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evaluation_kernels.h
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evaluation_kernels.h
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// ---------------------------------------------------------------------
//
// Copyright (C) 2017 - 2021 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.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------
#ifndef dealii_matrix_free_evaluation_kernels_h
#define dealii_matrix_free_evaluation_kernels_h
#include <deal.II/base/config.h>
#include <deal.II/base/utilities.h>
#include <deal.II/base/vectorization.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/matrix_free/dof_info.h>
#include <deal.II/matrix_free/evaluation_flags.h>
#include <deal.II/matrix_free/fe_evaluation_data.h>
#include <deal.II/matrix_free/hanging_nodes_internal.h>
#include <deal.II/matrix_free/shape_info.h>
#include <deal.II/matrix_free/tensor_product_kernels.h>
DEAL_II_NAMESPACE_OPEN
namespace internal
{
// Select evaluator type from element shape function type
template <MatrixFreeFunctions::ElementType element, bool is_long>
struct EvaluatorSelector
{};
template <bool is_long>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_general, is_long>
{
static const EvaluatorVariant variant = evaluate_general;
};
template <>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric, false>
{
static const EvaluatorVariant variant = evaluate_symmetric;
};
template <>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric, true>
{
static const EvaluatorVariant variant = evaluate_evenodd;
};
template <bool is_long>
struct EvaluatorSelector<MatrixFreeFunctions::truncated_tensor, is_long>
{
static const EvaluatorVariant variant = evaluate_general;
};
template <>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric_plus_dg0,
false>
{
static const EvaluatorVariant variant = evaluate_general;
};
template <>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric_plus_dg0, true>
{
static const EvaluatorVariant variant = evaluate_evenodd;
};
template <bool is_long>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_symmetric_collocation,
is_long>
{
static const EvaluatorVariant variant = evaluate_evenodd;
};
template <bool is_long>
struct EvaluatorSelector<MatrixFreeFunctions::tensor_raviart_thomas, is_long>
{
static const EvaluatorVariant variant = evaluate_raviart_thomas;
};
/**
* This struct performs the evaluation of function values, gradients and
* Hessians for tensor-product finite elements. The operation is used for
* both the symmetric and non-symmetric case, which use different apply
* functions 'values', 'gradients' in the individual coordinate
* directions. The apply functions for values are provided through one of
* the template classes EvaluatorTensorProduct which in turn are selected
* from the MatrixFreeFunctions::ElementType template argument.
*
* There are two specialized implementation classes
* FEEvaluationImplCollocation (for Gauss-Lobatto elements where the nodal
* points and the quadrature points coincide and the 'values' operation is
* identity) and FEEvaluationImplTransformToCollocation (which can be
* transformed to a collocation space and can then use the identity in these
* spaces), which both allow for shorter code.
*/
template <MatrixFreeFunctions::ElementType type,
int dim,
int fe_degree,
int n_q_points_1d,
typename Number>
struct FEEvaluationImpl
{
static const EvaluatorVariant variant =
EvaluatorSelector<type, (fe_degree + n_q_points_1d > 4)>::variant;
using Eval = EvaluatorTensorProduct<variant,
dim,
fe_degree + 1,
n_q_points_1d,
Number>;
static void
evaluate(const unsigned int n_components,
const EvaluationFlags::EvaluationFlags evaluation_flag,
const Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval);
static void
integrate(const unsigned int n_components,
const EvaluationFlags::EvaluationFlags integration_flag,
Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval,
const bool add_into_values_array);
static Eval
create_evaluator_tensor_product(
const MatrixFreeFunctions::UnivariateShapeData<Number>
*univariate_shape_data)
{
if (variant == evaluate_evenodd)
return Eval(univariate_shape_data->shape_values_eo,
univariate_shape_data->shape_gradients_eo,
univariate_shape_data->shape_hessians_eo,
univariate_shape_data->fe_degree + 1,
univariate_shape_data->n_q_points_1d);
else
return Eval(univariate_shape_data->shape_values,
univariate_shape_data->shape_gradients,
univariate_shape_data->shape_hessians,
univariate_shape_data->fe_degree + 1,
univariate_shape_data->n_q_points_1d);
}
};
/**
* Specialization for MatrixFreeFunctions::tensor_none, which cannot use the
* sum-factorization kernels.
