/
mapping_fe_field.cc
2428 lines (2129 loc) · 95 KB
/
mapping_fe_field.cc
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// ---------------------------------------------------------------------
//
// Copyright (C) 2001 - 2019 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.
//
// ---------------------------------------------------------------------
#include <deal.II/base/array_view.h>
#include <deal.II/base/memory_consumption.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/qprojector.h>
#include <deal.II/base/quadrature.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/std_cxx14/memory.h>
#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/base/utilities.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_system.h>
#include <deal.II/fe/fe_tools.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/fe/mapping.h>
#include <deal.II/fe/mapping_fe_field.h>
#include <deal.II/fe/mapping_q1.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/lac/block_vector.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/lac/la_parallel_block_vector.h>
#include <deal.II/lac/la_parallel_vector.h>
#include <deal.II/lac/la_vector.h>
#include <deal.II/lac/petsc_block_vector.h>
#include <deal.II/lac/petsc_vector.h>
#include <deal.II/lac/trilinos_epetra_vector.h>
#include <deal.II/lac/trilinos_parallel_block_vector.h>
#include <deal.II/lac/trilinos_tpetra_vector.h>
#include <deal.II/lac/trilinos_vector.h>
#include <deal.II/lac/vector.h>
#include <deal.II/numerics/vector_tools.h>
#include <fstream>
#include <memory>
#include <numeric>
DEAL_II_NAMESPACE_OPEN
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::InternalData::
InternalData(const FiniteElement<dim, spacedim> &fe,
const ComponentMask & mask)
: unit_tangentials()
, n_shape_functions(fe.dofs_per_cell)
, mask(mask)
, local_dof_indices(fe.dofs_per_cell)
, local_dof_values(fe.dofs_per_cell)
{}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
std::size_t
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::InternalData::
memory_consumption() const
{
Assert(false, ExcNotImplemented());
return 0;
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
double &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::shape(
const unsigned int qpoint,
const unsigned int shape_nr)
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr, shape_values.size());
return shape_values[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
const Tensor<1, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
derivative(const unsigned int qpoint, const unsigned int shape_nr) const
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_derivatives.size());
return shape_derivatives[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
Tensor<1, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
derivative(const unsigned int qpoint, const unsigned int shape_nr)
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_derivatives.size());
return shape_derivatives[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
const Tensor<2, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
second_derivative(const unsigned int qpoint,
const unsigned int shape_nr) const
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_second_derivatives.size());
return shape_second_derivatives[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
Tensor<2, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
second_derivative(const unsigned int qpoint, const unsigned int shape_nr)
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_second_derivatives.size());
return shape_second_derivatives[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
const Tensor<3, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
third_derivative(const unsigned int qpoint, const unsigned int shape_nr) const
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_third_derivatives.size());
return shape_third_derivatives[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
Tensor<3, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
third_derivative(const unsigned int qpoint, const unsigned int shape_nr)
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_third_derivatives.size());
return shape_third_derivatives[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
const Tensor<4, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
fourth_derivative(const unsigned int qpoint,
const unsigned int shape_nr) const
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_fourth_derivatives.size());
return shape_fourth_derivatives[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename DoFHandlerType, typename VectorType>
Tensor<4, dim> &
MappingFEField<dim, spacedim, DoFHandlerType, VectorType>::InternalData::
fourth_derivative(const unsigned int qpoint, const unsigned int shape_nr)
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr,
shape_fourth_derivatives.size());
return shape_fourth_derivatives[qpoint * n_shape_functions + shape_nr];
}
namespace
{
// Construct a quadrature formula containing the vertices of the reference
// cell in dimension dim (with invalid weights)
template <int dim>
Quadrature<dim> &
get_vertex_quadrature()
{
static Quadrature<dim> quad;
if (quad.size() == 0)
{
std::vector<Point<dim>> points(GeometryInfo<dim>::vertices_per_cell);
for (unsigned int i = 0; i < GeometryInfo<dim>::vertices_per_cell; ++i)
points[i] = GeometryInfo<dim>::unit_cell_vertex(i);
quad = Quadrature<dim>(points);
}
return quad;
}
} // namespace
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::MappingFEField(
const DoFHandlerType &euler_dof_handler,
const VectorType & euler_vector,
const ComponentMask & mask)
: uses_level_dofs(false)
, euler_vector({&euler_vector})
, euler_dof_handler(&euler_dof_handler)
, fe_mask(mask.size() ?
