/usr/include/deal.II/matrix_free/fe_evaluation.h is in libdeal.ii-dev 8.1.0-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// $Id: fe_evaluation.h 31932 2013-12-08 02:15:54Z heister $
//
// Copyright (C) 2011 - 2013 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 __deal2__matrix_free_fe_evaluation_h
#define __deal2__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/matrix_free/matrix_free.h>
DEAL_II_NAMESPACE_OPEN
namespace parallel
{
namespace distributed
{
template <typename> class Vector;
}
}
namespace internal
{
DeclException0 (ExcAccessToUninitializedField);
template <typename FEEval>
void do_evaluate (FEEval &, const bool, const bool, const bool);
template <typename FEEval>
void do_integrate (FEEval &, const bool, const bool);
}
/**
* This is the base class for the FEEvaluation classes. This class is a base
* class and needs usually not be called in user code. Use one of the derived
* classes FEEvaluationGeneral, FEEvaluation or FEEvaluationGL 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 five template arguments:
*
* @param dim Dimension in which this class is to be used
*
* @param dofs_per_cell Number of degrees of freedom of the FE per cell,
* usually (fe_degree+1)^dim for elements based on a tensor
* product
*
* @param n_q_points Number of points in the quadrature formula, usually
* (fe_degree+1)^dim for tensor-product quadrature formulas
*
* @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 dofs_per_cell_, int n_q_points_,
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_;
static const unsigned int dofs_per_cell = dofs_per_cell_;
static const unsigned int n_q_points = n_q_points_;
/**
* @name 1: General operations
*/
//@{
/**
* Initializes the operation pointer to the current cell. Unlike the
* FEValues::reinit function, 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);
/**
* 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;
//@}
/**
* @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.
*/
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.
*/
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. Note that if
* vectorization is enabled, the DoF values for several cells are used.
*/
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. Note that 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.
*/
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 ();
//@}
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 = 0,
const unsigned int quad_no = 0);
/**
* 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. Since all array lengths are
* known at compile time and since they are rarely more than a few
* kilobytes, allocate them 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.
*
* 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][dofs_per_cell>0?dofs_per_cell:1];
/**
* 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][n_q_points>0?n_q_points:1];
/**
* 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][n_q_points>0?n_q_points:1];
/**
* 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][n_q_points>0?n_q_points:1];
/**
* 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 reference to the underlying data.
*/
const MatrixFree<dim,Number> &matrix_info;
/**
* Stores a reference 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 reference 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;
/**
* Stores a reference to the unit cell 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;
};
/**
* 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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
class FEEvaluationAccess :
public FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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_;
static const unsigned int dofs_per_cell = dofs_per_cell_;
static const unsigned int n_q_points = n_q_points_;
typedef FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 = 0,
const unsigned int quad_no = 0);
};
/**
* 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, int dofs_per_cell_, int n_q_points_, typename Number>
class FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number> :
public FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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;
static const unsigned int dofs_per_cell = dofs_per_cell_;
static const unsigned int n_q_points = n_q_points_;
typedef FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 = 0,
const unsigned int quad_no = 0);
};
/**
* 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, int dofs_per_cell_, int n_q_points_, typename Number>
class FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,dim,Number> :
public FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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;
static const unsigned int dofs_per_cell = dofs_per_cell_;
static const unsigned int n_q_points = n_q_points_;
typedef FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 constribution 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 = 0,
const unsigned int quad_no = 0);
};
/**
* 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 times as fast,
* depending on the polynomial order). Access to the data fields is provided
* through functionality in the class FEEvaluationAccess.
*
* This class is designed for general local finite element operations based on
* tensor products of 1D polynomials and quadrature points. Often, there are
* some symmetries or zeros in the unit cell data that allow for a more
* efficient operator application. FEEvaluation is specialized to standard
* FE_Q/FE_DGQ elements and quadrature points symmetric around 0.5 (like Gauss
* quadrature), and hence the most common situation. FEEvaluationGL is a
* specialization for elements where quadrature formula and support points are
* chosen so that a orthogonal relation between the values holds. This is the
* case for FE_Q based on Gauss-Lobatto support points with Gauss-Lobatto
* quadrature formula of the same order.
*
* 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,
* usually chosen as 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)
*
* @param Number Number format, usually @p double or @p float
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011
*/
template <int dim, int fe_degree, int n_q_points_1d = fe_degree+1,
int n_components_ = 1, typename Number = double >
class FEEvaluationGeneral :
public FEEvaluationAccess<dim,
Utilities::fixed_int_power<fe_degree+1,dim>::value,
Utilities::fixed_int_power<n_q_points_1d,dim>::value,
n_components_,Number>
{
public:
typedef FEEvaluationAccess<dim,
Utilities::fixed_int_power<fe_degree+1,dim>::value,
Utilities::fixed_int_power<n_q_points_1d,dim>::value,
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 dofs_per_cell = BaseClass::dofs_per_cell;
static const unsigned int n_q_points = BaseClass::n_q_points;
/**
* 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.
*/
FEEvaluationGeneral (const MatrixFree<dim,Number> &matrix_free,
const unsigned int fe_no = 0,
const unsigned int quad_no = 0);
/**
* 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. 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 return useful information.
*/
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;
protected:
/**
* Internal function that applies the function values of the tensor product
* in a given coordinate direction (first template argument), from
* polynomials to values on quadrature points (second flag set to true) or
* in an integration loop from values on quadrature points to values tested
* by different test function (second flag set to false), and if the result
* is to be added to previous content in the data fields or not.
*/
template <int direction, bool dof_to_quad, bool add>
void apply_values (const VectorizedArray<Number> in [],
VectorizedArray<Number> out []);
/**
* Internal function that applies the gradient operation of the tensor
* product in a given coordinate direction (first template argument), from
* polynomials to values on quadrature points (second flag set to true) or
* in an integration loop from values on quadrature points to values tested
* by different test function (second flag set to false), and if the result
* is to be added to previous content in the data fields or not.
*/
template <int direction, bool dof_to_quad, bool add>
void apply_gradients (const VectorizedArray<Number> in [],
VectorizedArray<Number> out []);
/**
* Internal function that applies the second derivative operation (Hessian)
* of the tensor product in a given coordinate direction (first template
* argument), from polynomials to values on quadrature points (second flag
* set to true) or in an integration loop from values on quadrature points
* to values tested by different test function (second flag set to false),
* and if the result is to be added to previous content in the data fields
* or not.
*/
template <int direction, bool dof_to_quad, bool add>
void apply_hessians (const VectorizedArray<Number> in [],
VectorizedArray<Number> out []);
/**
* Friend declaration.
