedArray<Number> fac =
(this->cell_type == internal::MatrixFreeFunctions::general ?
this->J_value[q_point] : this->J_value[0] *
this->quadrature_weights[q_point]) * div_in;
for (unsigned int d=0; d<dim; ++d)
{
for (unsigned int e=0; e<dim; ++e)
this->gradients_quad[d][e][q_point] = jac[d][e] * fac;
}
}
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,dim,Number>
::submit_symmetric_gradient(const SymmetricTensor<2,dim,VectorizedArray<Number> >
sym_grad,
const unsigned int q_point)
{
// could have used base class operator, but that involves some overhead
// which is inefficient. it is nice to have the symmetric tensor because
// that saves some operations
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->gradients_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
const VectorizedArray<Number> JxW = this->J_value[0] * this->quadrature_weights[q_point];
for (unsigned int d=0; d<dim; ++d)
this->gradients_quad[d][d][q_point] = (sym_grad.access_raw_entry(d) *
JxW *
this->cartesian_data[0][d]);
for (unsigned int e=0, counter=dim; e<dim; ++e)
for (unsigned int d=e+1; d<dim; ++d, ++counter)
{
const VectorizedArray<Number> value = sym_grad.access_raw_entry(counter) * JxW;
this->gradients_quad[e][d][q_point] = (value *
this->cartesian_data[0][d]);
this->gradients_quad[d][e][q_point] = (value *
this->cartesian_data[0][e]);
}
}
// general/affine cell type
else
{
const VectorizedArray<Number> JxW =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->J_value[q_point] : this->J_value[0] * this->quadrature_weights[q_point];
const Tensor<2,dim,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->jacobian[q_point] : this->jacobian[0];
VectorizedArray<Number> weighted [dim][dim];
for (unsigned int i=0; i<dim; ++i)
weighted[i][i] = sym_grad.access_raw_entry(i) * JxW;
for (unsigned int i=0, counter=dim; i<dim; ++i)
for (unsigned int j=i+1; j<dim; ++j, ++counter)
{
const VectorizedArray<Number> value = sym_grad.access_raw_entry(counter) * JxW;
weighted[i][j] = value;
weighted[j][i] = value;
}
for (unsigned int comp=0; comp<dim; ++comp)
for (unsigned int d=0; d<dim; ++d)
{
VectorizedArray<Number> new_val = jac[0][d] * weighted[comp][0];
for (unsigned int e=1; e<dim; ++e)
new_val += jac[e][d] * weighted[comp][e];
this->gradients_quad[comp][d][q_point] = new_val;
}
}
}
template <int dim, typename Number>
inline
void
FEEvaluationAccess<dim,dim,Number>
::submit_curl (const Tensor<1,dim==2?1:dim,VectorizedArray<Number> > curl,
const unsigned int q_point)
{
Tensor<2,dim,VectorizedArray<Number> > grad;
switch (dim)
{
case 1:
Assert (false,
ExcMessage("Testing by the curl in 1d is not a useful operation"));
break;
case 2:
grad[1][0] = curl[0];
grad[0][1] = -curl[0];
break;
case 3:
grad[2][1] = curl[0];
grad[1][2] = -curl[0];
grad[0][2] = curl[1];
grad[2][0] = -curl[1];
grad[1][0] = curl[2];
grad[0][1] = -curl[2];
break;
default:
Assert (false, ExcNotImplemented());
}
submit_gradient (grad, q_point);
}
/*-------------------- FEEvaluationAccess scalar for 1d ----------------------------*/
template <typename Number>
inline
FEEvaluationAccess<1,1,Number>
::FEEvaluationAccess (const MatrixFree<1,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no_in,
const unsigned int fe_degree,
const unsigned int n_q_points)
:
FEEvaluationBase <1,1,Number>
(data_in, fe_no, quad_no_in, fe_degree, n_q_points)
{}
template <typename Number>
template <int n_components_other>
inline
FEEvaluationAccess<1,1,Number>
::FEEvaluationAccess (const Mapping<1> &mapping,
const FiniteElement<1> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component,
const FEEvaluationBase<1,n_components_other,Number> *other)
:
FEEvaluationBase <1,1,Number> (mapping, fe, quadrature, update_flags,
first_selected_component, other)
{}
template <typename Number>
inline
FEEvaluationAccess<1,1,Number>
::FEEvaluationAccess (const FEEvaluationAccess<1,1,Number> &other)
:
FEEvaluationBase <1,1,Number>(other)
{}
template <typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<1,1,Number>
::get_dof_value (const unsigned int dof) const
{
AssertIndexRange (dof, this->data->dofs_per_cell);
return this->values_dofs[0][dof];
}
template <typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<1,1,Number>
::get_value (const unsigned int q_point) const
{
Assert (this->values_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
return this->values_quad[0][q_point];
}
template <typename Number>
inline
Tensor<1,1,VectorizedArray<Number> >
FEEvaluationAccess<1,1,Number>
::get_gradient (const unsigned int q_point) const
{
// could use the base class gradient, but that involves too many inefficient
// initialization operations on tensors
Assert (this->gradients_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, this->data->n_q_points);
Tensor<1,1,VectorizedArray<Number> > grad_out;
// Cartesian cell
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
grad_out[0] = (this->gradients_quad[0][0][q_point] *
this->cartesian_data[0][0]);
}
// cell with general/constant Jacobian
else
{
const Tensor<2,1,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->jacobian[q_point] : this->jacobian[0];
grad_out[0] = (jac[0][0] * this->gradients_quad[0][0][q_point]);
}
return grad_out;
}
template <typename Number>
inline
Tensor<2,1,VectorizedArray<Number> >
FEEvaluationAccess<1,1,Number>
::get_hessian (const unsigned int q_point) const
{
return BaseClass::get_hessian(q_point)[0];
}
template <typename Number>
inline
Tensor<1,1,VectorizedArray<Number> >
FEEvaluationAccess<1,1,Number>
::get_hessian_diagonal (const unsigned int q_point) const
{
return BaseClass::get_hessian_diagonal(q_point)[0];
}
template <typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<1,1,Number>
::get_laplacian (const unsigned int q_point) const
{
return BaseClass::get_laplacian(q_point)[0];
}
template <typename Number>
inline
void
FEEvaluationAccess<1,1,Number>
::submit_dof_value (const VectorizedArray<Number> val_in,
const unsigned int dof)
{
#ifdef DEBUG
this->dof_values_initialized = true;
AssertIndexRange (dof, this->data->dofs_per_cell);
#endif
this->values_dofs[0][dof] = val_in;
}
template <typename Number>
inline
void
FEEvaluationAccess<1,1,Number>
::submit_value (const VectorizedArray<Number> val_in,
const unsigned int q_point)
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->values_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::general)
{
const VectorizedArray<Number> JxW = this->J_value[q_point];
this->values_quad[0][q_point] = val_in * JxW;
}
else //if (this->cell_type < internal::MatrixFreeFunctions::general)
{
const VectorizedArray<Number> JxW = this->J_value[0] * this->quadrature_weights[q_point];
this->values_quad[0][q_point] = val_in * JxW;
}
}
template <typename Number>
inline
void
FEEvaluationAccess<1,1,Number>
::submit_gradient (const Tensor<1,1,VectorizedArray<Number> > grad_in,
const unsigned int q_point)
{
#ifdef DEBUG
Assert (this->cell != numbers::invalid_unsigned_int, ExcNotInitialized());
AssertIndexRange (q_point, this->data->n_q_points);
this->gradients_quad_submitted = true;
#endif
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
const VectorizedArray<Number> JxW = this->J_value[0] * this->quadrature_weights[q_point];
this->gradients_quad[0][0][q_point] = (grad_in[0] *
this->cartesian_data[0][0] *
JxW);
}
// general/affine cell type
else
{
const Tensor<2,1,VectorizedArray<Number> > &jac =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->jacobian[q_point] : this->jacobian[0];
const VectorizedArray<Number> JxW =
this->cell_type == internal::MatrixFreeFunctions::general ?
this->J_value[q_point] : this->J_value[0] * this->quadrature_weights[q_point];
this->gradients_quad[0][0][q_point] = jac[0][0] * grad_in[0] * JxW;
}
}
template <typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<1,1,Number>
::integrate_value () const
{
return BaseClass::integrate_value()[0];
}
namespace internal
{
/**
* In this namespace, the evaluator routines that evaluate the tensor
* products are implemented.