*/
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
struct FEEvaluationImpl<MatrixFreeFunctions::tensor_none,
dim,
fe_degree,
n_q_points_1d,
Number>
{
static void
evaluate(const unsigned int n_components,
const EvaluationFlags::EvaluationFlags evaluation_flag,
const Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval);
static void
integrate(const unsigned int n_components,
const EvaluationFlags::EvaluationFlags integration_flag,
Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval,
const bool add_into_values_array);
};
/**
* Specialization for MatrixFreeFunctions::tensor_raviart_thomas, which use
* specific sum-factorization kernels and with normal/tangential shape_data
*/
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
struct FEEvaluationImpl<MatrixFreeFunctions::tensor_raviart_thomas,
dim,
fe_degree,
n_q_points_1d,
Number>
{
using EvalNormal =
EvaluatorTensorProduct<evaluate_raviart_thomas,
dim,
(fe_degree == -1) ? 1 : fe_degree + 1,
n_q_points_1d,
Number>;
using EvalTangent =
EvaluatorTensorProduct<evaluate_raviart_thomas,
dim,
(fe_degree == -1) ? 1 : fe_degree,
n_q_points_1d,
Number>;
template <bool integrate>
static void
evaluate_or_integrate(
const EvaluationFlags::EvaluationFlags evaluation_flag,
Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval,
const bool add_into_values_array = false);
private:
template <typename EvalType>
static EvalType
create_evaluator_tensor_product(
const MatrixFreeFunctions::ShapeInfo<Number> &shape_info)
{
// Shape_data is of size 2 with normal direction in [0] and tangential
// direction in [1]. See shape_info.template.h
const MatrixFreeFunctions::UnivariateShapeData<Number> *shape_data;
if (std::is_same<EvalType, EvalNormal>::value)
{
shape_data = &shape_info.data[0];
}
else
{
shape_data = &shape_info.data[1];
}
return EvalType(shape_data->shape_values,
shape_data->shape_gradients,
shape_data->shape_hessians);
}
template <int normal_dir, bool integrate>
static void
evaluate_tensor_product_per_component(
const EvaluationFlags::EvaluationFlags evaluation_flag,
Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval,
const bool add_into_values_array = false);
};
template <MatrixFreeFunctions::ElementType type,
int dim,
int fe_degree,
int n_q_points_1d,
typename Number>
inline void
FEEvaluationImpl<type, dim, fe_degree, n_q_points_1d, Number>::evaluate(
const unsigned int n_components,
const EvaluationFlags::EvaluationFlags evaluation_flag,
const Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval)
{
if (evaluation_flag == EvaluationFlags::nothing)
return;
std::array<const MatrixFreeFunctions::UnivariateShapeData<Number> *, 3>
univariate_shape_data;
const auto &shape_data = fe_eval.get_shape_info().data;
univariate_shape_data.fill(&shape_data.front());
if (shape_data.size() == dim)
for (int i = 1; i < dim; ++i)
univariate_shape_data[i] = &shape_data[i];
Eval eval0 = create_evaluator_tensor_product(univariate_shape_data[0]);
Eval eval1 = create_evaluator_tensor_product(univariate_shape_data[1]);
Eval eval2 = create_evaluator_tensor_product(univariate_shape_data[2]);
const unsigned int temp_size =
Eval::n_rows_of_product == numbers::invalid_unsigned_int ?
0 :
(Eval::n_rows_of_product > Eval::n_columns_of_product ?