*/
template <typename FEEval> friend void
internal::do_evaluate (FEEval &, const bool, const bool, const bool);
template <typename FEEval> friend void
internal::do_integrate (FEEval &, const bool, const bool);
};
/**
* 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).
*
* This class is a specialization of FEEvaluationGeneral designed for standard
* FE_Q or FE_DGQ elements and quadrature points symmetric around 0.5 (like
* Gauss quadrature), and hence the most common situation. 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,
* usually chosen as 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)
*
* @param Number Number format, usually @p double or @p float
*
* @author Katharina Kormann and Martin Kronbichler, 2010, 2011
*/
template <int dim, int fe_degree, int n_q_points_1d = fe_degree+1,
int n_components_ = 1, typename Number = double >
class FEEvaluation :
public FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,n_components_,Number>
{
public:
typedef FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,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 dofs_per_cell = BaseClass::dofs_per_cell;
static const unsigned int n_q_points = BaseClass::n_q_points;
/**
* 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);
/**
* 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);
protected:
/**
* Internal function that applies the function values of the tensor product
* in a given coordinate direction (first template argument), from
* polynomials to values on quadrature points (second flag set to true) or
* in an integration loop from values on quadrature points to values tested
* by different test function (second flag set to false), and if the result
* is to be added to previous content in the data fields or not.
*/
template <int direction, bool dof_to_quad, bool add>
void apply_values (const VectorizedArray<Number> in [],
VectorizedArray<Number> out []);
/**
* Internal function that applies the gradient operation of the tensor
* product in a given coordinate direction (first template argument), from
* polynomials to values on quadrature points (second flag set to true) or
* in an integration loop from values on quadrature points to values tested
* by different test function (second flag set to false), and if the result
* is to be added to previous content in the data fields or not.
*/
template <int direction, bool dof_to_quad, bool add>
void apply_gradients (const VectorizedArray<Number> in [],
VectorizedArray<Number> out []);
/**
* Internal function that applies the second derivative operation (Hessian)
* of the tensor product in a given coordinate direction (first template
* argument), from polynomials to values on quadrature points (second flag
* set to true) or in an integration loop from values on quadrature points
* to values tested by different test function (second flag set to false),
* and if the result is to be added to previous content in the data fields
* or not.
*/
template <int direction, bool dof_to_quad, bool add>
void apply_hessians (const VectorizedArray<Number> in [],
VectorizedArray<Number> out []);
VectorizedArray<Number> shape_val_evenodd[fe_degree+1][(n_q_points_1d+1)/2];
VectorizedArray<Number> shape_gra_evenodd[fe_degree+1][(n_q_points_1d+1)/2];
VectorizedArray<Number> shape_hes_evenodd[fe_degree+1][(n_q_points_1d+1)/2];
/**
* Friend declarations.
*/
template <typename FEEval> friend void
internal::do_evaluate (FEEval &, const bool, const bool, const bool);
template <typename FEEval> friend void
internal::do_integrate (FEEval &, const bool, const bool);
};
/**
* 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).
*
* This class is a specialization of FEEvaluation for elements where
* quadrature formula and support points are chosen so that a orthonormal
* relation between the values holds. This is the case for FE_Q based on
* Gauss-Lobatto support points with Gauss-Lobatto quadrature formula of the
* same order (QGaussLobatto). In that case, application of values is trivial
* (as the transformation is the identity matrix), and application of
* gradients is considerably simpler (since all value applications in
* directions other than the gradient direction are again identity
* operations).
*
* This class has four 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. The quadrature formula is tied to the choice of
* the element by setting n_q_points_1d = fe_degree+1, which
* gives a diagonal mass matrix
*
* @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 fe_degree, int n_components_ = 1, typename Number = double >
class FEEvaluationGL :
public FEEvaluation<dim,fe_degree,fe_degree+1,n_components_,Number>
{
public:
typedef FEEvaluation<dim,fe_degree,fe_degree+1,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 dofs_per_cell = BaseClass::dofs_per_cell;
static const unsigned int n_q_points = BaseClass::n_q_points;
/**
* 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.
*/
FEEvaluationGL (const MatrixFree<dim,Number> &matrix_free,
const unsigned int fe_no = 0,
const unsigned int quad_no = 0);
/**
* Evaluates the function values, the gradients, and the Hessians of the FE
* function given at the DoF values in the input vector at the quadrature
* points of 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_lapl = 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);
protected:
/**
* Internal function that applies the gradient operation of the tensor
* product in a given coordinate direction (first template argument), from
* polynomials to values on quadrature points (second flag set to true) or
* in an integration loop from values on quadrature points to values tested
* by different test function (second flag set to false), and if the result
* is to be added to some previous results or not.
*/
template <int direction, bool dof_to_quad, bool add>
void apply_gradients (const VectorizedArray<Number> in [],
VectorizedArray<Number> out []);
};
/*----------------------- Inline functions ----------------------------------*/
#ifndef DOXYGEN
/*----------------------- FEEvaluationBase ----------------------------------*/
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::FEEvaluationBase (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no_in,
const unsigned int quad_no_in)
:
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_dofs_per_cell
(dofs_per_cell_ * n_fe_components)),
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)
{
Assert (matrix_info.mapping_initialized() == true,
ExcNotInitialized());
AssertDimension (matrix_info.get_size_info().vectorization_length,
VectorizedArray<Number>::n_array_elements);
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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::reinit (const unsigned int cell_in)
{
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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
unsigned int
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_cell_data_number () const
{
Assert (cell != numbers::invalid_unsigned_int, ExcNotInitialized());
return cell_data_number;
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
internal::MatrixFreeFunctions::CellType
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_cell_type () const
{
Assert (cell != numbers::invalid_unsigned_int, ExcNotInitialized());
return cell_type;
}
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);
}
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;
}
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;
}
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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType, typename VectorOperation>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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.
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 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: loop bounds are known, compiler can
// unroll without checks
AssertDimension (dof_info.end_indices(cell)-dof_indices,
static_cast<int>(n_local_dofs));
for (unsigned int j=0; j<n_local_dofs; ++j)
for (unsigned int comp=0; comp<n_components; ++comp)
operation.process_dof (dof_indices[j], *src[comp],
local_data[comp][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 ( ; 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: loop bounds are known, compiler can
// unroll without checks
AssertDimension (dof_info.end_indices(cell)-dof_indices,
static_cast<int>(n_local_dofs));
for (unsigned int j=0; j<n_local_dofs; ++j)
operation.process_dof (dof_indices[j], *src[0],
local_data[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 ( ; 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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
template<typename VectorType>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::read_dof_values_plain (const VectorType *src[])
{
// this is different from the other three operations because we do not use
// constraints here, so this is a separate function.