*/
enum EvaluatorVariant
{
evaluate_general,
evaluate_symmetric,
evaluate_evenodd
};
/**
* Generic evaluator framework
*/
template <EvaluatorVariant variant, int dim, int fe_degree, int n_q_points_1d,
typename Number>
struct EvaluatorTensorProduct
{};
/**
* Internal evaluator for 1d-3d shape function using the tensor product form
* of the basis functions
*/
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
struct EvaluatorTensorProduct<evaluate_general,dim,fe_degree,n_q_points_1d,Number>
{
static const unsigned int dofs_per_cell = Utilities::fixed_int_power<fe_degree+1,dim>::value;
static const unsigned int n_q_points = Utilities::fixed_int_power<n_q_points_1d,dim>::value;
/**
* Empty constructor. Does nothing. Be careful when using 'values' and
* related methods because they need to be filled with the other pointer
*/
EvaluatorTensorProduct ()
:
shape_values (0),
shape_gradients (0),
shape_hessians (0)
{}
/**
* Constructor, taking the data from ShapeInfo
*/
EvaluatorTensorProduct (const AlignedVector<Number> &shape_values,
const AlignedVector<Number> &shape_gradients,
const AlignedVector<Number> &shape_hessians)
:
shape_values (shape_values.begin()),
shape_gradients (shape_gradients.begin()),
shape_hessians (shape_hessians.begin())
{}
template <int direction, bool dof_to_quad, bool add>
void
values (const Number in [],
Number out[]) const
{
apply<direction,dof_to_quad,add>(shape_values, in, out);
}
template <int direction, bool dof_to_quad, bool add>
void
gradients (const Number in [],
Number out[]) const
{
apply<direction,dof_to_quad,add>(shape_gradients, in, out);
}
template <int direction, bool dof_to_quad, bool add>
void
hessians (const Number in [],
Number out[]) const
{
apply<direction,dof_to_quad,add>(shape_hessians, in, out);
}
template <int direction, bool dof_to_quad, bool add>
static void apply (const Number *shape_data,
const Number in [],
Number out []);
const Number *shape_values;
const Number *shape_gradients;
const Number *shape_hessians;
};
// evaluates the given shape data in 1d-3d using the tensor product
// form. does not use a particular layout of entries in the matrices
// like the functions below and corresponds to a usual matrix-matrix
// product
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
EvaluatorTensorProduct<evaluate_general,dim,fe_degree,n_q_points_1d,Number>
::apply (const Number *shape_data,
const Number in [],
Number out [])
{
AssertIndexRange (direction, dim);
const int mm = dof_to_quad ? (fe_degree+1) : n_q_points_1d,
nn = dof_to_quad ? n_q_points_1d : (fe_degree+1);
const int n_blocks1 = (dim > 1 ? (direction > 0 ? nn : mm) : 1);
const int n_blocks2 = (dim > 2 ? (direction > 1 ? nn : mm) : 1);
const int stride = Utilities::fixed_int_power<nn,direction>::value;
for (int i2=0; i2<n_blocks2; ++i2)
{
for (int i1=0; i1<n_blocks1; ++i1)
{
for (int col=0; col<nn; ++col)
{
Number val0;
if (dof_to_quad == true)
val0 = shape_data[col];
else
val0 = shape_data[col*n_q_points_1d];
Number res0 = val0 * in[0];
for (int ind=1; ind<mm; ++ind)
{
if (dof_to_quad == true)
val0 = shape_data[ind*n_q_points_1d+col];
else
val0 = shape_data[col*n_q_points_1d+ind];
res0 += val0 * in[stride*ind];
}
if (add == false)
out[stride*col] = res0;
else
out[stride*col] += res0;
}
// increment: in regular case, just go to the next point in
// x-direction. If we are at the end of one chunk in x-dir, need
// to jump over to the next layer in z-direction
switch (direction)
{
case 0:
in += mm;
out += nn;
break;
case 1:
case 2:
++in;
++out;
break;
default:
Assert (false, ExcNotImplemented());
}
}
if (direction == 1)
{
in += nn*(mm-1);
out += nn*(nn-1);
}
}
}
// This method applies the tensor product operation to produce face values
// out from cell values. As opposed to the apply_tensor_product method, this
// method assumes that the directions orthogonal to the face have
// fe_degree+1 degrees of freedom per direction and not n_q_points_1d for
// those directions lower than the one currently applied
template <int dim, int fe_degree, typename Number, int face_direction,
bool dof_to_quad, bool add>
inline
void
apply_tensor_product_face (const Number *shape_data,
const Number in [],
Number out [])
{
const int n_blocks1 = dim > 1 ? (fe_degree+1) : 1;
const int n_blocks2 = dim > 2 ? (fe_degree+1) : 1;
AssertIndexRange (face_direction, dim);
const int mm = dof_to_quad ? (fe_degree+1) : 1,
nn = dof_to_quad ? 1 : (fe_degree+1);
const int stride = Utilities::fixed_int_power<fe_degree+1,face_direction>::value;
for (int i2=0; i2<n_blocks2; ++i2)
{
for (int i1=0; i1<n_blocks1; ++i1)
{
if (dof_to_quad == true)
{
Number res0 = shape_data[0] * in[0];
for (int ind=1; ind<mm; ++ind)
res0 += shape_data[ind] * in[stride*ind];
if (add == false)
out[0] = res0;
else
out[0] += res0;
}
else
{
for (int col=0; col<nn; ++col)
if (add == false)
out[col*stride] = shape_data[col] * in[0];
else
out[col*stride] += shape_data[col] * in[0];
}
// increment: in regular case, just go to the next point in
// x-direction. If we are at the end of one chunk in x-dir, need
// to jump over to the next layer in z-direction
switch (face_direction)
{
case 0:
in += mm;
out += nn;
break;
case 1:
++in;
++out;
// faces 2 and 3 in 3D use local coordinate system zx, which
// is the other way around compared to the tensor
// product. Need to take that into account.
if (dim == 3)
{
if (dof_to_quad)
out += fe_degree;
else
in += fe_degree;
}
break;
case 2:
++in;
++out;
break;
default:
Assert (false, ExcNotImplemented());
}
}
if (face_direction == 1 && dim == 3)
{
in += mm*(mm-1);
out += nn*(nn-1);
// adjust for local coordinate system zx
if (dof_to_quad)
out -= (fe_degree+1)*(fe_degree+1)-1;
else
in -= (fe_degree+1)*(fe_degree+1)-1;
}
}
}
// This class specializes the general application of tensor-product based
// elements for "symmetric" finite elements, i.e., when the shape functions
// are symmetric about 0.5 and the quadrature points are, too.
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
struct EvaluatorTensorProduct<evaluate_symmetric,dim,fe_degree,n_q_points_1d,Number>
{
static const unsigned int dofs_per_cell = Utilities::fixed_int_power<fe_degree+1,dim>::value;
static const unsigned int n_q_points = Utilities::fixed_int_power<n_q_points_1d,dim>::value;
/**
* Constructor, taking the data from ShapeInfo
*/
EvaluatorTensorProduct (const AlignedVector<Number> &shape_values,
const AlignedVector<Number> &shape_gradients,
const AlignedVector<Number> &shape_hessians)
:
shape_values (shape_values.begin()),
shape_gradients (shape_gradients.begin()),
shape_hessians (shape_hessians.begin())
{}
template <int direction, bool dof_to_quad, bool add>
void
values (const Number in [],
Number out[]) const;
template <int direction, bool dof_to_quad, bool add>
void
gradients (const Number in [],
Number out[]) const;
template <int direction, bool dof_to_quad, bool add>
void
hessians (const Number in [],
Number out[]) const;
const Number *shape_values;
const Number *shape_gradients;
const Number *shape_hessians;
};
// In this case, the 1D shape values read (sorted lexicographically, rows
// run over 1D dofs, columns over quadrature points):
// Q2 --> [ 0.687 0 -0.087 ]
// [ 0.4 1 0.4 ]
// [-0.087 0 0.687 ]
// Q3 --> [ 0.66 0.003 0.002 0.049 ]
// [ 0.521 1.005 -0.01 -0.230 ]
// [-0.230 -0.01 1.005 0.521 ]
// [ 0.049 0.002 0.003 0.66 ]
// Q4 --> [ 0.658 0.022 0 -0.007 -0.032 ]
// [ 0.608 1.059 0 0.039 0.176 ]
// [-0.409 -0.113 1 -0.113 -0.409 ]
// [ 0.176 0.039 0 1.059 0.608 ]
// [-0.032 -0.007 0 0.022 0.658 ]
//
// In these matrices, we want to use avoid computations involving zeros and
// ones and in addition use the symmetry in entries to reduce the number of
// read operations.
