/usr/include/deal.II/matrix_free/operators.h is in libdeal.ii-dev 8.4.2-2+b1.
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//
// Copyright (C) 2011 - 2015 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__matrix_free_operators_h
#define dealii__matrix_free_operators_h
#include <deal.II/base/exceptions.h>
#include <deal.II/base/vectorization.h>
#include <deal.II/matrix_free/fe_evaluation.h>
DEAL_II_NAMESPACE_OPEN
namespace MatrixFreeOperators
{
/**
* This class implements the operation of the action of the inverse of a
* mass matrix on an element for the special case of an evaluation object
* with as many quadrature points as there are cell degrees of freedom. It
* uses algorithms from FEEvaluation and produces the exact mass matrix for
* DGQ elements. This algorithm uses tensor products of inverse 1D shape
* matrices over quadrature points, so the inverse operation is exactly as
* expensive as applying the forward operator on each cell. Of course, for
* continuous finite elements this operation does not produce the inverse of
* a mass operation as the coupling between the elements cannot be
* considered by this operation.
*
* The equation may contain variable coefficients, so the user is required
* to provide an array for the inverse of the local coefficient (this class
* provide a helper method 'fill_inverse_JxW_values' to get the inverse of a
* constant-coefficient operator).
*
* @author Martin Kronbichler, 2014
*/
template <int dim, int fe_degree, int n_components = 1, typename Number = double>
class CellwiseInverseMassMatrix
{
public:
/**
* Constructor. Initializes the shape information from the ShapeInfo field
* in the class FEEval.
*/
CellwiseInverseMassMatrix (const FEEvaluationBase<dim,n_components,Number> &fe_eval);
/**
* Applies the inverse mass matrix operation on an input array. It is
* assumed that the passed input and output arrays are of correct size,
* namely FEEval::dofs_per_cell * n_components long. The inverse of the
* local coefficient (also containing the inverse JxW values) must be
* passed as first argument. Passing more than one component in the
* coefficient is allowed.
*/
void apply(const AlignedVector<VectorizedArray<Number> > &inverse_coefficient,
const unsigned int n_actual_components,
const VectorizedArray<Number> *in_array,
VectorizedArray<Number> *out_array) const;
/**
* Fills the given array with the inverse of the JxW values, i.e., a mass
* matrix with coefficient 1. Non-unit coefficients must be multiplied (in
* inverse form) to this array.
*/
void fill_inverse_JxW_values(AlignedVector<VectorizedArray<Number> > &inverse_jxw) const;
private:
/**
* A reference to the FEEvaluation object for getting the JxW_values.
*/
const FEEvaluationBase<dim,n_components,Number> &fe_eval;
/**
* A structure to hold inverse shape functions
*/
AlignedVector<VectorizedArray<Number> > inverse_shape;
};
// ------------------------------------ inline functions ---------------------
template <int dim, int fe_degree, int n_components, typename Number>
inline
CellwiseInverseMassMatrix<dim,fe_degree,n_components,Number>
::CellwiseInverseMassMatrix (const FEEvaluationBase<dim,n_components,Number> &fe_eval)
:
fe_eval (fe_eval)
{
FullMatrix<double> shapes_1d(fe_degree+1, fe_degree+1);
for (unsigned int i=0, c=0; i<shapes_1d.m(); ++i)
for (unsigned int j=0; j<shapes_1d.n(); ++j, ++c)
shapes_1d(i,j) = fe_eval.get_shape_info().shape_values_number[c];
shapes_1d.gauss_jordan();
const unsigned int stride = (fe_degree+2)/2;
inverse_shape.resize(stride*(fe_degree+1));
for (unsigned int i=0; i<stride; ++i)
for (unsigned int q=0; q<(fe_degree+2)/2; ++q)