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 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 dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_dof_values () const
{
return &values_dofs[0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_dof_values ()
{
#ifdef DEBUG
dof_values_initialized = true;
#endif
return &values_dofs[0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_values () const
{
Assert (values_quad_initialized || values_quad_submitted,
ExcNotInitialized());
return &values_quad[0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_values ()
{
#ifdef DEBUG
values_quad_submitted = true;
#endif
return &values_quad[0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_gradients () const
{
Assert (gradients_quad_initialized || gradients_quad_submitted,
ExcNotInitialized());
return &gradients_quad[0][0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_gradients ()
{
#ifdef DEBUG
gradients_quad_submitted = true;
#endif
return &gradients_quad[0][0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
const VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_hessians () const
{
Assert (hessians_quad_initialized, ExcNotInitialized());
return &hessians_quad[0][0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components, typename Number>
inline
VectorizedArray<Number> *
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components,Number>::
begin_hessians ()
{
return &hessians_quad[0][0][0];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_dof_value (const unsigned int dof) const
{
AssertIndexRange (dof, dofs_per_cell);
Tensor<1,n_components_,VectorizedArray<Number> > return_value (false);
for (unsigned int comp=0; comp<n_components; comp++)
return_value[comp] = this->values_dofs[comp][dof];
return return_value;
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_value (const unsigned int q_point) const
{
Assert (this->values_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, n_q_points);
Tensor<1,n_components_,VectorizedArray<Number> > return_value (false);
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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > >
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_gradient (const unsigned int q_point) const
{
Assert (this->gradients_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, n_q_points);
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > > grad_out (false);
// 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 <int dim, int n_q_points, typename Number>
inline
void
hessian_unit_times_jac (const Tensor<2,dim,VectorizedArray<Number> > &jac,
const VectorizedArray<Number> hessians_quad[][n_q_points],
const unsigned int q_point,
VectorizedArray<Number> tmp[dim][dim])
{
for (unsigned int d=0; d<dim; ++d)
{
switch (dim)
{
case 1:
tmp[0][0] = jac[0][0] * hessians_quad[0][q_point];
break;
case 2:
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]);
break;
case 3:
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]);
break;
default:
Assert (false, ExcNotImplemented());
}
}
}
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
Tensor<1,n_components_,Tensor<2,dim,VectorizedArray<Number> > >
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_hessian (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, 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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > >
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_hessian_diagonal (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, n_q_points);
Tensor<1,n_components_,Tensor<1,dim,VectorizedArray<Number> > > hessian_out (false);
// 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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::get_laplacian (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, n_q_points);
Tensor<1,n_components_,VectorizedArray<Number> > laplacian_out (false);
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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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, dofs_per_cell);
for (unsigned int comp=0; comp<n_components; comp++)
this->values_dofs[comp][dof] = val_in[comp];
}
template <int dim, int dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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, 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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
void
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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, 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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
Tensor<1,n_components_,VectorizedArray<Number> >
FEEvaluationBase<dim,dofs_per_cell_,n_q_points_,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 (false);
for (unsigned int comp=0; comp<n_components; ++comp)
return_value[comp] = this->values_quad[comp][0];
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 dofs_per_cell_, int n_q_points_,
int n_components_, typename Number>
inline
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,n_components_,Number>
::FEEvaluationAccess (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no_in)
:
FEEvaluationBase <dim,dofs_per_cell_,n_q_points_,n_components_,Number>
(data_in, fe_no, quad_no_in)
{}
/*-------------------- FEEvaluationAccess scalar ----------------------------*/
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::FEEvaluationAccess (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no_in)
:
FEEvaluationBase <dim,dofs_per_cell_,n_q_points_,1,Number>
(data_in, fe_no, quad_no_in)
{}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::get_dof_value (const unsigned int dof) const
{
AssertIndexRange (dof, dofs_per_cell);
return this->values_dofs[0][dof];
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::get_value (const unsigned int q_point) const
{
Assert (this->values_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, n_q_points);
return this->values_quad[0][q_point];
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
Tensor<1,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, n_q_points);
Tensor<1,dim,VectorizedArray<Number> > grad_out (false);
// 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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
Tensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::get_hessian (const unsigned int q_point) const
{
return BaseClass::get_hessian(q_point)[0];
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
Tensor<1,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::get_hessian_diagonal (const unsigned int q_point) const
{
return BaseClass::get_hessian_diagonal(q_point)[0];
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::get_laplacian (const unsigned int q_point) const
{
return BaseClass::get_laplacian(q_point)[0];
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::submit_dof_value (const VectorizedArray<Number> val_in,
const unsigned int dof)
{
#ifdef DEBUG
this->dof_values_initialized = true;
AssertIndexRange (dof, dofs_per_cell);
#endif
this->values_dofs[0][dof] = val_in;
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, 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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, 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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,1,Number>
::integrate_value () const
{
return BaseClass::integrate_value()[0];
}
/*----------------- FEEvaluationAccess vector-valued ------------------------*/
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,dim,Number>
::FEEvaluationAccess (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no_in)
:
FEEvaluationBase <dim,dofs_per_cell_,n_q_points_,dim,Number>
(data_in, fe_no, quad_no_in)
{}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
Tensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,dim,Number>
::get_gradient (const unsigned int q_point) const
{
return BaseClass::get_gradient (q_point);
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
VectorizedArray<Number>
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,dim,Number>
::get_divergence (const unsigned int q_point) const
{
Assert (this->gradients_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, 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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
SymmetricTensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
Tensor<1,dim==2?1:dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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 (false);
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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
Tensor<2,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,dim,Number>
::get_hessian_diagonal (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, n_q_points);
return BaseClass::get_hessian_diagonal (q_point);
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
Tensor<3,dim,VectorizedArray<Number> >
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,dim,Number>
::get_hessian (const unsigned int q_point) const
{
Assert (this->hessians_quad_initialized==true,
internal::ExcAccessToUninitializedField());
AssertIndexRange (q_point, n_q_points);
return BaseClass::get_hessian(q_point);
}
template <int dim, int dofs_per_cell_, int n_q_points_, typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, int dofs_per_cell_, int n_q_points_,
typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, 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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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, 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, int dofs_per_cell_, int n_q_points_, typename Number>
inline
void
FEEvaluationAccess<dim,dofs_per_cell_,n_q_points_,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);
}
/*----------------------- FEEvaluationGeneral -------------------------------*/
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,n_components_,Number>
::FEEvaluationGeneral (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no)
:
BaseClass (data_in, fe_no, quad_no)
{
#ifdef DEBUG
// print error message when the dimensions do not match. Propose a possible
// fix
if (dofs_per_cell != this->data.dofs_per_cell ||
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, ";
message += Utilities::int_to_string(fe_no) + ", ";
message += Utilities::int_to_string(quad_no) + ")\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 (dofs_per_cell == this->matrix_info.get_dof_info(fe_no).dofs_per_cell[this->active_fe_index])
proposed_dof_comp = fe_no;
else
for (unsigned int no=0; no<this->matrix_info.n_components(); ++no)
if (this->matrix_info.get_dof_info(no).dofs_per_cell[this->active_fe_index]
== dofs_per_cell)
{
proposed_dof_comp = no;
break;
}
if (n_q_points ==
this->mapping_info.mapping_data_gen[quad_no].n_q_points[this->active_quad_index])
proposed_quad_comp = 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, ";
message += Utilities::int_to_string(proposed_dof_comp) + ", ";
message += Utilities::int_to_string(proposed_quad_comp) + ")?\n";
std::string correct_pos;
if (proposed_dof_comp != fe_no)
correct_pos = " ^ ";
else
correct_pos = " ";
if (proposed_quad_comp != 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_fe_degree = static_cast<unsigned int>(std::pow(1.001*this->data.dofs_per_cell,1./dim))-1;
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(proposed_fe_degree) + ",";
message += Utilities::int_to_string(proposed_n_q_points_1d);
message += "," + Utilities::int_to_string(n_components);
message += ",Number>(data, ";
message += Utilities::int_to_string(fe_no) + ", ";
message += Utilities::int_to_string(quad_no) + ")?\n";
std::string correct_pos;
if (proposed_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 (dofs_per_cell == this->data.dofs_per_cell &&
n_q_points == this->data.n_q_points,
ExcMessage(message));
}
AssertDimension (n_q_points,
this->mapping_info.mapping_data_gen[this->quad_no].