mask :
ComponentMask(
euler_dof_handler.get_fe().get_nonzero_components(0).size(),
true))
, fe_to_real(fe_mask.size(), numbers::invalid_unsigned_int)
, fe_values(this->euler_dof_handler->get_fe(),
get_vertex_quadrature<dim>(),
update_values)
{
unsigned int size = 0;
for (unsigned int i = 0; i < fe_mask.size(); ++i)
{
if (fe_mask[i])
fe_to_real[i] = size++;
}
AssertDimension(size, spacedim);
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::MappingFEField(
const DoFHandlerType & euler_dof_handler,
const std::vector<VectorType> &euler_vector,
const ComponentMask & mask)
: uses_level_dofs(true)
, euler_dof_handler(&euler_dof_handler)
, fe_mask(mask.size() ?
mask :
ComponentMask(
euler_dof_handler.get_fe().get_nonzero_components(0).size(),
true))
, fe_to_real(fe_mask.size(), numbers::invalid_unsigned_int)
, fe_values(this->euler_dof_handler->get_fe(),
get_vertex_quadrature<dim>(),
update_values)
{
unsigned int size = 0;
for (unsigned int i = 0; i < fe_mask.size(); ++i)
{
if (fe_mask[i])
fe_to_real[i] = size++;
}
AssertDimension(size, spacedim);
Assert(euler_dof_handler.has_level_dofs(),
ExcMessage("The underlying DoFHandler object did not call "
"distribute_mg_dofs(). In this case, the construction via "
"level vectors does not make sense."));
AssertDimension(euler_vector.size(),
euler_dof_handler.get_triangulation().n_global_levels());
this->euler_vector.clear();
this->euler_vector.resize(euler_vector.size());
for (unsigned int i = 0; i < euler_vector.size(); ++i)
this->euler_vector[i] = &euler_vector[i];
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::MappingFEField(
const DoFHandlerType & euler_dof_handler,
const MGLevelObject<VectorType> &euler_vector,
const ComponentMask & mask)
: uses_level_dofs(true)
, euler_dof_handler(&euler_dof_handler)
, fe_mask(mask.size() ?
mask :
ComponentMask(
euler_dof_handler.get_fe().get_nonzero_components(0).size(),
true))
, fe_to_real(fe_mask.size(), numbers::invalid_unsigned_int)
, fe_values(this->euler_dof_handler->get_fe(),
get_vertex_quadrature<dim>(),
update_values)
{
unsigned int size = 0;
for (unsigned int i = 0; i < fe_mask.size(); ++i)
{
if (fe_mask[i])
fe_to_real[i] = size++;
}
AssertDimension(size, spacedim);
Assert(euler_dof_handler.has_level_dofs(),
ExcMessage("The underlying DoFHandler object did not call "
"distribute_mg_dofs(). In this case, the construction via "
"level vectors does not make sense."));
AssertDimension(euler_vector.max_level() + 1,
euler_dof_handler.get_triangulation().n_global_levels());
this->euler_vector.clear();
this->euler_vector.resize(
euler_dof_handler.get_triangulation().n_global_levels());
for (unsigned int i = euler_vector.min_level(); i <= euler_vector.max_level();
++i)
this->euler_vector[i] = &euler_vector[i];
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::MappingFEField(
const MappingFEField<dim, spacedim, VectorType, DoFHandlerType> &mapping)
: uses_level_dofs(mapping.uses_level_dofs)
, euler_vector(mapping.euler_vector)
, euler_dof_handler(mapping.euler_dof_handler)
, fe_mask(mapping.fe_mask)
, fe_to_real(mapping.fe_to_real)
, fe_values(mapping.euler_dof_handler->get_fe(),
get_vertex_quadrature<dim>(),
update_values)
{}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
inline const double &
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::InternalData::shape(
const unsigned int qpoint,
const unsigned int shape_nr) const
{
AssertIndexRange(qpoint * n_shape_functions + shape_nr, shape_values.size());
return shape_values[qpoint * n_shape_functions + shape_nr];
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
bool
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
preserves_vertex_locations() const
{
return false;
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
std::array<Point<spacedim>, GeometryInfo<dim>::vertices_per_cell>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::get_vertices(
const typename Triangulation<dim, spacedim>::cell_iterator &cell) const
{
// we transform our tria iterator into a dof iterator so we can access
// data not associated with triangulations
const typename DoFHandler<dim, spacedim>::cell_iterator dof_cell(
*cell, euler_dof_handler);
Assert(uses_level_dofs || dof_cell->is_active() == true, ExcInactiveCell());