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
EvaluatorTensorProduct<evaluate_symmetric,dim,fe_degree,n_q_points_1d,Number>
::values (const Number in [],
Number out []) const
{
AssertIndexRange (direction, dim);
const int mm = dof_to_quad ? (fe_degree+1) : n_q_points_1d,
nn = dof_to_quad ? n_q_points_1d : (fe_degree+1);
const int n_cols = nn / 2;
const int mid = mm / 2;
const int n_blocks1 = (dim > 1 ? (direction > 0 ? nn : mm) : 1);
const int n_blocks2 = (dim > 2 ? (direction > 1 ? nn : mm) : 1);
const int stride = Utilities::fixed_int_power<nn,direction>::value;
for (int i2=0; i2<n_blocks2; ++i2)
{
for (int i1=0; i1<n_blocks1; ++i1)
{
for (int col=0; col<n_cols; ++col)
{
Number val0, val1, in0, in1, res0, res1;
if (dof_to_quad == true)
{
val0 = shape_values[col];
val1 = shape_values[nn-1-col];
}
else
{
val0 = shape_values[col*n_q_points_1d];
val1 = shape_values[(col+1)*n_q_points_1d-1];
}
if (mid > 0)
{
in0 = in[0];
in1 = in[stride*(mm-1)];
res0 = val0 * in0;
res1 = val1 * in0;
res0 += val1 * in1;
res1 += val0 * in1;
for (int ind=1; ind<mid; ++ind)
{
if (dof_to_quad == true)
{
val0 = shape_values[ind*n_q_points_1d+col];
val1 = shape_values[ind*n_q_points_1d+nn-1-col];
}
else
{
val0 = shape_values[col*n_q_points_1d+ind];
val1 = shape_values[(col+1)*n_q_points_1d-1-ind];
}
in0 = in[stride*ind];
in1 = in[stride*(mm-1-ind)];
res0 += val0 * in0;
res1 += val1 * in0;
res0 += val1 * in1;
res1 += val0 * in1;
}
}
else
res0 = res1 = Number();
if (dof_to_quad == true)
{
if (mm % 2 == 1)
{
val0 = shape_values[mid*n_q_points_1d+col];
val1 = val0 * in[stride*mid];
res0 += val1;
res1 += val1;
}
}
else
{
if (mm % 2 == 1 && nn % 2 == 0)
{
val0 = shape_values[col*n_q_points_1d+mid];
val1 = val0 * in[stride*mid];
res0 += val1;
res1 += val1;
}
}
if (add == false)
{
out[stride*col] = res0;
out[stride*(nn-1-col)] = res1;
}
else
{
out[stride*col] += res0;
out[stride*(nn-1-col)] += res1;
}
}
if ( dof_to_quad == true && nn%2==1 && mm%2==1 )
{
if (add==false)
out[stride*n_cols] = in[stride*mid];
else
out[stride*n_cols] += in[stride*mid];
}
else if (dof_to_quad == true && nn%2==1)
{
Number res0;
Number val0 = shape_values[n_cols];
if (mid > 0)
{
res0 = in[0] + in[stride*(mm-1)];
res0 *= val0;
for (int ind=1; ind<mid; ++ind)
{
val0 = shape_values[ind*n_q_points_1d+n_cols];
Number val1 = in[stride*ind] + in[stride*(mm-1-ind)];
val1 *= val0;
res0 += val1;
}
}
else
res0 = Number();
if (add == false)
out[stride*n_cols] = res0;
else
out[stride*n_cols] += res0;
}
else if (dof_to_quad == false && nn%2 == 1)
{
Number res0;
if (mid > 0)
{
Number val0 = shape_values[n_cols*n_q_points_1d];
res0 = in[0] + in[stride*(mm-1)];
res0 *= val0;
for (int ind=1; ind<mid; ++ind)
{
val0 = shape_values[n_cols*n_q_points_1d+ind];
Number val1 = in[stride*ind] + in[stride*(mm-1-ind)];
val1 *= val0;
res0 += val1;
}
if (mm % 2)
res0 += in[stride*mid];
}
else
res0 = in[0];
if (add == false)
out[stride*n_cols] = res0;
else
out[stride*n_cols] += res0;
}
// increment: in regular case, just go to the next point in
// x-direction. If we are at the end of one chunk in x-dir, need to
// jump over to the next layer in z-direction
switch (direction)
{
case 0:
in += mm;
out += nn;
break;
case 1:
case 2:
++in;
++out;
break;
default:
Assert (false, ExcNotImplemented());
}
}
if (direction == 1)
{
in += nn*(mm-1);
out += nn*(nn-1);
}
}
}
// For the specialized loop used for the gradient computation in
// here, the 1D shape values read (sorted lexicographically, rows
// run over 1D dofs, columns over quadrature points):
// Q2 --> [-2.549 -1 0.549 ]
// [ 3.098 0 -3.098 ]
// [-0.549 1 2.549 ]
// Q3 --> [-4.315 -1.03 0.5 -0.44 ]
// [ 6.07 -1.44 -2.97 2.196 ]
// [-2.196 2.97 1.44 -6.07 ]
// [ 0.44 -0.5 1.03 4.315 ]
// Q4 --> [-6.316 -1.3 0.333 -0.353 0.413 ]
// [10.111 -2.76 -2.667 2.066 -2.306 ]
// [-5.688 5.773 0 -5.773 5.688 ]
// [ 2.306 -2.066 2.667 2.76 -10.111 ]
// [-0.413 0.353 -0.333 -0.353 0.413 ]
//
// In these matrices, we want to use avoid computations involving
// zeros and ones and in addition use the symmetry in entries to
// reduce the number of read operations.
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
EvaluatorTensorProduct<evaluate_symmetric,dim,fe_degree,n_q_points_1d,Number>
::gradients (const Number in [],
Number out []) const
{
AssertIndexRange (direction, dim);
const int mm = dof_to_quad ? (fe_degree+1) : n_q_points_1d,
nn = dof_to_quad ? n_q_points_1d : (fe_degree+1);
const int n_cols = nn / 2;
const int mid = mm / 2;
const int n_blocks1 = (dim > 1 ? (direction > 0 ? nn : mm) : 1);
const int n_blocks2 = (dim > 2 ? (direction > 1 ? nn : mm) : 1);
const int stride = Utilities::fixed_int_power<nn,direction>::value;
for (int i2=0; i2<n_blocks2; ++i2)
{
for (int i1=0; i1<n_blocks1; ++i1)
{
for (int col=0; col<n_cols; ++col)
{
Number val0, val1, in0, in1, res0, res1;
if (dof_to_quad == true)
{
val0 = shape_gradients[col];
val1 = shape_gradients[nn-1-col];
}
else
{
val0 = shape_gradients[col*n_q_points_1d];
val1 = shape_gradients[(nn-col-1)*n_q_points_1d];
}
if (mid > 0)
{
in0 = in[0];
in1 = in[stride*(mm-1)];
res0 = val0 * in0;
res1 = val1 * in0;
res0 -= val1 * in1;
res1 -= val0 * in1;
for (int ind=1; ind<mid; ++ind)
{
if (dof_to_quad == true)
{
val0 = shape_gradients[ind*n_q_points_1d+col];
val1 = shape_gradients[ind*n_q_points_1d+nn-1-col];
}
else
{
val0 = shape_gradients[col*n_q_points_1d+ind];
val1 = shape_gradients[(nn-col-1)*n_q_points_1d+ind];
}
in0 = in[stride*ind];
in1 = in[stride*(mm-1-ind)];
res0 += val0 * in0;
res1 += val1 * in0;
res0 -= val1 * in1;
res1 -= val0 * in1;
}
}
else
res0 = res1 = Number();
if (mm % 2 == 1)
{
if (dof_to_quad == true)
val0 = shape_gradients[mid*n_q_points_1d+col];
else
val0 = shape_gradients[col*n_q_points_1d+mid];
val1 = val0 * in[stride*mid];
res0 += val1;
res1 -= val1;
}
if (add == false)
{
out[stride*col] = res0;
out[stride*(nn-1-col)] = res1;
}
else
{
out[stride*col] += res0;
out[stride*(nn-1-col)] += res1;
}
}
if ( nn%2 == 1 )
{
Number val0, res0;
if (dof_to_quad == true)
val0 = shape_gradients[n_cols];
else
val0 = shape_gradients[n_cols*n_q_points_1d];
res0 = in[0] - in[stride*(mm-1)];
res0 *= val0;
for (int ind=1; ind<mid; ++ind)
{
if (dof_to_quad == true)
val0 = shape_gradients[ind*n_q_points_1d+n_cols];
else
val0 = shape_gradients[n_cols*n_q_points_1d+ind];
Number val1 = in[stride*ind] - in[stride*(mm-1-ind)];
val1 *= val0;
res0 += val1;
}
if (add == false)
out[stride*n_cols] = res0;
else
out[stride*n_cols] += res0;
}
// increment: in regular case, just go to the next point in
// x-direction. for y-part in 3D and if we are at the end of one
// chunk in x-dir, need to jump over to the next layer in
// z-direction
switch (direction)
{
case 0:
in += mm;
out += nn;
break;
case 1:
case 2:
++in;
++out;
break;
default:
Assert (false, ExcNotImplemented());
}
}
if (direction == 1)
{
in += nn * (mm-1);
out += nn * (nn-1);
}
}
}
// evaluates the given shape data in 1d-3d using the tensor product
// form assuming the symmetries of unit cell shape hessians for
// finite elements in FEEvaluation
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
EvaluatorTensorProduct<evaluate_symmetric,dim,fe_degree,n_q_points_1d,Number>