Eval::n_rows_of_product :
Eval::n_columns_of_product);
Number *temp1 = fe_eval.get_scratch_data().begin();
Number *temp2;
if (temp_size == 0)
{
temp2 = temp1 + std::max(Utilities::fixed_power<dim>(
shape_data.front().fe_degree + 1),
Utilities::fixed_power<dim>(
shape_data.front().n_q_points_1d));
}
else
{
temp2 = temp1 + temp_size;
}
const std::size_t n_q_points = temp_size == 0 ?
fe_eval.get_shape_info().n_q_points :
Eval::n_columns_of_product;
const std::size_t dofs_per_comp =
(type == MatrixFreeFunctions::truncated_tensor) ?
Utilities::pow(shape_data.front().fe_degree + 1, dim) :
fe_eval.get_shape_info().dofs_per_component_on_cell;
const Number *values_dofs = values_dofs_actual;
if (type == MatrixFreeFunctions::truncated_tensor)
{
const std::size_t n_dofs_per_comp =
fe_eval.get_shape_info().dofs_per_component_on_cell;
Number *values_dofs_tmp =
temp1 + 2 * (std::max(n_dofs_per_comp, n_q_points));
const int degree =
fe_degree != -1 ? fe_degree : shape_data.front().fe_degree;
for (unsigned int c = 0; c < n_components; ++c)
for (int i = 0, count_p = 0, count_q = 0;
i < (dim > 2 ? degree + 1 : 1);
++i)
{
for (int j = 0; j < (dim > 1 ? degree + 1 - i : 1); ++j)
{
for (int k = 0; k < degree + 1 - j - i;
++k, ++count_p, ++count_q)
values_dofs_tmp[c * dofs_per_comp + count_q] =
values_dofs_actual[c * n_dofs_per_comp + count_p];
for (int k = degree + 1 - j - i; k < degree + 1;
++k, ++count_q)
values_dofs_tmp[c * dofs_per_comp + count_q] = Number();
}
for (int j = degree + 1 - i; j < degree + 1; ++j)
for (int k = 0; k < degree + 1; ++k, ++count_q)
values_dofs_tmp[c * dofs_per_comp + count_q] = Number();
}
values_dofs = values_dofs_tmp;
}
Number *values_quad = fe_eval.begin_values();
Number *gradients_quad = fe_eval.begin_gradients();
Number *hessians_quad = fe_eval.begin_hessians();
switch (dim)
{
case 1:
for (unsigned int c = 0; c < n_components; ++c)
{
if (evaluation_flag & EvaluationFlags::values)
eval0.template values<0, true, false>(values_dofs, values_quad);
if (evaluation_flag & EvaluationFlags::gradients)
eval0.template gradients<0, true, false>(values_dofs,
gradients_quad);
if (evaluation_flag & EvaluationFlags::hessians)
eval0.template hessians<0, true, false>(values_dofs,
hessians_quad);
// advance the next component in 1D array
values_dofs += dofs_per_comp;
values_quad += n_q_points;
gradients_quad += n_q_points;
hessians_quad += n_q_points;
}
break;
case 2:
for (unsigned int c = 0; c < n_components; ++c)
{
// grad x
if (evaluation_flag & EvaluationFlags::gradients)
{
eval0.template gradients<0, true, false>(values_dofs, temp1);
eval1.template values<1, true, false>(temp1, gradients_quad);
}
if (evaluation_flag & EvaluationFlags::hessians)
{
// grad xy
if (!(evaluation_flag & EvaluationFlags::gradients))
eval0.template gradients<0, true, false>(values_dofs,
temp1);
eval1.template gradients<1, true, false>(temp1,
hessians_quad +
2 * n_q_points);
// grad xx
eval0.template hessians<0, true, false>(values_dofs, temp1);
eval1.template values<1, true, false>(temp1, hessians_quad);
}
// grad y
eval0.template values<0, true, false>(values_dofs, temp1);
if (evaluation_flag & EvaluationFlags::gradients)
eval1.template gradients<1, true, false>(temp1,
gradients_quad +
n_q_points);
// grad yy
if (evaluation_flag & EvaluationFlags::hessians)
eval1.template hessians<1, true, false>(temp1,
hessians_quad +
n_q_points);
// val: can use values applied in x
if (evaluation_flag & EvaluationFlags::values)
eval1.template values<1, true, false>(temp1, values_quad);
// advance to the next component in 1D array
values_dofs += dofs_per_comp;
values_quad += n_q_points;
gradients_quad += 2 * n_q_points;
hessians_quad += 3 * n_q_points;
}
break;
case 3:
for (unsigned int c = 0; c < n_components; ++c)
{
if (evaluation_flag & EvaluationFlags::gradients)
{
// grad x