n_q_points[this->active_quad_index]);
AssertDimension (dofs_per_cell * this->n_fe_components,
this->dof_info.dofs_per_cell[this->active_fe_index]);
#endif
}
namespace internal
{
// 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,
int direction, bool dof_to_quad, bool add>
inline
void
apply_tensor_product (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:
case 2:
++in;
++out;
break;
default:
Assert (false, ExcNotImplemented());
}
}
if (face_direction == 1)
{
in += mm*(mm-1);
out += nn*(nn-1);
}
}
}
// This method 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. In that 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,
int direction, bool dof_to_quad, bool add>
inline
void
apply_tensor_product_values (const Number *shape_values,
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_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);
}
}
}
// evaluates the given shape data in 1d-3d using the tensor product
// form assuming the symmetries of unit cell shape gradients for
// finite elements in FEEvaluation
// 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,
int direction, bool dof_to_quad, bool add>
inline
void
apply_tensor_product_gradients (const Number *shape_gradients,
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_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,
int direction, bool dof_to_quad, bool add>
inline
void
apply_tensor_product_hessians (const Number *shape_hessians,
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_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 method 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,
int direction, bool dof_to_quad, bool add, int type>
inline
void
apply_tensor_product_evenodd (const Number shapes [][(n_q_points_1d+1)/2],
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;
// 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], xm[mid];
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[0][col] * xp[0];
r1 = shapes[fe_degree][col] * xm[0];
}
else
{
r0 = shapes[col][0] * xp[0];
r1 = shapes[fe_degree-col][0] * xm[0];
}
for (int ind=1; ind<mid; ++ind)
{
if (dof_to_quad == true)
{
r0 += shapes[ind][col] * xp[ind];
r1 += shapes[fe_degree-ind][col] * xm[ind];
}
else
{
r0 += shapes[col][ind] * xp[ind];
r1 += shapes[fe_degree-col][ind] * xm[ind];
}
}
}
else
r0 = r1 = Number();
if (mm % 2 == 1 && dof_to_quad == true)
{
if (type == 1)
r1 += shapes[mid][col] * in[stride*mid];
else
r0 += shapes[mid][col] * in[stride*mid];
}
else if (mm % 2 == 1 && (nn % 2 == 0 || type > 0))
r0 += shapes[col][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[0][n_cols] * xp[0];
for (int ind=1; ind<mid; ++ind)
r0 += shapes[ind][n_cols] * xp[ind];
}
else
r0 = Number();
if (type != 1 && mm % 2 == 1)
r0 += shapes[mid][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][0] * xm[0];
for (int ind=1; ind<mid; ++ind)
r0 += shapes[n_cols][ind] * xm[ind];
}
else
{
r0 = shapes[n_cols][0] * xp[0];
for (int ind=1; ind<mid; ++ind)
r0 += shapes[n_cols][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][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);
}
}
}
// evaluates the given shape data in 1d-3d using the tensor product
// form assuming the symmetries of unit cell shape gradients for
// finite elements in FEEvaluationGL
// This function specializes the application of the tensor product loop for
// Gauss-Lobatto elements which are symmetric about 0.5 just as the general
// class of elements treated by FEEvaluation, have diagonal shape matrices
// for the values and have the following gradient matrices (notice the zeros
// on the diagonal in the interior points, which is due to the construction
// of Legendre polynomials):
// Q2 --> [-3 -1 1 ]
// [ 4 0 -4 ]
// [-1 1 3 ]
// Q3 --> [-6 -1.618 0.618 -1 ]
// [ 8.09 0 -2.236 3.09 ]
// [-3.09 2.236 0 -8.09 ]
// [ 1 -0.618 1.618 6 ]
// Q4 --> [-10 -2.482 0.75 -0.518 1 ]
// [ 13.51 0 -2.673 1.528 -2.82 ]
// [-5.333 3.491 0 -3.491 5.333 ]
// [ 2.82 -1.528 2.673 0 -13.51 ]
// [-1 0.518 -0.75 2.482 10 ]
template <int dim, int fe_degree, typename Number,
int direction, bool dof_to_quad, bool add>
inline
void
apply_tensor_product_gradients_gl (const Number *shape_gradients,
const Number in [],
Number out [])
{
AssertIndexRange (direction, dim);
const int mm = fe_degree+1;
const int nn = 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 (mid > 0)
{
if (dof_to_quad == true)
{
val0 = shape_gradients[col];
val1 = shape_gradients[nn-1-col];
}
else
{
val0 = shape_gradients[col*mm];
val1 = shape_gradients[(nn-col-1)*mm];
}
in0 = in[0];
in1 = in[stride*(mm-1)];
if (col == 0)
{
if ((mm+dof_to_quad)%2 == 1)
{
res0 = val0 * in0;
res1 = -in0;
res0 += in1;
res1 -= val0 * in1;
}
else
{
res0 = val0 * in0;
res0 -= in1;
res1 = in0;
res1 -= val0 * in1;
}
}
else
{
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*mm+col];
val1 = shape_gradients[ind*mm+nn-1-col];
}
else
{
val0 = shape_gradients[col*mm+ind];
val1 = shape_gradients[(nn-col-1)*mm+ind];
}
// at inner points, the gradient is zero for ind==col
in0 = in[stride*ind];
in1 = in[stride*(mm-1-ind)];
if (ind == col)
{
res1 += val1 * in0;
res0 -= val1 * in1;
}
else
{
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*mm+col];
else
val0 = shape_gradients[col*mm+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*mm];
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_gradients[ind*mm+n_cols];
else
val0 = shape_gradients[n_cols*mm+ind];
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;
}
// 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);
}
}
}
// This performs the evaluation of function values, gradients and Hessians
// for tensor-product finite elements. The operation is used for both
// FEEvaluationGeneral and FEEvaluation, which provide different functions
// apply_values, apply_gradients in the individual coordinate directions
template <typename FEEval>
inline
void
do_evaluate (FEEval &fe_eval,
const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl)
{
Assert (fe_eval.cell != numbers::invalid_unsigned_int,
ExcNotInitialized());
Assert (fe_eval.dof_values_initialized == true,
internal::ExcAccessToUninitializedField());
const unsigned int temp_size = FEEval::dofs_per_cell > FEEval::n_q_points ?