::hessians (const Number in [],
Number out []) const
{
AssertIndexRange (direction, dim);
const int mm = dof_to_quad ? (fe_degree+1) : n_q_points_1d,
nn = dof_to_quad ? n_q_points_1d : (fe_degree+1);
const int n_cols = nn / 2;
const int mid = mm / 2;
const int n_blocks1 = (dim > 1 ? (direction > 0 ? nn : mm) : 1);
const int n_blocks2 = (dim > 2 ? (direction > 1 ? nn : mm) : 1);
const int stride = Utilities::fixed_int_power<nn,direction>::value;
for (int i2=0; i2<n_blocks2; ++i2)
{
for (int i1=0; i1<n_blocks1; ++i1)
{
for (int col=0; col<n_cols; ++col)
{
Number val0, val1, in0, in1, res0, res1;
if (dof_to_quad == true)
{
val0 = shape_hessians[col];
val1 = shape_hessians[nn-1-col];
}
else
{
val0 = shape_hessians[col*n_q_points_1d];
val1 = shape_hessians[(col+1)*n_q_points_1d-1];
}
if (mid > 0)
{
in0 = in[0];
in1 = in[stride*(mm-1)];
res0 = val0 * in0;
res1 = val1 * in0;
res0 += val1 * in1;
res1 += val0 * in1;
for (int ind=1; ind<mid; ++ind)
{
if (dof_to_quad == true)
{
val0 = shape_hessians[ind*n_q_points_1d+col];
val1 = shape_hessians[ind*n_q_points_1d+nn-1-col];
}
else
{
val0 = shape_hessians[col*n_q_points_1d+ind];
val1 = shape_hessians[(col+1)*n_q_points_1d-1-ind];
}
in0 = in[stride*ind];
in1 = in[stride*(mm-1-ind)];
res0 += val0 * in0;
res1 += val1 * in0;
res0 += val1 * in1;
res1 += val0 * in1;
}
}
else
res0 = res1 = Number();
if (mm % 2 == 1)
{
if (dof_to_quad == true)
val0 = shape_hessians[mid*n_q_points_1d+col];
else
val0 = shape_hessians[col*n_q_points_1d+mid];
val1 = val0 * in[stride*mid];
res0 += val1;
res1 += val1;
}
if (add == false)
{
out[stride*col] = res0;
out[stride*(nn-1-col)] = res1;
}
else
{
out[stride*col] += res0;
out[stride*(nn-1-col)] += res1;
}
}
if ( nn%2 == 1 )
{
Number val0, res0;
if (dof_to_quad == true)
val0 = shape_hessians[n_cols];
else
val0 = shape_hessians[n_cols*n_q_points_1d];
if (mid > 0)
{
res0 = in[0] + in[stride*(mm-1)];
res0 *= val0;
for (int ind=1; ind<mid; ++ind)
{
if (dof_to_quad == true)
val0 = shape_hessians[ind*n_q_points_1d+n_cols];
else
val0 = shape_hessians[n_cols*n_q_points_1d+ind];
Number val1 = in[stride*ind] + in[stride*(mm-1-ind)];
val1 *= val0;
res0 += val1;
}
}
else
res0 = Number();
if (mm % 2 == 1)
{
if (dof_to_quad == true)
val0 = shape_hessians[mid*n_q_points_1d+n_cols];
else
val0 = shape_hessians[n_cols*n_q_points_1d+mid];
res0 += val0 * in[stride*mid];
}
if (add == false)
out[stride*n_cols] = res0;
else
out[stride*n_cols] += res0;
}
// increment: in regular case, just go to the next point in
// x-direction. If we are at the end of one chunk in x-dir, need to
// jump over to the next layer in z-direction
switch (direction)
{
case 0:
in += mm;
out += nn;
break;
case 1:
case 2:
++in;
++out;
break;
default:
Assert (false, ExcNotImplemented());
}
}
if (direction == 1)
{
in += nn*(mm-1);
out += nn*(nn-1);
}
}
}
// This class implements a different approach to the symmetric case for
// values, gradients, and Hessians also treated with the above functions: It
// is possible to reduce the cost per dimension from N^2 to N^2/2, where N
// is the number of 1D dofs (there are only N^2/2 different entries in the
// shape matrix, so this is plausible). The approach is based on the idea of
// applying the operator on the even and odd part of the input vectors
// separately, given that the shape functions evaluated on quadrature points
// are symmetric. This method is presented e.g. in the book "Implementing
// Spectral Methods for Partial Differential Equations" by David A. Kopriva,
// Springer, 2009, section 3.5.3 (Even-Odd-Decomposition). Even though the
// experiments in the book say that the method is not efficient for N<20, it
// is more efficient in the context where the loop bounds are compile-time
// constants (templates).
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
struct EvaluatorTensorProduct<evaluate_evenodd,dim,fe_degree,n_q_points_1d,Number>
{
static const unsigned int dofs_per_cell = Utilities::fixed_int_power<fe_degree+1,dim>::value;
static const unsigned int n_q_points = Utilities::fixed_int_power<n_q_points_1d,dim>::value;
/**
* Empty constructor. Does nothing. Be careful when using 'values' and
* related methods because they need to be filled with the other pointer
*/
EvaluatorTensorProduct ()
:
shape_values (0),
shape_gradients (0),
shape_hessians (0)
{}
/**
* Constructor, taking the data from ShapeInfo (using the even-odd
* variants stored there)
*/
EvaluatorTensorProduct (const AlignedVector<Number> &shape_values,
const AlignedVector<Number> &shape_gradients,
const AlignedVector<Number> &shape_hessians)
:
shape_values (shape_values.begin()),
shape_gradients (shape_gradients.begin()),
shape_hessians (shape_hessians.begin())
{}
template <int direction, bool dof_to_quad, bool add>
void
values (const Number in [],
Number out[]) const
{
apply<direction,dof_to_quad,add,0>(shape_values, in, out);
}
template <int direction, bool dof_to_quad, bool add>
void
gradients (const Number in [],
Number out[]) const
{
apply<direction,dof_to_quad,add,1>(shape_gradients, in, out);
}
template <int direction, bool dof_to_quad, bool add>
void
hessians (const Number in [],
Number out[]) const
{
apply<direction,dof_to_quad,add,2>(shape_hessians, in, out);
}
template <int direction, bool dof_to_quad, bool add, int type>
static void apply (const Number *shape_data,
const Number in [],
Number out []);
const Number *shape_values;
const Number *shape_gradients;
const Number *shape_hessians;
};
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
template <int direction, bool dof_to_quad, bool add, int type>
inline
void
EvaluatorTensorProduct<evaluate_evenodd,dim,fe_degree,n_q_points_1d,Number>
::apply (const Number *shapes,
const Number in [],
Number out [])
{
AssertIndexRange (type, 3);
AssertIndexRange (direction, dim);
const int mm = dof_to_quad ? (fe_degree+1) : n_q_points_1d,
nn = dof_to_quad ? n_q_points_1d : (fe_degree+1);
const int n_cols = nn / 2;
const int mid = mm / 2;
const int n_blocks1 = (dim > 1 ? (direction > 0 ? nn : mm) : 1);
const int n_blocks2 = (dim > 2 ? (direction > 1 ? nn : mm) : 1);
const int stride = Utilities::fixed_int_power<nn,direction>::value;
const int offset = (n_q_points_1d+1)/2;
// this code may look very inefficient at first sight due to the many
// different cases with if's at the innermost loop part, but all of the
// conditionals can be evaluated at compile time because they are
// templates, so the compiler should optimize everything away
for (int i2=0; i2<n_blocks2; ++i2)
{
for (int i1=0; i1<n_blocks1; ++i1)
{
Number xp[mid>0?mid:1], xm[mid>0?mid:1];
for (int i=0; i<mid; ++i)
{
if (dof_to_quad == true && type == 1)
{
xp[i] = in[stride*i] - in[stride*(mm-1-i)];
xm[i] = in[stride*i] + in[stride*(mm-1-i)];
}
else
{
xp[i] = in[stride*i] + in[stride*(mm-1-i)];
xm[i] = in[stride*i] - in[stride*(mm-1-i)];
}
}
for (int col=0; col<n_cols; ++col)
{
Number r0, r1;
if (mid > 0)
{
if (dof_to_quad == true)
{
r0 = shapes[col] * xp[0];
r1 = shapes[fe_degree*offset + col] * xm[0];
}
else
{
r0 = shapes[col*offset] * xp[0];
r1 = shapes[(fe_degree-col)*offset] * xm[0];
}
for (int ind=1; ind<mid; ++ind)
{
if (dof_to_quad == true)
{
r0 += shapes[ind*offset+col] * xp[ind];