eval0.template gradients<0, true, false>(values_dofs, temp1);
eval1.template values<1, true, false>(temp1, temp2);
eval2.template values<2, true, false>(temp2, gradients_quad);
}
if (evaluation_flag & EvaluationFlags::hessians)
{
// grad xz
if (!(evaluation_flag & EvaluationFlags::gradients))
{
eval0.template gradients<0, true, false>(values_dofs,
temp1);
eval1.template values<1, true, false>(temp1, temp2);
}
eval2.template gradients<2, true, false>(temp2,
hessians_quad +
4 * n_q_points);
// grad xy
eval1.template gradients<1, true, false>(temp1, temp2);
eval2.template values<2, true, false>(temp2,
hessians_quad +
3 * n_q_points);
// grad xx
eval0.template hessians<0, true, false>(values_dofs, temp1);
eval1.template values<1, true, false>(temp1, temp2);
eval2.template values<2, true, false>(temp2, hessians_quad);
}
// grad y
eval0.template values<0, true, false>(values_dofs, temp1);
if (evaluation_flag & EvaluationFlags::gradients)
{
eval1.template gradients<1, true, false>(temp1, temp2);
eval2.template values<2, true, false>(temp2,
gradients_quad +
n_q_points);
}
if (evaluation_flag & EvaluationFlags::hessians)
{
// grad yz
if (!(evaluation_flag & EvaluationFlags::gradients))
eval1.template gradients<1, true, false>(temp1, temp2);
eval2.template gradients<2, true, false>(temp2,
hessians_quad +
5 * n_q_points);
// grad yy
eval1.template hessians<1, true, false>(temp1, temp2);
eval2.template values<2, true, false>(temp2,
hessians_quad +
n_q_points);
}
// grad z: can use the values applied in x direction stored in
// temp1
eval1.template values<1, true, false>(temp1, temp2);
if (evaluation_flag & EvaluationFlags::gradients)
eval2.template gradients<2, true, false>(temp2,
gradients_quad +
2 * n_q_points);
// grad zz: can use the values applied in x and y direction stored
// in temp2
if (evaluation_flag & EvaluationFlags::hessians)
eval2.template hessians<2, true, false>(temp2,
hessians_quad +
2 * n_q_points);
// val: can use the values applied in x & y direction stored in
// temp2
if (evaluation_flag & EvaluationFlags::values)
eval2.template values<2, true, false>(temp2, values_quad);
// advance to the next component in 1D array
values_dofs += dofs_per_comp;
values_quad += n_q_points;
gradients_quad += 3 * n_q_points;
hessians_quad += 6 * n_q_points;
}
break;
default:
AssertThrow(false, ExcNotImplemented());
}
// case additional dof for FE_Q_DG0: add values; gradients and second
// derivatives evaluate to zero
if (type == MatrixFreeFunctions::tensor_symmetric_plus_dg0 &&
(evaluation_flag & EvaluationFlags::values))
{
values_quad -= n_components * n_q_points;
values_dofs -= n_components * dofs_per_comp;
for (std::size_t c = 0; c < n_components; ++c)
for (std::size_t q = 0; q < n_q_points; ++q)
values_quad[c * n_q_points + q] +=
values_dofs[(c + 1) * dofs_per_comp - 1];
}
}
template <MatrixFreeFunctions::ElementType type,
int dim,
int fe_degree,
int n_q_points_1d,
typename Number>
inline void
FEEvaluationImpl<type, dim, fe_degree, n_q_points_1d, Number>::integrate(
const unsigned int n_components,
const EvaluationFlags::EvaluationFlags integration_flag,
Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval,
const bool add_into_values_array)
{
std::array<const MatrixFreeFunctions::UnivariateShapeData<Number> *, 3>
univariate_shape_data;
const auto &shape_data = fe_eval.get_shape_info().data;
univariate_shape_data.fill(&shape_data.front());
if (shape_data.size() == dim)
for (int i = 1; i < dim; ++i)
univariate_shape_data[i] = &shape_data[i];
Eval eval0 = create_evaluator_tensor_product(univariate_shape_data[0]);
Eval eval1 = create_evaluator_tensor_product(univariate_shape_data[1]);
Eval eval2 = create_evaluator_tensor_product(univariate_shape_data[2]);
const unsigned int temp_size =
Eval::n_rows_of_product == numbers::invalid_unsigned_int ?