AssertDimension(GeometryInfo<dim>::vertices_per_cell,
fe_values.n_quadrature_points);
AssertDimension(fe_to_real.size(),
euler_dof_handler->get_fe().n_components());
if (uses_level_dofs)
{
AssertIndexRange(cell->level(), euler_vector.size());
AssertDimension(euler_vector[cell->level()]->size(),
euler_dof_handler->n_dofs(cell->level()));
}
else
AssertDimension(euler_vector[0]->size(), euler_dof_handler->n_dofs());
{
std::lock_guard<std::mutex> lock(fe_values_mutex);
fe_values.reinit(dof_cell);
}
const unsigned int dofs_per_cell = euler_dof_handler->get_fe().dofs_per_cell;
std::vector<types::global_dof_index> dof_indices(dofs_per_cell);
if (uses_level_dofs)
dof_cell->get_mg_dof_indices(dof_indices);
else
dof_cell->get_dof_indices(dof_indices);
const VectorType &vector =
uses_level_dofs ? *euler_vector[cell->level()] : *euler_vector[0];
std::array<Point<spacedim>, GeometryInfo<dim>::vertices_per_cell> vertices;
for (unsigned int i = 0; i < dofs_per_cell; ++i)
{
const unsigned int comp = fe_to_real
[euler_dof_handler->get_fe().system_to_component_index(i).first];
if (comp != numbers::invalid_unsigned_int)
{
typename VectorType::value_type value =
internal::ElementAccess<VectorType>::get(vector, dof_indices[i]);
if (euler_dof_handler->get_fe().is_primitive(i))
for (unsigned int v = 0; v < GeometryInfo<dim>::vertices_per_cell;
++v)
vertices[v][comp] += fe_values.shape_value(i, v) * value;
else
Assert(false, ExcNotImplemented());
}
}
return vertices;
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
void
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
compute_shapes_virtual(
const std::vector<Point<dim>> &unit_points,
typename MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
InternalData &data) const
{
const auto fe = &euler_dof_handler->get_fe();
const unsigned int n_points = unit_points.size();
for (unsigned int point = 0; point < n_points; ++point)
{
if (data.shape_values.size() != 0)
for (unsigned int i = 0; i < data.n_shape_functions; ++i)
data.shape(point, i) = fe->shape_value(i, unit_points[point]);
if (data.shape_derivatives.size() != 0)
for (unsigned int i = 0; i < data.n_shape_functions; ++i)
data.derivative(point, i) = fe->shape_grad(i, unit_points[point]);
if (data.shape_second_derivatives.size() != 0)
for (unsigned int i = 0; i < data.n_shape_functions; ++i)
data.second_derivative(point, i) =
fe->shape_grad_grad(i, unit_points[point]);
if (data.shape_third_derivatives.size() != 0)
for (unsigned int i = 0; i < data.n_shape_functions; ++i)
data.third_derivative(point, i) =
fe->shape_3rd_derivative(i, unit_points[point]);
if (data.shape_fourth_derivatives.size() != 0)
for (unsigned int i = 0; i < data.n_shape_functions; ++i)
data.fourth_derivative(point, i) =
fe->shape_4th_derivative(i, unit_points[point]);
}
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
UpdateFlags
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
requires_update_flags(const UpdateFlags in) const
{
// add flags if the respective quantities are necessary to compute
// what we need. note that some flags appear in both conditions and
// in subsequent set operations. this leads to some circular
// logic. the only way to treat this is to iterate. since there are
// 5 if-clauses in the loop, it will take at most 4 iterations to
// converge. do them:
UpdateFlags out = in;
for (unsigned int i = 0; i < 5; ++i)
{
// The following is a little incorrect:
// If not applied on a face,
// update_boundary_forms does not
// make sense. On the other hand,
// it is necessary on a
// face. Currently,
// update_boundary_forms is simply
// ignored for the interior of a
// cell.
if (out & (update_JxW_values | update_normal_vectors))
out |= update_boundary_forms;
if (out & (update_covariant_transformation | update_JxW_values |
update_jacobians | update_jacobian_grads |
update_boundary_forms | update_normal_vectors))
out |= update_contravariant_transformation;
if (out &
(update_inverse_jacobians | update_jacobian_pushed_forward_grads |
update_jacobian_pushed_forward_2nd_derivatives |
update_jacobian_pushed_forward_3rd_derivatives))
out |= update_covariant_transformation;
// The contravariant transformation
// is a Piola transformation, which
// requires the determinant of the
// Jacobi matrix of the transformation.