r1 += shapes[(fe_degree-ind)*offset+col] * xm[ind];
}
else
{
r0 += shapes[col*offset+ind] * xp[ind];
r1 += shapes[(fe_degree-col)*offset+ind] * xm[ind];
}
}
}
else
r0 = r1 = Number();
if (mm % 2 == 1 && dof_to_quad == true)
{
if (type == 1)
r1 += shapes[mid*offset+col] * in[stride*mid];
else
r0 += shapes[mid*offset+col] * in[stride*mid];
}
else if (mm % 2 == 1 && (nn % 2 == 0 || type > 0))
r0 += shapes[col*offset+mid] * in[stride*mid];
if (add == false)
{
out[stride*col] = r0 + r1;
if (type == 1 && dof_to_quad == false)
out[stride*(nn-1-col)] = r1 - r0;
else
out[stride*(nn-1-col)] = r0 - r1;
}
else
{
out[stride*col] += r0 + r1;
if (type == 1 && dof_to_quad == false)
out[stride*(nn-1-col)] += r1 - r0;
else
out[stride*(nn-1-col)] += r0 - r1;
}
}
if ( type == 0 && dof_to_quad == true && nn%2==1 && mm%2==1 )
{
if (add==false)
out[stride*n_cols] = in[stride*mid];
else
out[stride*n_cols] += in[stride*mid];
}
else if (dof_to_quad == true && nn%2==1)
{
Number r0;
if (mid > 0)
{
r0 = shapes[n_cols] * xp[0];
for (int ind=1; ind<mid; ++ind)
r0 += shapes[ind*offset+n_cols] * xp[ind];
}
else
r0 = Number();
if (type != 1 && mm % 2 == 1)
r0 += shapes[mid*offset+n_cols] * in[stride*mid];
if (add == false)
out[stride*n_cols] = r0;
else
out[stride*n_cols] += r0;
}
else if (dof_to_quad == false && nn%2 == 1)
{
Number r0;
if (mid > 0)
{
if (type == 1)
{
r0 = shapes[n_cols*offset] * xm[0];
for (int ind=1; ind<mid; ++ind)
r0 += shapes[n_cols*offset+ind] * xm[ind];
}
else
{
r0 = shapes[n_cols*offset] * xp[0];
for (int ind=1; ind<mid; ++ind)
r0 += shapes[n_cols*offset+ind] * xp[ind];
}
}
else
r0 = Number();
if (type == 0 && mm % 2 == 1)
r0 += in[stride*mid];
else if (type == 2 && mm % 2 == 1)
r0 += shapes[n_cols*offset+mid] * in[stride*mid];
if (add == false)
out[stride*n_cols] = r0;
else
out[stride*n_cols] += r0;
}
// increment: in regular case, just go to the next point in
// x-direction. If we are at the end of one chunk in x-dir, need to
// jump over to the next layer in z-direction
switch (direction)
{
case 0:
in += mm;
out += nn;
break;
case 1:
case 2:
++in;
++out;
break;
default:
Assert (false, ExcNotImplemented());
}
}
if (direction == 1)
{
in += nn*(mm-1);
out += nn*(nn-1);
}
}
}
// Select evaluator type from element shape function type
template <MatrixFreeFunctions::ElementType element, bool is_long>
struct EvaluatorSelector {};
template <bool is_long>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_general,is_long>
{
static const EvaluatorVariant variant = evaluate_general;
};
template <>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric,false>
{
static const EvaluatorVariant variant = evaluate_symmetric;
};
template <> struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric,true>
{
static const EvaluatorVariant variant = evaluate_evenodd;
};
template <bool is_long>
struct EvaluatorSelector<MatrixFreeFunctions::truncated_tensor,is_long>
{
static const EvaluatorVariant variant = evaluate_general;
};
template <>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric_plus_dg0,false>
{
static const EvaluatorVariant variant = evaluate_symmetric;
};
template <>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric_plus_dg0,true>
{
static const EvaluatorVariant variant = evaluate_evenodd;
};
template <bool is_long>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_gausslobatto,is_long>
{
static const EvaluatorVariant variant = evaluate_evenodd;
};
// This struct performs the evaluation of function values, gradients and
// Hessians for tensor-product finite elements. The operation is used for
// both the symmetric and non-symmetric case, which use different apply
// functions 'values', 'gradients' in the individual coordinate
// directions. The apply functions for values are provided through one of
// the template classes EvaluatorTensorProduct which in turn are selected
// from the MatrixFreeFunctions::ElementType template argument.
//
// There is a specialization made for Gauss-Lobatto elements further down
// where the 'values' operation is identity, which allows us to write
// shorter code.
template <MatrixFreeFunctions::ElementType type, int dim, int fe_degree,
int n_q_points_1d, int n_components, typename Number>
struct FEEvaluationImpl
{
static
void evaluate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs_actual[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
VectorizedArray<Number> *hessians_quad[][(dim*(dim+1))/2],
const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl);
static
void integrate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs_actual[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
const bool evaluate_val,
const bool evaluate_grad);
};
template <MatrixFreeFunctions::ElementType type, int dim, int fe_degree,
int n_q_points_1d, int n_components, typename Number>
inline
void
FEEvaluationImpl<type,dim,fe_degree,n_q_points_1d,n_components,Number>
::evaluate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs_actual[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
VectorizedArray<Number> *hessians_quad[][(dim*(dim+1))/2],
const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl)
{
if (evaluate_val == false && evaluate_grad == false && evaluate_lapl == false)
return;
const EvaluatorVariant variant =
EvaluatorSelector<type,(fe_degree+n_q_points_1d>4)>::variant;
typedef EvaluatorTensorProduct<variant, dim, fe_degree, n_q_points_1d,
VectorizedArray<Number> > Eval;
Eval eval (variant == evaluate_evenodd ? shape_info.shape_val_evenodd :
shape_info.shape_values,
variant == evaluate_evenodd ? shape_info.shape_gra_evenodd :
shape_info.shape_gradients,
variant == evaluate_evenodd ? shape_info.shape_hes_evenodd :
shape_info.shape_hessians);
const unsigned int temp_size = Eval::dofs_per_cell > Eval::n_q_points ?
Eval::dofs_per_cell : Eval::n_q_points;
VectorizedArray<Number> **values_dofs = values_dofs_actual;
VectorizedArray<Number> data_array[type!=MatrixFreeFunctions::truncated_tensor ? 1 :
n_components*Eval::dofs_per_cell];
VectorizedArray<Number> *expanded_dof_values[n_components];
if (type == MatrixFreeFunctions::truncated_tensor)
{
for (unsigned int c=0; c<n_components; ++c)
expanded_dof_values[c] = &data_array[c*Eval::dofs_per_cell];
values_dofs = expanded_dof_values;
unsigned int count_p = 0, count_q = 0;
for (unsigned int i=0; i<(dim>2?fe_degree+1:1); ++i)
{
for (unsigned int j=0; j<(dim>1?fe_degree+1-i:1); ++j)
{
for (unsigned int k=0; k<fe_degree+1-j-i; ++k, ++count_p, ++count_q)
for (unsigned int c=0; c<n_components; ++c)
expanded_dof_values[c][count_q] = values_dofs_actual[c][count_p];
for (unsigned int k=fe_degree+1-j-i; k<fe_degree+1; ++k, ++count_q)
for (unsigned int c=0; c<n_components; ++c)
expanded_dof_values[c][count_q] = VectorizedArray<Number>();
}
for (unsigned int j=fe_degree+1-i; j<fe_degree+1; ++j)
for (unsigned int k=0; k<fe_degree+1; ++k, ++count_q)
for (unsigned int c=0; c<n_components; ++c)
expanded_dof_values[c][count_q] = VectorizedArray<Number>();
}
AssertDimension(count_q, Eval::dofs_per_cell);
}
// These avoid compiler errors; they are only used in sensible context but
// compilers typically cannot detect when we access something like
// gradients_quad[2] only for dim==3.