FEEval::dofs_per_cell : FEEval::n_q_points;
const unsigned int n_components = FEEval::n_components;
const unsigned int dim = FEEval::dimension;
for (unsigned int c=0; c<n_components; c++)
{
VectorizedArray<typename FEEval::number_type> temp1[temp_size];
VectorizedArray<typename FEEval::number_type> temp2[temp_size];
switch (dim)
{
case 3:
if (evaluate_grad == true)
{
// grad x
fe_eval.template apply_gradients<0,true,false>
(fe_eval.values_dofs[c], temp1);
fe_eval.template apply_values<1,true,false>
(temp1, temp2);
fe_eval.template apply_values<2,true,false>
(temp2, fe_eval.gradients_quad[c][0]);
}
if (evaluate_lapl == true)
{
// grad xz
if (evaluate_grad == false)
{
fe_eval.template apply_gradients<0,true,false>
(fe_eval.values_dofs[c], temp1);
fe_eval.template apply_values<1,true,false>
(temp1, temp2);
}
fe_eval.template apply_gradients<2,true,false>
(temp2, fe_eval.hessians_quad[c][4]);
// grad xy
fe_eval.template apply_gradients<1,true,false>
(temp1, temp2);
fe_eval.template apply_values<2,true,false>
(temp2, fe_eval.hessians_quad[c][3]);
// grad xx
fe_eval.template apply_hessians<0,true,false>
(fe_eval.values_dofs[c], temp1);
fe_eval.template apply_values<1,true,false>
(temp1, temp2);
fe_eval.template apply_values<2,true,false>
(temp2, fe_eval.hessians_quad[c][0]);
}
// grad y
fe_eval.template apply_values<0,true,false>
(fe_eval.values_dofs[c], temp1);
if (evaluate_grad == true)
{
fe_eval.template apply_gradients<1,true,false>
(temp1, temp2);
fe_eval.template apply_values<2,true,false>
(temp2, fe_eval.gradients_quad[c][1]);
}
if (evaluate_lapl == true)
{
// grad yz
if (evaluate_grad == false)
fe_eval.template apply_gradients<1,true,false>
(temp1, temp2);
fe_eval.template apply_gradients<2,true,false>
(temp2, fe_eval.hessians_quad[c][5]);
// grad yy
fe_eval.template apply_hessians<1,true,false>
(temp1, temp2);
fe_eval.template apply_values<2,true,false>
(temp2, fe_eval.hessians_quad[c][1]);
}
// grad z: can use the values applied in x direction stored in temp1
fe_eval.template apply_values<1,true,false>
(temp1, temp2);
if (evaluate_grad == true)
fe_eval.template apply_gradients<2,true,false>
(temp2, fe_eval.gradients_quad[c][2]);
// grad zz: can use the values applied in x and y direction stored
// in temp2
if (evaluate_lapl == true)
fe_eval.template apply_hessians<2,true,false>
(temp2, fe_eval.hessians_quad[c][2]);
// val: can use the values applied in x & y direction stored in temp2
if (evaluate_val == true)
fe_eval.template apply_values<2,true,false>
(temp2, fe_eval.values_quad[c]);
break;
case 2:
// grad x
if (evaluate_grad == true)
{
fe_eval.template apply_gradients<0,true,false>
(fe_eval.values_dofs[c], temp1);
fe_eval.template apply_values<1,true,false>
(temp1, fe_eval.gradients_quad[c][0]);
}
if (evaluate_lapl == true)
{
// grad xy
if (evaluate_grad == false)
fe_eval.template apply_gradients<0,true,false>
(fe_eval.values_dofs[c], temp1);
fe_eval.template apply_gradients<1,true,false>
(temp1, fe_eval.hessians_quad[c][2]);
// grad xx
fe_eval.template apply_hessians<0,true,false>
(fe_eval.values_dofs[c], temp1);
fe_eval.template apply_values<1,true,false>
(temp1, fe_eval.hessians_quad[c][0]);
}
// grad y
fe_eval.template apply_values<0,true,false>
(fe_eval.values_dofs[c], temp1);
if (evaluate_grad == true)
fe_eval.template apply_gradients<1,true,false>
(temp1, fe_eval.gradients_quad[c][1]);
// grad yy
if (evaluate_lapl == true)
fe_eval.template apply_hessians<1,true,false>
(temp1, fe_eval.hessians_quad[c][1]);
// val: can use values applied in x
if (evaluate_val == true)
fe_eval.template apply_values<1,true,false>
(temp1, fe_eval.values_quad[c]);
break;
case 1:
if (evaluate_val == true)
fe_eval.template apply_values<0,true,false>
(fe_eval.values_dofs[c], fe_eval.values_quad[c]);
if (evaluate_grad == true)
fe_eval.template apply_gradients<0,true,false>
(fe_eval.values_dofs[c], fe_eval.gradients_quad[c][0]);
if (evaluate_lapl == true)
fe_eval.template apply_hessians<0,true,false>
(fe_eval.values_dofs[c], fe_eval.hessians_quad[c][0]);
break;
default:
Assert (false, ExcNotImplemented());
}
}
#ifdef DEBUG
if (evaluate_val == true)
fe_eval.values_quad_initialized = true;
if (evaluate_grad == true)
fe_eval.gradients_quad_initialized = true;
if (evaluate_lapl == true)
fe_eval.hessians_quad_initialized = true;
#endif
}
template <typename FEEval>
inline
void
do_integrate (FEEval &fe_eval,
const bool integrate_val,
const bool integrate_grad)
{
Assert (fe_eval.cell != numbers::invalid_unsigned_int, ExcNotInitialized());
if (integrate_val == true)
Assert (fe_eval.values_quad_submitted == true,
ExcAccessToUninitializedField());
if (integrate_grad == true)
Assert (fe_eval.gradients_quad_submitted == true,
ExcAccessToUninitializedField());
const unsigned int temp_size = FEEval::dofs_per_cell > FEEval::n_q_points ?