{
inverse_shape[i*stride+q] =
0.5 * (shapes_1d(i,q) + shapes_1d(i,fe_degree-q));
inverse_shape[(fe_degree-i)*stride+q] =
0.5 * (shapes_1d(i,q) - shapes_1d(i,fe_degree-q));
}
if (fe_degree % 2 == 0)
for (unsigned int q=0; q<(fe_degree+2)/2; ++q)
inverse_shape[fe_degree/2*stride+q] = shapes_1d(fe_degree/2,q);
}
template <int dim, int fe_degree, int n_components, typename Number>
inline
void
CellwiseInverseMassMatrix<dim,fe_degree,n_components,Number>
::fill_inverse_JxW_values(AlignedVector<VectorizedArray<Number> > &inverse_jxw) const
{
const unsigned int dofs_per_cell = Utilities::fixed_int_power<fe_degree+1,dim>::value;
Assert(inverse_jxw.size() > 0 &&
inverse_jxw.size() % dofs_per_cell == 0,
ExcMessage("Expected diagonal to be a multiple of scalar dof per cells"));
// temporarily reduce size of inverse_jxw to dofs_per_cell to get JxW values
// from fe_eval (will not reallocate any memory)
const unsigned int previous_size = inverse_jxw.size();
inverse_jxw.resize(dofs_per_cell);
fe_eval.fill_JxW_values(inverse_jxw);
// invert
inverse_jxw.resize_fast(previous_size);
for (unsigned int q=0; q<dofs_per_cell; ++q)
inverse_jxw[q] = 1./inverse_jxw[q];
// copy values to rest of vector
for (unsigned int q=dofs_per_cell; q<previous_size; )
for (unsigned int i=0; i<dofs_per_cell; ++i, ++q)
inverse_jxw[q] = inverse_jxw[i];
}
template <int dim, int fe_degree, int n_components, typename Number>
inline
void
CellwiseInverseMassMatrix<dim,fe_degree,n_components,Number>
::apply(const AlignedVector<VectorizedArray<Number> > &inverse_coefficients,
const unsigned int n_actual_components,
const VectorizedArray<Number> *in_array,
VectorizedArray<Number> *out_array) const
{
const unsigned int dofs_per_cell = Utilities::fixed_int_power<fe_degree+1,dim>::value;
Assert(inverse_coefficients.size() > 0 &&
inverse_coefficients.size() % dofs_per_cell == 0,
ExcMessage("Expected diagonal to be a multiple of scalar dof per cells"));
if (inverse_coefficients.size() != dofs_per_cell)
AssertDimension(n_actual_components * dofs_per_cell, inverse_coefficients.size());
Assert(dim == 2 || dim == 3, ExcNotImplemented());
internal::EvaluatorTensorProduct<internal::evaluate_evenodd,dim,fe_degree,
fe_degree+1, VectorizedArray<Number> >
evaluator(inverse_shape, inverse_shape, inverse_shape);
const unsigned int shift_coefficient =
inverse_coefficients.size() > dofs_per_cell ? dofs_per_cell : 0;
const VectorizedArray<Number> *inv_coefficient = &inverse_coefficients[0];
VectorizedArray<Number> temp_data_field[dofs_per_cell];
for (unsigned int d=0; d<n_actual_components; ++d)
{
const VectorizedArray<Number> *in = in_array+d*dofs_per_cell;
VectorizedArray<Number> *out = out_array+d*dofs_per_cell;
// Need to select 'apply' method with hessian slot because values
// assume symmetries that do not exist in the inverse shapes
evaluator.template hessians<0,false,false> (in, temp_data_field);
evaluator.template hessians<1,false,false> (temp_data_field, out);
if (dim == 3)
{
evaluator.template hessians<2,false,false> (out, temp_data_field);
for (unsigned int q=0; q<dofs_per_cell; ++q)
temp_data_field[q] *= inv_coefficient[q];
evaluator.template hessians<2,true,false> (temp_data_field, out);
}
else if (dim == 2)
for (unsigned int q=0; q<dofs_per_cell; ++q)
out[q] *= inv_coefficient[q];
evaluator.template hessians<1,true,false>(out, temp_data_field);
evaluator.template hessians<0,true,false>(temp_data_field, out);
inv_coefficient += shift_coefficient;
}
}
} // end of namespace MatrixFreeOperators
DEAL_II_NAMESPACE_CLOSE
#endif
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