0 :
(Eval::n_rows_of_product > Eval::n_columns_of_product ?
Eval::n_rows_of_product :
Eval::n_columns_of_product);
Number *temp1 = fe_eval.get_scratch_data().begin();
Number *temp2;
if (temp_size == 0)
{
temp2 = temp1 + std::max(Utilities::fixed_power<dim>(
shape_data.front().fe_degree + 1),
Utilities::fixed_power<dim>(
shape_data.front().n_q_points_1d));
}
else
{
temp2 = temp1 + temp_size;
}
const std::size_t n_q_points = temp_size == 0 ?
fe_eval.get_shape_info().n_q_points :
Eval::n_columns_of_product;
const unsigned int dofs_per_comp =
(type == MatrixFreeFunctions::truncated_tensor) ?
Utilities::fixed_power<dim>(shape_data.front().fe_degree + 1) :
fe_eval.get_shape_info().dofs_per_component_on_cell;
// expand dof_values to tensor product for truncated tensor products
Number *values_dofs =
(type == MatrixFreeFunctions::truncated_tensor) ?
temp1 + 2 * (std::max<std::size_t>(
fe_eval.get_shape_info().dofs_per_component_on_cell,
n_q_points)) :
values_dofs_actual;
Number *values_quad = fe_eval.begin_values();
Number *gradients_quad = fe_eval.begin_gradients();
Number *hessians_quad = fe_eval.begin_hessians();
switch (dim)
{
case 1:
for (unsigned int c = 0; c < n_components; ++c)
{
if (integration_flag & EvaluationFlags::values)
{
if (add_into_values_array == false)
eval0.template values<0, false, false>(values_quad,
values_dofs);
else
eval0.template values<0, false, true>(values_quad,
values_dofs);
}
if (integration_flag & EvaluationFlags::gradients)
{
if (integration_flag & EvaluationFlags::values ||
add_into_values_array == true)
eval0.template gradients<0, false, true>(gradients_quad,
values_dofs);
else
eval0.template gradients<0, false, false>(gradients_quad,
values_dofs);
}
if ((integration_flag & EvaluationFlags::hessians) != 0u)
{
if ((integration_flag & EvaluationFlags::values) != 0u ||
(integration_flag & EvaluationFlags::gradients) != 0u ||
add_into_values_array == true)
eval0.template hessians<0, false, true>(hessians_quad,
values_dofs);
else
eval0.template hessians<0, false, false>(hessians_quad,
values_dofs);
}
// advance to the next component in 1D array
values_dofs += dofs_per_comp;
values_quad += n_q_points;
gradients_quad += n_q_points;
hessians_quad += n_q_points;
}
break;
case 2:
for (unsigned int c = 0; c < n_components; ++c)
{
if ((integration_flag & EvaluationFlags::values) &&
!(integration_flag & EvaluationFlags::gradients))
{
eval1.template values<1, false, false>(values_quad, temp1);
if (add_into_values_array == false)
eval0.template values<0, false, false>(temp1, values_dofs);
else
eval0.template values<0, false, true>(temp1, values_dofs);
}
if (integration_flag & EvaluationFlags::gradients)
{
eval1.template gradients<1, false, false>(gradients_quad +
n_q_points,
temp1);
if (integration_flag & EvaluationFlags::values)
eval1.template values<1, false, true>(values_quad, temp1);
if (add_into_values_array == false)
eval0.template values<0, false, false>(temp1, values_dofs);
else
eval0.template values<0, false, true>(temp1, values_dofs);
eval1.template values<1, false, false>(gradients_quad, temp1);
eval0.template gradients<0, false, true>(temp1, values_dofs);