FEEval::dofs_per_cell : FEEval::n_q_points;
const unsigned int n_components = FEEval::n_components;
const unsigned int dim = FEEval::dimension;
for (unsigned int c=0; c<n_components; c++)
{
VectorizedArray<typename FEEval::number_type> temp1[temp_size];
VectorizedArray<typename FEEval::number_type> temp2[temp_size];
switch (dim)
{
case 3:
if (integrate_val == true)
{
// val
fe_eval.template apply_values<0,false,false>
(fe_eval.values_quad[c], temp1);
}
if (integrate_grad == true)
{
// grad x: can sum to temporary value in temp1
if (integrate_val == true)
fe_eval.template apply_gradients<0,false,true>
(fe_eval.gradients_quad[c][0], temp1);
else
fe_eval.template apply_gradients<0,false,false>
(fe_eval.gradients_quad[c][0], temp1);
}
fe_eval.template apply_values<1,false,false>
(temp1, temp2);
if (integrate_grad == true)
{
// grad y: can sum to temporary x value in temp2
fe_eval.template apply_values<0,false,false>
(fe_eval.gradients_quad[c][1], temp1);
fe_eval.template apply_gradients<1,false,true>
(temp1, temp2);
}
fe_eval.template apply_values<2,false,false>
(temp2, fe_eval.values_dofs[c]);
if (integrate_grad == true)
{
// grad z: can sum to temporary x and y value in output
fe_eval.template apply_values<0,false,false>
(fe_eval.gradients_quad[c][2], temp1);
fe_eval.template apply_values<1,false,false>
(temp1, temp2);
fe_eval.template apply_gradients<2,false,true>
(temp2, fe_eval.values_dofs[c]);
}
break;
case 2:
// val
if (integrate_val == true)
fe_eval.template apply_values<0,false,false>
(fe_eval.values_quad[c], temp1);
if (integrate_grad == true)
{
//grad x
if (integrate_val == true)
fe_eval.template apply_gradients<0,false,true>
(fe_eval.gradients_quad[c][0], temp1);
else
fe_eval.template apply_gradients<0,false,false>
(fe_eval.gradients_quad[c][0], temp1);
}
fe_eval.template apply_values<1,false,false>
(temp1, fe_eval.values_dofs[c]);
if (integrate_grad == true)
{
// grad y
fe_eval.template apply_values<0,false,false>
(fe_eval.gradients_quad[c][1], temp1);
fe_eval.template apply_gradients<1,false,true>
(temp1, fe_eval.values_dofs[c]);
}
break;
case 1:
if (integrate_grad == true)
fe_eval.template apply_gradients<0,false,false>
(fe_eval.gradients_quad[c][0], fe_eval.values_dofs[c]);
if (integrate_val == true)
{
if (integrate_grad == true)
fe_eval.template apply_values<0,false,true>
(fe_eval.values_quad[c], fe_eval.values_dofs[c]);
else
fe_eval.template apply_values<0,false,false>
(fe_eval.values_quad[c], fe_eval.values_dofs[c]);
}
break;
default:
Assert (false, ExcNotImplemented());
}
}
#ifdef DEBUG
fe_eval.dof_values_initialized = true;
#endif
}
} // end of namespace internal
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
void
FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,n_components_,Number>
::evaluate (const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl)
{
internal::do_evaluate (*this, evaluate_val, evaluate_grad, evaluate_lapl);
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
void
FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,n_components_,Number>
::integrate (const bool integrate_val,
const bool integrate_grad)
{
internal::do_integrate (*this, integrate_val, integrate_grad);
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
inline
Point<dim,VectorizedArray<Number> >
FEEvaluationGeneral<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 (false);
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>
template <int direction, bool dof_to_quad, bool add>
inline
void
FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,n_components_,Number>
::apply_values(const VectorizedArray<Number> in [],
VectorizedArray<Number> out [])
{
internal::apply_tensor_product<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add>
(this->data.shape_values.begin(), in, out);
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,n_components_,Number>
::apply_gradients(const VectorizedArray<Number> in [],
VectorizedArray<Number> out [])
{
internal::apply_tensor_product<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add>
(this->data.shape_gradients.begin(), in, out);
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
FEEvaluationGeneral<dim,fe_degree,n_q_points_1d,n_components_,Number>
::apply_hessians(const VectorizedArray<Number> in [],
VectorizedArray<Number> out [])
{
internal::apply_tensor_product<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add>
(this->data.shape_hessians.begin(), in, out);
}
/*-------------------------- 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)
{
// check whether element is appropriate
#ifdef DEBUG
const double zero_tol =
types_are_equal<Number,double>::value==true?1e-8:1e-7;
std::string error_message = "FEEvaluation not appropriate.\n";
error_message += " It assumes symmetry of quadrature points w.r.t. 0.5 \n";
error_message += " and the basis functions starting from left and right.\n";
error_message += "Try FEEvaluationGeneral<...> instead!";
// symmetry for values
const unsigned int n_dofs_1d = fe_degree + 1;
for (unsigned int i=0; i<(n_dofs_1d+1)/2; ++i)
for (unsigned int j=0; j<n_q_points_1d; ++j)
Assert (std::fabs(this->data.shape_values[i*n_q_points_1d+j][0] -
this->data.shape_values[(n_dofs_1d-i)*n_q_points_1d
-j-1][0]) < zero_tol,
ExcMessage(error_message));
// shape values should be zero at for all basis functions except for one
// where they are one in the middle
if (n_q_points_1d%2 == 1 && n_dofs_1d%2 == 1)
{
for (int i=0; i<static_cast<int>(n_dofs_1d/2); ++i)
Assert (std::fabs(this->data.shape_values[i*n_q_points_1d+
n_q_points_1d/2][0]) < zero_tol,
ExcMessage(error_message));
Assert (std::fabs(this->data.shape_values[(n_dofs_1d/2)*n_q_points_1d+
n_q_points_1d/2][0]-1.)< zero_tol,
ExcMessage(error_message));
}
// skew-symmetry for gradient, zero of middle basis function in middle