const unsigned int d1 = dim>1?1:0;
const unsigned int d2 = dim>2?2:0;
const unsigned int d3 = dim>2?3:0;
const unsigned int d4 = dim>2?4:0;
const unsigned int d5 = dim>2?5:0;
switch (dim)
{
case 1:
for (unsigned int c=0; c<n_components; c++)
{
if (evaluate_val == true)
eval.template values<0,true,false> (values_dofs[c], values_quad[c]);
if (evaluate_grad == true)
eval.template gradients<0,true,false>(values_dofs[c], gradients_quad[c][0]);
if (evaluate_lapl == true)
eval.template hessians<0,true,false> (values_dofs[c], hessians_quad[c][0]);
}
break;
case 2:
for (unsigned int c=0; c<n_components; c++)
{
VectorizedArray<Number> temp1[temp_size];
// grad x
if (evaluate_grad == true)
{
eval.template gradients<0,true,false> (values_dofs[c], temp1);
eval.template values<1,true,false> (temp1, gradients_quad[c][0]);
}
if (evaluate_lapl == true)
{
// grad xy
if (evaluate_grad == false)
eval.template gradients<0,true,false>(values_dofs[c], temp1);
eval.template gradients<1,true,false> (temp1, hessians_quad[c][d1+d1]);
// grad xx
eval.template hessians<0,true,false>(values_dofs[c], temp1);
eval.template values<1,true,false> (temp1, hessians_quad[c][0]);
}
// grad y
eval.template values<0,true,false> (values_dofs[c], temp1);
if (evaluate_grad == true)
eval.template gradients<1,true,false> (temp1, gradients_quad[c][d1]);
// grad yy
if (evaluate_lapl == true)
eval.template hessians<1,true,false> (temp1, hessians_quad[c][d1]);
// val: can use values applied in x
if (evaluate_val == true)
eval.template values<1,true,false> (temp1, values_quad[c]);
}
break;
case 3:
for (unsigned int c=0; c<n_components; c++)
{
VectorizedArray<Number> temp1[temp_size];
VectorizedArray<Number> temp2[temp_size];
if (evaluate_grad == true)
{
// grad x
eval.template gradients<0,true,false> (values_dofs[c], temp1);
eval.template values<1,true,false> (temp1, temp2);
eval.template values<2,true,false> (temp2, gradients_quad[c][0]);
}
if (evaluate_lapl == true)
{
// grad xz
if (evaluate_grad == false)
{
eval.template gradients<0,true,false> (values_dofs[c], temp1);
eval.template values<1,true,false> (temp1, temp2);
}
eval.template gradients<2,true,false> (temp2, hessians_quad[c][d4]);
// grad xy
eval.template gradients<1,true,false> (temp1, temp2);
eval.template values<2,true,false> (temp2, hessians_quad[c][d3]);
// grad xx
eval.template hessians<0,true,false>(values_dofs[c], temp1);
eval.template values<1,true,false> (temp1, temp2);
eval.template values<2,true,false> (temp2, hessians_quad[c][0]);
}
// grad y
eval.template values<0,true,false> (values_dofs[c], temp1);
if (evaluate_grad == true)
{
eval.template gradients<1,true,false>(temp1, temp2);
eval.template values<2,true,false> (temp2, gradients_quad[c][d1]);
}
if (evaluate_lapl == true)
{
// grad yz
if (evaluate_grad == false)
eval.template gradients<1,true,false>(temp1, temp2);
eval.template gradients<2,true,false> (temp2, hessians_quad[c][d5]);
// grad yy
eval.template hessians<1,true,false> (temp1, temp2);
eval.template values<2,true,false> (temp2, hessians_quad[c][d1]);
}
// grad z: can use the values applied in x direction stored in temp1
eval.template values<1,true,false> (temp1, temp2);
if (evaluate_grad == true)
eval.template gradients<2,true,false> (temp2, gradients_quad[c][d2]);
// grad zz: can use the values applied in x and y direction stored
// in temp2
if (evaluate_lapl == true)
eval.template hessians<2,true,false>(temp2, hessians_quad[c][d2]);
// val: can use the values applied in x & y direction stored in temp2
if (evaluate_val == true)
eval.template values<2,true,false> (temp2, values_quad[c]);
}
break;
default:
AssertThrow(false, ExcNotImplemented());
}
// case additional dof for FE_Q_DG0: add values; gradients and second
// derivatives evaluate to zero
if (type == MatrixFreeFunctions::tensor_symmetric_plus_dg0 && evaluate_val)
for (unsigned int c=0; c<n_components; ++c)
for (unsigned int q=0; q<Eval::n_q_points; ++q)
values_quad[c][q] += values_dofs[c][Eval::dofs_per_cell];
}
template <MatrixFreeFunctions::ElementType type, int dim, int fe_degree,
int n_q_points_1d, int n_components, typename Number>
inline
void
FEEvaluationImpl<type,dim,fe_degree,n_q_points_1d,n_components,Number>
::integrate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs_actual[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
const bool integrate_val,
const bool integrate_grad)
{
const EvaluatorVariant variant =
EvaluatorSelector<type,(fe_degree+n_q_points_1d>4)>::variant;
typedef EvaluatorTensorProduct<variant, dim, fe_degree, n_q_points_1d,
VectorizedArray<Number> > Eval;
Eval eval (variant == evaluate_evenodd ? shape_info.shape_val_evenodd :
shape_info.shape_values,
variant == evaluate_evenodd ? shape_info.shape_gra_evenodd :
shape_info.shape_gradients,
variant == evaluate_evenodd ? shape_info.shape_hes_evenodd :
shape_info.shape_hessians);
const unsigned int temp_size = Eval::dofs_per_cell > Eval::n_q_points ?
Eval::dofs_per_cell : Eval::n_q_points;
VectorizedArray<Number> temp1[temp_size];
VectorizedArray<Number> temp2[temp_size];
// expand dof_values to tensor product for truncated tensor products
VectorizedArray<Number> **values_dofs = values_dofs_actual;
VectorizedArray<Number> data_array[type!=MatrixFreeFunctions::truncated_tensor ? 1 :
n_components*Eval::dofs_per_cell];
VectorizedArray<Number> *expanded_dof_values[n_components];
if (type == MatrixFreeFunctions::truncated_tensor)
{
for (unsigned int c=0; c<n_components; ++c)
expanded_dof_values[c] = &data_array[c*Eval::dofs_per_cell];
values_dofs = expanded_dof_values;
}
// These avoid compiler errors; they are only used in sensible context but
// compilers typically cannot detect when we access something like
// gradients_quad[2] only for dim==3.
const unsigned int d1 = dim>1?1:0;
const unsigned int d2 = dim>2?2:0;
switch (dim)
{
case 1:
for (unsigned int c=0; c<n_components; c++)
{
if (integrate_val == true)
eval.template values<0,false,false> (values_quad[c], values_dofs[c]);
if (integrate_grad == true)
{
if (integrate_val == true)
eval.template gradients<0,false,true> (gradients_quad[c][0], values_dofs[c]);
else
eval.template gradients<0,false,false> (gradients_quad[c][0], values_dofs[c]);
}
}
break;
case 2:
for (unsigned int c=0; c<n_components; c++)
{
if (integrate_val == true)
{
// val
eval.template values<0,false,false> (values_quad[c], temp1);
//grad x
if (integrate_grad == true)
eval.template gradients<0,false,true> (gradients_quad[c][0], temp1);
eval.template values<1,false,false>(temp1, values_dofs[c]);
}
if (integrate_grad == true)
{
// grad y
eval.template values<0,false,false> (gradients_quad[c][d1], temp1);
if (integrate_val == false)
{
eval.template gradients<1,false,false>(temp1, values_dofs[c]);
//grad x
eval.template gradients<0,false,false> (gradients_quad[c][0], temp1);
eval.template values<1,false,true> (temp1, values_dofs[c]);
}
else
eval.template gradients<1,false,true>(temp1, values_dofs[c]);
}
}
break;
case 3:
for (unsigned int c=0; c<n_components; c++)
{
if (integrate_val == true)
{
// val
eval.template values<0,false,false> (values_quad[c], temp1);
//grad x: can sum to temporary value in temp1
if (integrate_grad == true)
eval.template gradients<0,false,true> (gradients_quad[c][0], temp1);
eval.template values<1,false,false>(temp1, temp2);
if (integrate_grad == true)
{
eval.template values<0,false,false> (gradients_quad[c][d1], temp1);
eval.template gradients<1,false,true>(temp1, temp2);
}
eval.template values<2,false,false> (temp2, values_dofs[c]);
}
else if (integrate_grad == true)
{
eval.template gradients<0,false,false>(gradients_quad[c][0], temp1);
eval.template values<1,false,false> (temp1, temp2);
eval.template values<0,false,false> (gradients_quad[c][d1], temp1);
eval.template gradients<1,false,true>(temp1, temp2);
eval.template values<2,false,false> (temp2, values_dofs[c]);
}
if (integrate_grad == true)
{
// grad z: can sum to temporary x and y value in output
eval.template values<0,false,false> (gradients_quad[c][d2], temp1);
eval.template values<1,false,false> (temp1, temp2);
eval.template gradients<2,false,true> (temp2, values_dofs[c]);
}
}
break;
default:
AssertThrow(false, ExcNotImplemented());
}
// case FE_Q_DG0: add values, gradients and second derivatives are zero
if (type == MatrixFreeFunctions::tensor_symmetric_plus_dg0)
{
if (integrate_val)
for (unsigned int c=0; c<n_components; ++c)
{
values_dofs[c][Eval::dofs_per_cell] = values_quad[c][0];
for (unsigned int q=1; q<Eval::n_q_points; ++q)
values_dofs[c][Eval::dofs_per_cell] += values_quad[c][q];
}
else
for (unsigned int c=0; c<n_components; ++c)
values_dofs[c][Eval::dofs_per_cell] = VectorizedArray<Number>();
}
if (type == MatrixFreeFunctions::truncated_tensor)
{
unsigned int count_p = 0, count_q = 0;
for (unsigned int i=0; i<(dim>2?fe_degree+1:1); ++i)
{
for (unsigned int j=0; j<(dim>1?fe_degree+1-i:1); ++j)
{
for (unsigned int k=0; k<fe_degree+1-j-i; ++k, ++count_p, ++count_q)
{
for (unsigned int c=0; c<n_components; ++c)
values_dofs_actual[c][count_p] = expanded_dof_values[c][count_q];
}
count_q += j+i;
}
count_q += i*(fe_degree+1);
}
AssertDimension(count_q, Eval::dofs_per_cell);
}
}
// This a specialization for Gauss-Lobatto elements where the 'values'
// operation is identity, which allows us to write shorter code.