}
if ((integration_flag & EvaluationFlags::hessians) != 0u)
{
// grad xx
eval1.template values<1, false, false>(hessians_quad, temp1);
if ((integration_flag & EvaluationFlags::values) != 0u ||
(integration_flag & EvaluationFlags::gradients) != 0u ||
add_into_values_array == true)
eval0.template hessians<0, false, true>(temp1, values_dofs);
else
eval0.template hessians<0, false, false>(temp1,
values_dofs);
// grad yy
eval1.template hessians<1, false, false>(hessians_quad +
n_q_points,
temp1);
eval0.template values<0, false, true>(temp1, values_dofs);
// grad xy
eval1.template gradients<1, false, false>(hessians_quad +
2 * n_q_points,
temp1);
eval0.template gradients<0, false, true>(temp1, values_dofs);
}
// advance to the next component in 1D array
values_dofs += dofs_per_comp;
values_quad += n_q_points;
gradients_quad += 2 * n_q_points;
hessians_quad += 3 * n_q_points;
}
break;
case 3:
for (unsigned int c = 0; c < n_components; ++c)
{
if ((integration_flag & EvaluationFlags::values) &&
!(integration_flag & EvaluationFlags::gradients))
{
eval2.template values<2, false, false>(values_quad, temp1);
eval1.template values<1, false, false>(temp1, temp2);
if (add_into_values_array == false)
eval0.template values<0, false, false>(temp2, values_dofs);
else
eval0.template values<0, false, true>(temp2, values_dofs);
}
if (integration_flag & EvaluationFlags::gradients)
{
eval2.template gradients<2, false, false>(gradients_quad +
2 * n_q_points,
temp1);
if (integration_flag & EvaluationFlags::values)
eval2.template values<2, false, true>(values_quad, temp1);
eval1.template values<1, false, false>(temp1, temp2);
eval2.template values<2, false, false>(gradients_quad +
n_q_points,
temp1);
eval1.template gradients<1, false, true>(temp1, temp2);
if (add_into_values_array == false)
eval0.template values<0, false, false>(temp2, values_dofs);
else
eval0.template values<0, false, true>(temp2, values_dofs);
eval2.template values<2, false, false>(gradients_quad, temp1);
eval1.template values<1, false, false>(temp1, temp2);
eval0.template gradients<0, false, true>(temp2, values_dofs);
}
if ((integration_flag & EvaluationFlags::hessians) != 0u)
{
// grad xx
eval2.template values<2, false, false>(hessians_quad, temp1);
eval1.template values<1, false, false>(temp1, temp2);
if ((integration_flag & EvaluationFlags::values) != 0u ||
(integration_flag & EvaluationFlags::gradients) != 0u ||
add_into_values_array == true)
eval0.template hessians<0, false, true>(temp2, values_dofs);
else
eval0.template hessians<0, false, false>(temp2,
values_dofs);
// grad yy
eval2.template values<2, false, false>(hessians_quad +
n_q_points,
temp1);
eval1.template hessians<1, false, false>(temp1, temp2);
eval0.template values<0, false, true>(temp2, values_dofs);
// grad zz
eval2.template hessians<2, false, false>(hessians_quad +
2 * n_q_points,
temp1);
eval1.template values<1, false, false>(temp1, temp2);
eval0.template values<0, false, true>(temp2, values_dofs);
// grad xy
eval2.template values<2, false, false>(hessians_quad +
3 * n_q_points,
temp1);
eval1.template gradients<1, false, false>(temp1, temp2);