// quadrature point
for (unsigned int i=0; i<(n_dofs_1d+1)/2; ++i)
for (unsigned int j=0; j<n_q_points_1d; ++j)
Assert (std::fabs(this->data.shape_gradients[i*n_q_points_1d+j][0] +
this->data.shape_gradients[(n_dofs_1d-i)*n_q_points_1d-
j-1][0]) < zero_tol,
ExcMessage(error_message));
if (n_dofs_1d%2 == 1 && n_q_points_1d%2 == 1)
Assert (std::fabs(this->data.shape_gradients[(n_dofs_1d/2)*n_q_points_1d+
(n_q_points_1d/2)][0]) < zero_tol,
ExcMessage(error_message));
// symmetry for Laplacian
for (unsigned int i=0; i<(n_dofs_1d+1)/2; ++i)
for (unsigned int j=0; j<n_q_points_1d; ++j)
Assert (std::fabs(this->data.shape_hessians[i*n_q_points_1d+j][0] -
this->data.shape_hessians[(n_dofs_1d-i)*n_q_points_1d-
j-1][0]) < zero_tol,
ExcMessage(error_message));
#endif
// Compute symmetric and skew-symmetric part of shape values for even-odd
// decomposition
for (unsigned int i=0; i<(fe_degree+1)/2; ++i)
for (unsigned int q=0; q<(n_q_points_1d+1)/2; ++q)
{
shape_val_evenodd[i][q] =
0.5 * (this->data.shape_values[i*n_q_points_1d+q] +
this->data.shape_values[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_val_evenodd[fe_degree-i][q] =
0.5 * (this->data.shape_values[i*n_q_points_1d+q] -
this->data.shape_values[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_gra_evenodd[i][q] =
0.5 * (this->data.shape_gradients[i*n_q_points_1d+q] +
this->data.shape_gradients[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_gra_evenodd[fe_degree-i][q] =
0.5 * (this->data.shape_gradients[i*n_q_points_1d+q] -
this->data.shape_gradients[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_hes_evenodd[i][q] =
0.5 * (this->data.shape_hessians[i*n_q_points_1d+q] +
this->data.shape_hessians[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_hes_evenodd[fe_degree-i][q] =
0.5 * (this->data.shape_hessians[i*n_q_points_1d+q] -
this->data.shape_hessians[i*n_q_points_1d+n_q_points_1d-1-q]);
}
if (fe_degree % 2 == 0)
for (unsigned int q=0; q<(n_q_points_1d+1)/2; ++q)
{
shape_val_evenodd[fe_degree/2][q] =
this->data.shape_values[(fe_degree/2)*n_q_points_1d+q];
shape_gra_evenodd[fe_degree/2][q] =
this->data.shape_gradients[(fe_degree/2)*n_q_points_1d+q];
shape_hes_evenodd[fe_degree/2][q] =
this->data.shape_hessians[(fe_degree/2)*n_q_points_1d+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)
{
internal::do_evaluate (*this, evaluate_val, evaluate_grad, evaluate_lapl);
}
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)
{
internal::do_integrate (*this, integrate_val, integrate_grad);
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::apply_values (const VectorizedArray<Number> in [],
VectorizedArray<Number> out [])
{
// for linear elements, the even-odd decomposition is slower than the plain
// evaluation (additions to create the symmetric and anti-symmetric part),
// for all other orders, we choose even-odd
if (fe_degree > 1 || n_q_points_1d > 3)
internal::apply_tensor_product_evenodd<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add, 0>
(shape_val_evenodd, in, out);
else
internal::apply_tensor_product_values<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add>
(this->data.shape_values.begin(), in, out);
}
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::apply_gradients (const VectorizedArray<Number> in [],
VectorizedArray<Number> out [])
{
if (fe_degree > 1 || n_q_points_1d > 3)
internal::apply_tensor_product_evenodd<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add, 1>
(shape_gra_evenodd, in, out);
else
internal::apply_tensor_product_gradients<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add>
(this->data.shape_gradients.begin(), in, out);
}
// Laplacian operator application. Very similar to value application because
// the same symmetry relations hold. However, it is not possible to omit some
// values that are zero for the values
template <int dim, int fe_degree, int n_q_points_1d, int n_components_,
typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
FEEvaluation<dim,fe_degree,n_q_points_1d,n_components_,Number>
::apply_hessians (const VectorizedArray<Number> in [],
VectorizedArray<Number> out [])
{
if (fe_degree > 1 || n_q_points_1d > 3)
internal::apply_tensor_product_evenodd<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add, 2>
(shape_hes_evenodd, in, out);
else
internal::apply_tensor_product_hessians<dim,fe_degree,n_q_points_1d,
VectorizedArray<Number>, direction, dof_to_quad, add>
(this->data.shape_hessians.begin(), in, out);
}
/*------------------------- FEEvaluationGL ----------------------------------*/
template <int dim, int fe_degree, int n_components_, typename Number>
inline
FEEvaluationGL<dim,fe_degree,n_components_,Number>
::FEEvaluationGL (const MatrixFree<dim,Number> &data_in,
const unsigned int fe_no,
const unsigned int quad_no)
:
BaseClass (data_in, fe_no, quad_no)
{
#ifdef DEBUG
std::string error_mess = "FEEvaluationGL not appropriate. It assumes:\n";
error_mess += " - identity operation for shape values\n";
error_mess += " - zero diagonal at interior points for gradients\n";
error_mess += " - gradient equal to unity at element boundary\n";
error_mess += "Try FEEvaluation<...> instead!";
const double zero_tol =
types_are_equal<Number,double>::value==true?1e-9:1e-7;
const unsigned int n_points_1d = fe_degree+1;
for (unsigned int i=0; i<n_points_1d; ++i)
for (unsigned int j=0; j<n_points_1d; ++j)
if (i!=j)
{
Assert (std::fabs(this->data.shape_values[i*n_points_1d+j][0])<zero_tol,
ExcMessage (error_mess.c_str()));
}
else
{
Assert (std::fabs(this->data.shape_values[i*n_points_1d+
j][0]-1.)<zero_tol,
ExcMessage (error_mess.c_str()));
}
for (unsigned int i=1; i<n_points_1d-1; ++i)
Assert (std::fabs(this->data.shape_gradients[i*n_points_1d+i][0])<zero_tol,
ExcMessage (error_mess.c_str()));