template <int dim, int fe_degree, int n_q_points_1d, int n_components, typename Number>
struct FEEvaluationImpl<MatrixFreeFunctions::tensor_gausslobatto, dim,
fe_degree, n_q_points_1d, n_components, Number>
{
static
void evaluate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
VectorizedArray<Number> *hessians_quad[][(dim*(dim+1))/2],
const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl);
static
void integrate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
const bool integrate_val,
const bool integrate_grad);
};
template <int dim, int fe_degree, int n_q_points_1d, int n_components, typename Number>
inline
void
FEEvaluationImpl<MatrixFreeFunctions::tensor_gausslobatto, dim,
fe_degree, n_q_points_1d, n_components, Number>
::evaluate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
VectorizedArray<Number> *hessians_quad[][(dim*(dim+1))/2],
const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl)
{
typedef EvaluatorTensorProduct<evaluate_evenodd, dim, fe_degree, fe_degree+1,
VectorizedArray<Number> > Eval;
Eval eval (shape_info.shape_val_evenodd, shape_info.shape_gra_evenodd,
shape_info.shape_hes_evenodd);
// These avoid compiler errors; they are only used in sensible context but
// compilers typically cannot detect when we access something like
// gradients_quad[2] only for dim==3.
const unsigned int d1 = dim>1?1:0;
const unsigned int d2 = dim>2?2:0;
const unsigned int d3 = dim>2?3:0;
const unsigned int d4 = dim>2?4:0;
const unsigned int d5 = dim>2?5:0;
switch (dim)
{
case 1:
if (evaluate_val == true)
std::memcpy (values_quad[0], values_dofs[0],
eval.dofs_per_cell * n_components *
sizeof (values_dofs[0][0]));
for (unsigned int c=0; c<n_components; c++)
{
if (evaluate_grad == true)
eval.template gradients<0,true,false>(values_dofs[c], gradients_quad[c][0]);
if (evaluate_lapl == true)
eval.template hessians<0,true,false> (values_dofs[c], hessians_quad[c][0]);
}
break;
case 2:
if (evaluate_val == true)
{
std::memcpy (values_quad[0], values_dofs[0],
Eval::dofs_per_cell * n_components *
sizeof (values_dofs[0][0]));
}
if (evaluate_grad == true)
for (unsigned int comp=0; comp<n_components; comp++)
{
// grad x
eval.template gradients<0,true,false> (values_dofs[comp],
gradients_quad[comp][0]);
// grad y
eval.template gradients<1,true,false> (values_dofs[comp],
gradients_quad[comp][d1]);
}
if (evaluate_lapl == true)
for (unsigned int comp=0; comp<n_components; comp++)
{
// hess x
eval.template hessians<0,true,false> (values_dofs[comp],
hessians_quad[comp][0]);
// hess y
eval.template hessians<1,true,false> (values_dofs[comp],
hessians_quad[comp][d1]);
VectorizedArray<Number> temp1[Eval::dofs_per_cell];
// grad x grad y
eval.template gradients<0,true,false> (values_dofs[comp], temp1);
eval.template gradients<1,true,false> (temp1, hessians_quad[comp][d1+d1]);
}
break;
case 3:
if (evaluate_val == true)
{
std::memcpy (values_quad[0], values_dofs[0],
Eval::dofs_per_cell * n_components *
sizeof (values_dofs[0][0]));
}
if (evaluate_grad == true)
for (unsigned int comp=0; comp<n_components; comp++)
{
// grad x
eval.template gradients<0,true,false> (values_dofs[comp],
gradients_quad[comp][0]);
// grad y
eval.template gradients<1,true,false> (values_dofs[comp],
gradients_quad[comp][d1]);
// grad y
eval.template gradients<2,true,false> (values_dofs[comp],
gradients_quad[comp][d2]);
}
if (evaluate_lapl == true)
for (unsigned int comp=0; comp<n_components; comp++)
{
// grad x
eval.template hessians<0,true,false> (values_dofs[comp],
hessians_quad[comp][0]);
// grad y
eval.template hessians<1,true,false> (values_dofs[comp],
hessians_quad[comp][d1]);
// grad y
eval.template hessians<2,true,false> (values_dofs[comp],
hessians_quad[comp][d2]);
VectorizedArray<Number> temp1[Eval::dofs_per_cell];
// grad xy
eval.template gradients<0,true,false> (values_dofs[comp], temp1);
eval.template gradients<1,true,false> (temp1, hessians_quad[comp][d3]);
// grad xz
eval.template gradients<2,true,false> (temp1, hessians_quad[comp][d4]);
// grad yz
eval.template gradients<1,true,false> (values_dofs[comp], temp1);
eval.template gradients<2,true,false> (temp1, hessians_quad[comp][d5]);
}
break;
default:
AssertThrow(false, ExcNotImplemented());
}
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components, typename Number>
inline
void
FEEvaluationImpl<MatrixFreeFunctions::tensor_gausslobatto, dim,
fe_degree, n_q_points_1d, n_components, Number>
::integrate (const MatrixFreeFunctions::ShapeInfo<Number> &shape_info,
VectorizedArray<Number> *values_dofs[],
VectorizedArray<Number> *values_quad[],
VectorizedArray<Number> *gradients_quad[][dim],
const bool integrate_val,
const bool integrate_grad)
{
typedef EvaluatorTensorProduct<evaluate_evenodd, dim, fe_degree, fe_degree+1,
VectorizedArray<Number> > Eval;
Eval eval (shape_info.shape_val_evenodd, shape_info.shape_gra_evenodd,
shape_info.shape_hes_evenodd);
// These avoid compiler errors; they are only used in sensible context but
// compilers typically cannot detect when we access something like
// gradients_quad[2] only for dim==3.
const unsigned int d1 = dim>1?1:0;
const unsigned int d2 = dim>2?2:0;
if (integrate_val == true)
std::memcpy (values_dofs[0], values_quad[0],
Eval::dofs_per_cell * n_components *
sizeof (values_dofs[0][0]));
switch (dim)
{
case 1:
for (unsigned int c=0; c<n_components; c++)
{
if (integrate_grad == true)
{
if (integrate_val == true)
eval.template gradients<0,false,true> (gradients_quad[c][0],
values_dofs[c]);
else
eval.template gradients<0,false,false> (gradients_quad[c][0],
values_dofs[c]);
}
}
break;
case 2:
if (integrate_grad == true)
for (unsigned int comp=0; comp<n_components; comp++)
{
// grad x: If integrate_val == true we have to add to the
// previous output
if (integrate_val == true)
eval.template gradients<0, false, true> (gradients_quad[comp][0],
values_dofs[comp]);
else
eval.template gradients<0, false, false> (gradients_quad[comp][0],
values_dofs[comp]);
// grad y
eval.template gradients<1, false, true> (gradients_quad[comp][d1],
values_dofs[comp]);
}
break;
case 3:
if (integrate_grad == true)
for (unsigned int comp=0; comp<n_components; comp++)
{
// grad x: If integrate_val == true we have to add to the
// previous output
if (integrate_val == true)
eval.template gradients<0, false, true> (gradients_quad[comp][0],
values_dofs[comp]);
else
eval.template gradients<0, false, false> (gradients_quad[comp][0],
values_dofs[comp]);
// grad y
eval.template gradients<1, false, true> (gradients_quad[comp][d1],
values_dofs[comp]);
// grad z
eval.template gradients<2, false, true> (gradients_quad[comp][d2],
values_dofs[comp]);
}
break;
default:
AssertThrow(false, ExcNotImplemented());
}
}
} // end of namespace internal
/*-------------------------- FEEvaluation -----------------------------------*/
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::FEEvaluation (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no)
:
BaseClass (data_in, fe_no, quad_no, fe_degree, n_q_points),
dofs_per_cell (this->data->dofs_per_cell)
{
check_template_arguments(fe_no);
set_data_pointers();
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::FEEvaluation (const Mapping<dim> &mapping,
const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component)
:
BaseClass (mapping, fe, quadrature, update_flags,
first_selected_component,
static_cast<FEEvaluationBase<dim,1,Number>*>(0)),
dofs_per_cell (this->data->dofs_per_cell)
{
check_template_arguments(numbers::invalid_unsigned_int);
set_data_pointers();
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::FEEvaluation (const FiniteElement<dim> &fe,
const Quadrature<1> &quadrature,
const UpdateFlags update_flags,
const unsigned int first_selected_component)
:
BaseClass (StaticMappingQ1<dim>::mapping, fe, quadrature, update_flags,
first_selected_component,
static_cast<FEEvaluationBase<dim,1,Number>*>(0)),
dofs_per_cell (this->data->dofs_per_cell)
{
check_template_arguments(numbers::invalid_unsigned_int);
set_data_pointers();
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
template <int n_components_other>
inline
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::FEEvaluation (const FiniteElement<dim> &fe,
const FEEvaluationBase<dim,n_components_other,Number> &other,
const unsigned int first_selected_component)
:
BaseClass (other.mapped_geometry->get_fe_values().get_mapping(),
fe, other.mapped_geometry->get_quadrature(),
other.mapped_geometry->get_fe_values().get_update_flags(),
first_selected_component, &other),
dofs_per_cell (this->data->dofs_per_cell)
{
check_template_arguments(numbers::invalid_unsigned_int);
set_data_pointers();
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::FEEvaluation (const FEEvaluation &other)
:
BaseClass (other),
dofs_per_cell (this->data->dofs_per_cell)
{
set_data_pointers();
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
void
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::set_data_pointers()
{
AssertIndexRange(this->data->dofs_per_cell, tensor_dofs_per_cell+2);
const unsigned int desired_dofs_per_cell = this->data->dofs_per_cell;
// set the pointers to the correct position in the data array
for (unsigned int c=0; c<n_components_; ++c)
{
this->values_dofs[c] = &my_data_array[c*desired_dofs_per_cell];