// Therefore these values have to be
// updated for each cell.
if (out & update_contravariant_transformation)
out |= update_JxW_values;
if (out & update_normal_vectors)
out |= update_JxW_values;
}
return out;
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
void
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::compute_data(
const UpdateFlags update_flags,
const Quadrature<dim> &q,
const unsigned int n_original_q_points,
InternalData & data) const
{
// store the flags in the internal data object so we can access them
// in fill_fe_*_values(). use the transitive hull of the required
// flags
data.update_each = requires_update_flags(update_flags);
const unsigned int n_q_points = q.size();
// see if we need the (transformation) shape function values
// and/or gradients and resize the necessary arrays
if (data.update_each & update_quadrature_points)
data.shape_values.resize(data.n_shape_functions * n_q_points);
if (data.update_each &
(update_covariant_transformation | update_contravariant_transformation |
update_JxW_values | update_boundary_forms | update_normal_vectors |
update_jacobians | update_jacobian_grads | update_inverse_jacobians))
data.shape_derivatives.resize(data.n_shape_functions * n_q_points);
if (data.update_each & update_covariant_transformation)
data.covariant.resize(n_original_q_points);
if (data.update_each & update_contravariant_transformation)
data.contravariant.resize(n_original_q_points);
if (data.update_each & update_volume_elements)
data.volume_elements.resize(n_original_q_points);
if (data.update_each &
(update_jacobian_grads | update_jacobian_pushed_forward_grads))
data.shape_second_derivatives.resize(data.n_shape_functions * n_q_points);
if (data.update_each & (update_jacobian_2nd_derivatives |
update_jacobian_pushed_forward_2nd_derivatives))
data.shape_third_derivatives.resize(data.n_shape_functions * n_q_points);
if (data.update_each & (update_jacobian_3rd_derivatives |
update_jacobian_pushed_forward_3rd_derivatives))
data.shape_fourth_derivatives.resize(data.n_shape_functions * n_q_points);
compute_shapes_virtual(q.get_points(), data);
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
void
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::compute_face_data(
const UpdateFlags update_flags,
const Quadrature<dim> &q,
const unsigned int n_original_q_points,
InternalData & data) const
{
compute_data(update_flags, q, n_original_q_points, data);
if (dim > 1)
{
if (data.update_each & update_boundary_forms)
{
data.aux.resize(
dim - 1, std::vector<Tensor<1, spacedim>>(n_original_q_points));
// Compute tangentials to the unit cell.
for (unsigned int i = 0; i < GeometryInfo<dim>::faces_per_cell; ++i)
{
data.unit_tangentials[i].resize(n_original_q_points);
std::fill(data.unit_tangentials[i].begin(),
data.unit_tangentials[i].end(),
GeometryInfo<dim>::unit_tangential_vectors[i][0]);
if (dim > 2)
{
data.unit_tangentials[GeometryInfo<dim>::faces_per_cell + i]
.resize(n_original_q_points);
std::fill(
data.unit_tangentials[GeometryInfo<dim>::faces_per_cell + i]
.begin(),
data.unit_tangentials[GeometryInfo<dim>::faces_per_cell + i]
.end(),
GeometryInfo<dim>::unit_tangential_vectors[i][1]);
}
}
}
}
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
typename std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::get_data(
const UpdateFlags update_flags,
const Quadrature<dim> &quadrature) const
{
std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
std_cxx14::make_unique<InternalData>(euler_dof_handler->get_fe(), fe_mask);
auto &data = dynamic_cast<InternalData &>(*data_ptr);
this->compute_data(update_flags, quadrature, quadrature.size(), data);
return data_ptr;
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::get_face_data(
const UpdateFlags update_flags,
const Quadrature<dim - 1> &quadrature) const
{
std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
std_cxx14::make_unique<InternalData>(euler_dof_handler->get_fe(), fe_mask);
auto & data = dynamic_cast<InternalData &>(*data_ptr);
const Quadrature<dim> q(QProjector<dim>::project_to_all_faces(quadrature));
this->compute_face_data(update_flags, q, quadrature.size(), data);
return data_ptr;
}
template <int dim, int spacedim, typename VectorType, typename DoFHandlerType>
std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::get_subface_data(
const UpdateFlags update_flags,
const Quadrature<dim - 1> &quadrature) const
{
std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
std_cxx14::make_unique<InternalData>(euler_dof_handler->get_fe(), fe_mask);
auto & data = dynamic_cast<InternalData &>(*data_ptr);
const Quadrature<dim> q(QProjector<dim>::project_to_all_subfaces(quadrature));
this->compute_face_data(update_flags, q, quadrature.size(), data);
return data_ptr;
}
namespace internal
{
namespace MappingFEFieldImplementation
{
namespace
{
/**
* Compute the locations of quadrature points on the object described by
* the first argument (and the cell for which the mapping support points
* have already been set), but only if the update_flags of the @p data
* argument indicate so.