eval0.template gradients<0, false, true>(temp2, values_dofs);
// grad xz
eval2.template gradients<2, false, false>(hessians_quad +
4 * n_q_points,
temp1);
eval1.template values<1, false, false>(temp1, temp2);
eval0.template gradients<0, false, true>(temp2, values_dofs);
// grad yz
eval2.template gradients<2, false, false>(hessians_quad +
5 * n_q_points,
temp1);
eval1.template gradients<1, false, false>(temp1, temp2);
eval0.template values<0, false, true>(temp2, values_dofs);
}
// advance to the next component in 1D array
values_dofs += dofs_per_comp;
values_quad += n_q_points;
gradients_quad += 3 * n_q_points;
hessians_quad += 6 * n_q_points;
}
break;
default:
AssertThrow(false, ExcNotImplemented());
}
// case FE_Q_DG0: add values, gradients and second derivatives are zero
if (type == MatrixFreeFunctions::tensor_symmetric_plus_dg0)
{
values_dofs -= n_components * dofs_per_comp - dofs_per_comp + 1;
values_quad -= n_components * n_q_points;
if (integration_flag & EvaluationFlags::values)
for (unsigned int c = 0; c < n_components; ++c)
{
values_dofs[0] = values_quad[0];
for (unsigned int q = 1; q < n_q_points; ++q)
values_dofs[0] += values_quad[q];
values_dofs += dofs_per_comp;
values_quad += n_q_points;
}
else
{
for (unsigned int c = 0; c < n_components; ++c)
values_dofs[c * dofs_per_comp] = Number();
values_dofs += n_components * dofs_per_comp;
}
}
if (type == MatrixFreeFunctions::truncated_tensor)
{
const std::size_t n_dofs_per_comp =
fe_eval.get_shape_info().dofs_per_component_on_cell;
values_dofs -= dofs_per_comp * n_components;
const int degree =
fe_degree != -1 ? fe_degree : shape_data.front().fe_degree;
for (unsigned int c = 0; c < n_components; ++c)
for (int i = 0, count_p = 0, count_q = 0;
i < (dim > 2 ? degree + 1 : 1);
++i)
{
for (int j = 0; j < (dim > 1 ? degree + 1 - i : 1); ++j)
{
for (int k = 0; k < degree + 1 - j - i;
++k, ++count_p, ++count_q)
values_dofs_actual[c * n_dofs_per_comp + count_p] =
values_dofs[c * dofs_per_comp + count_q];
count_q += j + i;
}
count_q += i * (degree + 1);
}
}
}
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
inline void
FEEvaluationImpl<
MatrixFreeFunctions::tensor_none,
dim,
fe_degree,
n_q_points_1d,
Number>::evaluate(const unsigned int n_components,
const EvaluationFlags::EvaluationFlags evaluation_flag,
const Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> & fe_eval)
{
const std::size_t n_dofs =
fe_eval.get_shape_info().dofs_per_component_on_cell;
const std::size_t n_q_points = fe_eval.get_shape_info().n_q_points;
const auto &shape_data = fe_eval.get_shape_info().data;
using Eval =
EvaluatorTensorProduct<evaluate_general, 1, 0, 0, Number, Number>;
if (evaluation_flag & EvaluationFlags::values)
{
const auto shape_values = shape_data.front().shape_values.data();
auto values_quad_ptr = fe_eval.begin_values();
auto values_dofs_actual_ptr = values_dofs_actual;
Eval eval(shape_values, nullptr, nullptr, n_dofs, n_q_points);
for (unsigned int c = 0; c < n_components; ++c)
{
eval.template values<0, true, false>(values_dofs_actual_ptr,
values_quad_ptr);
values_quad_ptr += n_q_points;