this->values_quad[c] = &my_data_array[n_components*desired_dofs_per_cell+c*n_q_points];
for (unsigned int d=0; d<dim; ++d)
this->gradients_quad[c][d] = &my_data_array[n_components*(desired_dofs_per_cell+
n_q_points)
+
(c*dim+d)*n_q_points];
for (unsigned int d=0; d<(dim*dim+dim)/2; ++d)
this->hessians_quad[c][d] = &my_data_array[n_components*((dim+1)*n_q_points+
desired_dofs_per_cell)
+
(c*(dim*dim+dim)+d)*n_q_points];
}
switch (this->data->element_type)
{
case internal::MatrixFreeFunctions::tensor_symmetric:
evaluate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_symmetric,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::evaluate;
integrate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_symmetric,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::integrate;
break;
case internal::MatrixFreeFunctions::tensor_symmetric_plus_dg0:
evaluate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_symmetric_plus_dg0,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::evaluate;
integrate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_symmetric_plus_dg0,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::integrate;
break;
case internal::MatrixFreeFunctions::tensor_general:
evaluate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_general,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::evaluate;
integrate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_general,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::integrate;
break;
case internal::MatrixFreeFunctions::tensor_gausslobatto:
evaluate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_gausslobatto,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::evaluate;
integrate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::tensor_gausslobatto,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::integrate;
break;
case internal::MatrixFreeFunctions::truncated_tensor:
evaluate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::truncated_tensor,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::evaluate;
integrate_funct =
internal::FEEvaluationImpl<internal::MatrixFreeFunctions::truncated_tensor,
dim, fe_degree, n_q_points_1d, n_components_,
Number>::integrate;
break;
default:
AssertThrow(false, ExcNotImplemented());
}
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
void
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::check_template_arguments(const unsigned int fe_no)
{
#ifdef DEBUG
// print error message when the dimensions do not match. Propose a possible
// fix
if (fe_degree != this->data->fe_degree
||
n_q_points != this->data->n_q_points)
{
std::string message =
"-------------------------------------------------------\n";
message += "Illegal arguments in constructor/wrong template arguments!\n";
message += " Called --> FEEvaluation<dim,";
message += Utilities::int_to_string(fe_degree) + ",";
message += Utilities::int_to_string(n_q_points_1d);
message += "," + Utilities::int_to_string(n_components);
message += ",Number>(data";
if (fe_no != numbers::invalid_unsigned_int)
{
message += ", " + Utilities::int_to_string(fe_no) + ", ";
message += Utilities::int_to_string(this->quad_no);
}
message += ")\n";
// check whether some other vector component has the correct number of
// points
unsigned int proposed_dof_comp = numbers::invalid_unsigned_int,
proposed_quad_comp = numbers::invalid_unsigned_int;
if (fe_no != numbers::invalid_unsigned_int)
{
if (fe_degree == this->data->fe_degree)
proposed_dof_comp = fe_no;
else
for (unsigned int no=0; no<this->matrix_info->n_components(); ++no)
if (this->matrix_info->get_shape_info(no,0,this->active_fe_index,0).fe_degree
== fe_degree)
{
proposed_dof_comp = no;
break;
}
if (n_q_points ==
this->mapping_info->mapping_data_gen[this->quad_no].n_q_points[this->active_quad_index])
proposed_quad_comp = this->quad_no;
else
for (unsigned int no=0; no<this->mapping_info->mapping_data_gen.size(); ++no)
if (this->mapping_info->mapping_data_gen[no].n_q_points[this->active_quad_index]
== n_q_points)
{
proposed_quad_comp = no;
break;
}
}
if (proposed_dof_comp != numbers::invalid_unsigned_int &&
proposed_quad_comp != numbers::invalid_unsigned_int)
{
if (proposed_dof_comp != fe_no)
message += "Wrong vector component selection:\n";
else
message += "Wrong quadrature formula selection:\n";
message += " Did you mean FEEvaluation<dim,";
message += Utilities::int_to_string(fe_degree) + ",";
message += Utilities::int_to_string(n_q_points_1d);
message += "," + Utilities::int_to_string(n_components);
message += ",Number>(data";
if (fe_no != numbers::invalid_unsigned_int)
{
message += ", " + Utilities::int_to_string(proposed_dof_comp) + ", ";
message += Utilities::int_to_string(proposed_quad_comp);
}
message += ")?\n";
std::string correct_pos;
if (proposed_dof_comp != fe_no)
correct_pos = " ^ ";
else
correct_pos = " ";
if (proposed_quad_comp != this->quad_no)
correct_pos += " ^\n";
else
correct_pos += " \n";
message += " " + correct_pos;
}
// ok, did not find the numbers specified by the template arguments in
// the given list. Suggest correct template arguments
const unsigned int proposed_n_q_points_1d = static_cast<unsigned int>(std::pow(1.001*this->data->n_q_points,1./dim));
message += "Wrong template arguments:\n";
message += " Did you mean FEEvaluation<dim,";
message += Utilities::int_to_string(this->data->fe_degree) + ",";
message += Utilities::int_to_string(proposed_n_q_points_1d);
message += "," + Utilities::int_to_string(n_components);
message += ",Number>(data";
if (fe_no != numbers::invalid_unsigned_int)
{
message += ", " + Utilities::int_to_string(fe_no) + ", ";
message += Utilities::int_to_string(this->quad_no);
}
message += ")?\n";
std::string correct_pos;
if (this->data->fe_degree != fe_degree)
correct_pos = " ^";
else
correct_pos = " ";
if (proposed_n_q_points_1d != n_q_points_1d)
correct_pos += " ^\n";
else
correct_pos += " \n";
message += " " + correct_pos;
Assert (fe_degree == this->data->fe_degree &&
n_q_points == this->data->n_q_points,
ExcMessage(message));
}
if (fe_no != numbers::invalid_unsigned_int)
{
AssertDimension (n_q_points,
this->mapping_info->mapping_data_gen[this->quad_no].
n_q_points[this->active_quad_index]);
AssertDimension (this->data->dofs_per_cell * this->n_fe_components,
this->dof_info->dofs_per_cell[this->active_fe_index]);
}
#endif
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
Point<dim,VectorizedArray<Number> >
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::quadrature_point (const unsigned int q) const
{
Assert (this->mapping_info->quadrature_points_initialized == true,
ExcNotInitialized());
AssertIndexRange (q, n_q_points);
// Cartesian mesh: not all quadrature points are stored, only the
// diagonal. Hence, need to find the tensor product index and retrieve the
// value from that
if (this->cell_type == internal::MatrixFreeFunctions::cartesian)
{
Point<dim,VectorizedArray<Number> > point;
switch (dim)
{
case 1:
return this->quadrature_points[q];
case 2:
point[0] = this->quadrature_points[q%n_q_points_1d][0];
point[1] = this->quadrature_points[q/n_q_points_1d][1];
return point;
case 3:
point[0] = this->quadrature_points[q%n_q_points_1d][0];
point[1] = this->quadrature_points[(q/n_q_points_1d)%n_q_points_1d][1];
point[2] = this->quadrature_points[q/(n_q_points_1d*n_q_points_1d)][2];
return point;
default:
Assert (false, ExcNotImplemented());
return point;
}
}
// all other cases: just return the respective data as it is fully stored
else
return this->quadrature_points[q];
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
void
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::evaluate (const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl)
{
Assert (this->dof_values_initialized == true,
internal::ExcAccessToUninitializedField());
Assert(this->matrix_info != 0 ||
this->mapped_geometry->is_initialized(), ExcNotInitialized());
// Select algorithm matching the element type at run time (the function
// pointer is easy to predict, so negligible in cost)
evaluate_funct (*this->data, &this->values_dofs[0],
this->values_quad, this->gradients_quad, this->hessians_quad,
evaluate_val, evaluate_grad, evaluate_lapl);
#ifdef DEBUG
if (evaluate_val == true)
this->values_quad_initialized = true;
if (evaluate_grad == true)
this->gradients_quad_initialized = true;
if (evaluate_lapl == true)
this->hessians_quad_initialized = true;
#endif
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
void
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::integrate (bool integrate_val,bool integrate_grad)
{
if (integrate_val == true)
Assert (this->values_quad_submitted == true,
internal::ExcAccessToUninitializedField());
if (integrate_grad == true)
Assert (this->gradients_quad_submitted == true,
internal::ExcAccessToUninitializedField());
Assert(this->matrix_info != 0 ||
this->mapped_geometry->is_initialized(), ExcNotInitialized());
// Select algorithm matching the element type at run time (the function
// pointer is easy to predict, so negligible in cost)
integrate_funct (*this->data, this->values_dofs, this->values_quad,
this->gradients_quad, integrate_val, integrate_grad);
#ifdef DEBUG
this->dof_values_initialized = true;
#endif
}
#endif // ifndef DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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