Assert (std::fabs(this->data.shape_gradients[n_points_1d-1][0]-
(n_points_1d%2==0 ? -1. : 1.)) < zero_tol,
ExcMessage (error_mess.c_str()));
#endif
}
template <int dim, int fe_degree, int n_components_, typename Number>
inline
void
FEEvaluationGL<dim,fe_degree,n_components_,Number>
::evaluate (const bool evaluate_val,
const bool evaluate_grad,
const bool evaluate_lapl)
{
Assert (this->cell != numbers::invalid_unsigned_int,
ExcNotInitialized());
Assert (this->dof_values_initialized == true,
internal::ExcAccessToUninitializedField());
if (evaluate_val == true)
{
std::memcpy (&this->values_quad[0][0], &this->values_dofs[0][0],
dofs_per_cell * n_components *
sizeof (this->values_dofs[0][0]));
#ifdef DEBUG
this->values_quad_initialized = true;
#endif
}
// separate implementation here compared to the general case because the
// values are an identity operation
if (evaluate_grad == true)
{
for (unsigned int comp=0; comp<n_components; comp++)
{
if (dim == 3)
{
// grad x
apply_gradients<0,true,false> (this->values_dofs[comp],
this->gradients_quad[comp][0]);
// grad y
apply_gradients<1,true,false> (this->values_dofs[comp],
this->gradients_quad[comp][1]);
// grad y
apply_gradients<2,true,false> (this->values_dofs[comp],
this->gradients_quad[comp][2]);
}
else if (dim == 2)
{
// grad x
apply_gradients<0,true,false> (this->values_dofs[comp],
this->gradients_quad[comp][0]);
// grad y
apply_gradients<1,true,false> (this->values_dofs[comp],
this->gradients_quad[comp][1]);
}
else if (dim == 1)
apply_gradients<0,true,false> (this->values_dofs[comp],
this->gradients_quad[comp][0]);
}
#ifdef DEBUG
this->gradients_quad_initialized = true;
#endif
}
if (evaluate_lapl == true)
{
for (unsigned int comp=0; comp<n_components; comp++)
{
if (dim == 3)
{
// grad x
this->template apply_hessians<0,true,false> (this->values_dofs[comp],
this->hessians_quad[comp][0]);
// grad y
this->template apply_hessians<1,true,false> (this->values_dofs[comp],
this->hessians_quad[comp][1]);
// grad y
this->template apply_hessians<2,true,false> (this->values_dofs[comp],
this->hessians_quad[comp][2]);
VectorizedArray<Number> temp1[n_q_points];
// grad xy
apply_gradients<0,true,false> (this->values_dofs[comp], temp1);
apply_gradients<1,true,false> (temp1, this->hessians_quad[comp][3]);
// grad xz
apply_gradients<2,true,false> (temp1, this->hessians_quad[comp][4]);
// grad yz
apply_gradients<1,true,false> (this->values_dofs[comp], temp1);
apply_gradients<2,true,false> (temp1, this->hessians_quad[comp][5]);
}
else if (dim == 2)
{
// grad x
this->template apply_hessians<0,true,false> (this->values_dofs[comp],
this->hessians_quad[comp][0]);
// grad y
this->template apply_hessians<1,true,false> (this->values_dofs[comp],
this->hessians_quad[comp][1]);
VectorizedArray<Number> temp1[n_q_points];
// grad xy
apply_gradients<0,true,false> (this->values_dofs[comp], temp1);
apply_gradients<1,true,false> (temp1, this->hessians_quad[comp][2]);
}
else if (dim == 1)
this->template apply_hessians<0,true,false> (this->values_dofs[comp],
this->hessians_quad[comp][0]);
}
#ifdef DEBUG
this->hessians_quad_initialized = true;
#endif
}
}
template <int dim, int fe_degree, int n_components_, typename Number>
inline
void
FEEvaluationGL<dim,fe_degree,n_components_,Number>
::integrate (const bool integrate_val, const bool integrate_grad)
{
Assert (this->cell != numbers::invalid_unsigned_int,
ExcNotInitialized());
if (integrate_val == true)
Assert (this->values_quad_submitted == true,
internal::ExcAccessToUninitializedField());
if (integrate_grad == true)
Assert (this->gradients_quad_submitted == true,
internal::ExcAccessToUninitializedField());
if (integrate_val == true)
std::memcpy (&this->values_dofs[0][0], &this->values_quad[0][0],
dofs_per_cell * n_components *
sizeof (this->values_dofs[0][0]));
if (integrate_grad == true)
{
for (unsigned int comp=0; comp<n_components; comp++)
{
if (dim == 3)
{
// grad x: If integrate_val == true we have to add to the previous output
if (integrate_val == true)
apply_gradients<0, false, true> (this->gradients_quad[comp][0],
this->values_dofs[comp]);
else
apply_gradients<0, false, false> (this->gradients_quad[comp][0],
this->values_dofs[comp]);
// grad y: can sum to temporary x value in temp2
apply_gradients<1, false, true> (this->gradients_quad[comp][1],
this->values_dofs[comp]);
// grad z: can sum to temporary x and y value in output
apply_gradients<2, false, true> (this->gradients_quad[comp][2],
this->values_dofs[comp]);
}
else if (dim == 2)
{
// grad x: If integrate_val == true we have to add to the previous output
if (integrate_val == true)
apply_gradients<0, false, true> (this->gradients_quad[comp][0],
this->values_dofs[comp]);
else
apply_gradients<0, false, false> (this->gradients_quad[comp][0],
this->values_dofs[comp]);
// grad y: can sum to temporary x value in temp2
apply_gradients<1, false, true> (this->gradients_quad[comp][1],
this->values_dofs[comp]);
}
else if (dim == 1)
{
if (integrate_val == true)
apply_gradients<0, false, true> (this->gradients_quad[comp][0],
this->values_dofs[comp]);
else
apply_gradients<0, false, false> (this->gradients_quad[comp][0],
this->values_dofs[comp]);
}
}
}
#ifdef DEBUG
this->dof_values_initialized = true;
#endif
}
template <int dim, int fe_degree, int n_components_, typename Number>
template <int direction, bool dof_to_quad, bool add>
inline
void
FEEvaluationGL<dim,fe_degree,n_components_,Number>
::apply_gradients (const VectorizedArray<Number> in [],
VectorizedArray<Number> out [])
{
internal::apply_tensor_product_gradients_gl<dim,fe_degree,
VectorizedArray<Number>, direction, dof_to_quad, add>
(this->data.shape_gradients.begin(), in, out);
}
#endif // ifndef DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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