values_dofs_actual_ptr += n_dofs;
}
}
if (evaluation_flag & EvaluationFlags::gradients)
{
const auto shape_gradients = shape_data.front().shape_gradients.data();
auto gradients_quad_ptr = fe_eval.begin_gradients();
auto values_dofs_actual_ptr = values_dofs_actual;
for (unsigned int c = 0; c < n_components; ++c)
{
for (unsigned int d = 0; d < dim; ++d)
{
Eval eval(nullptr,
shape_gradients + n_q_points * n_dofs * d,
nullptr,
n_dofs,
n_q_points);
eval.template gradients<0, true, false>(values_dofs_actual_ptr,
gradients_quad_ptr);
gradients_quad_ptr += n_q_points;
}
values_dofs_actual_ptr += n_dofs;
}
}
if (evaluation_flag & EvaluationFlags::hessians)
Assert(false, ExcNotImplemented());
}
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
inline void
FEEvaluationImpl<
MatrixFreeFunctions::tensor_none,
dim,
fe_degree,
n_q_points_1d,
Number>::integrate(const unsigned int n_components,
const EvaluationFlags::EvaluationFlags integration_flag,
Number * values_dofs_actual,
FEEvaluationData<dim, Number, false> &fe_eval,
const bool add_into_values_array)
{
// TODO: implement hessians
AssertThrow(!(integration_flag & EvaluationFlags::hessians),
ExcNotImplemented());
const std::size_t n_dofs =
fe_eval.get_shape_info().dofs_per_component_on_cell;
const std::size_t n_q_points = fe_eval.get_shape_info().n_q_points;
const auto &shape_data = fe_eval.get_shape_info().data;
using Eval =
EvaluatorTensorProduct<evaluate_general, 1, 0, 0, Number, Number>;
if (integration_flag & EvaluationFlags::values)
{
const auto shape_values = shape_data.front().shape_values.data();
auto values_quad_ptr = fe_eval.begin_values();
auto values_dofs_actual_ptr = values_dofs_actual;
Eval eval(shape_values, nullptr, nullptr, n_dofs, n_q_points);
for (unsigned int c = 0; c < n_components; ++c)
{
if (add_into_values_array == false)
eval.template values<0, false, false>(values_quad_ptr,
values_dofs_actual_ptr);
else
eval.template values<0, false, true>(values_quad_ptr,
values_dofs_actual_ptr);
values_quad_ptr += n_q_points;
values_dofs_actual_ptr += n_dofs;
}
}
if (integration_flag & EvaluationFlags::gradients)
{
const auto shape_gradients = shape_data.front().shape_gradients.data();
auto gradients_quad_ptr = fe_eval.begin_gradients();
auto values_dofs_actual_ptr = values_dofs_actual;
for (unsigned int c = 0; c < n_components; ++c)
{
for (unsigned int d = 0; d < dim; ++d)
{
Eval eval(nullptr,
shape_gradients + n_q_points * n_dofs * d,
nullptr,
n_dofs,
n_q_points);
if ((add_into_values_array == false &&
!(integration_flag & EvaluationFlags::values)) &&
d == 0)
eval.template gradients<0, false, false>(
gradients_quad_ptr, values_dofs_actual_ptr);
else
eval.template gradients<0, false, true>(
gradients_quad_ptr, values_dofs_actual_ptr);
gradients_quad_ptr += n_q_points;
}
values_dofs_actual_ptr += n_dofs;
}
}
}
template <int dim, int fe_degree, int n_q_points_1d, typename Number>
template <bool integrate>
inline void
FEEvaluationImpl<MatrixFreeFunctions::tensor_raviart_thomas,
dim,
fe_degree,
n_q_points_1d,
Number>::
evaluate_or_integrate(
const EvaluationFlags::EvaluationFlags evaluation_flag,
Number * values_dofs_actual,