*/
template <int dim,
int spacedim,
typename VectorType,
typename DoFHandlerType>
void
maybe_compute_q_points(
const typename dealii::QProjector<dim>::DataSetDescriptor data_set,
const typename dealii::
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
InternalData & data,
const FiniteElement<dim, spacedim> &fe,
const ComponentMask & fe_mask,
const std::vector<unsigned int> & fe_to_real,
std::vector<Point<spacedim>> & quadrature_points)
{
const UpdateFlags update_flags = data.update_each;
if (update_flags & update_quadrature_points)
{
for (unsigned int point = 0; point < quadrature_points.size();
++point)
{
Point<spacedim> result;
const double * shape = &data.shape(point + data_set, 0);
for (unsigned int k = 0; k < data.n_shape_functions; ++k)
{
unsigned int comp_k = fe.system_to_component_index(k).first;
if (fe_mask[comp_k])
result[fe_to_real[comp_k]] +=
data.local_dof_values[k] * shape[k];
}
quadrature_points[point] = result;
}
}
}
/**
* Update the co- and contravariant matrices as well as their determinant,
* for the cell described stored in the data object, but only if the
* update_flags of the @p data argument indicate so.
*
* Skip the computation if possible as indicated by the first argument.
*/
template <int dim,
int spacedim,
typename VectorType,
typename DoFHandlerType>
void
maybe_update_Jacobians(
const CellSimilarity::Similarity cell_similarity,
const typename dealii::QProjector<dim>::DataSetDescriptor data_set,
const typename dealii::
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
InternalData & data,
const FiniteElement<dim, spacedim> &fe,
const ComponentMask & fe_mask,
const std::vector<unsigned int> & fe_to_real)
{
const UpdateFlags update_flags = data.update_each;
// then Jacobians
if (update_flags & update_contravariant_transformation)
{
// if the current cell is just a translation of the previous one, no
// need to recompute jacobians...
if (cell_similarity != CellSimilarity::translation)
{
const unsigned int n_q_points = data.contravariant.size();
Assert(data.n_shape_functions > 0, ExcInternalError());
for (unsigned int point = 0; point < n_q_points; ++point)
{
const Tensor<1, dim> *data_derv =
&data.derivative(point + data_set, 0);
Tensor<1, dim> result[spacedim];
for (unsigned int k = 0; k < data.n_shape_functions; ++k)
{
unsigned int comp_k =
fe.system_to_component_index(k).first;
if (fe_mask[comp_k])
result[fe_to_real[comp_k]] +=
data.local_dof_values[k] * data_derv[k];
}
// write result into contravariant data
for (unsigned int i = 0; i < spacedim; ++i)
{
data.contravariant[point][i] = result[i];
}
}
}
}
if (update_flags & update_covariant_transformation)
{
AssertDimension(data.covariant.size(), data.contravariant.size());
if (cell_similarity != CellSimilarity::translation)
for (unsigned int point = 0; point < data.contravariant.size();
++point)
data.covariant[point] =
(data.contravariant[point]).covariant_form();
}
if (update_flags & update_volume_elements)
{
AssertDimension(data.contravariant.size(),
data.volume_elements.size());
if (cell_similarity != CellSimilarity::translation)
for (unsigned int point = 0; point < data.contravariant.size();
++point)
data.volume_elements[point] =
data.contravariant[point].determinant();
}
}
/**
* Update the Hessian of the transformation from unit to real cell, the
* Jacobian gradients.
*
* Skip the computation if possible as indicated by the first argument.
*/
template <int dim,
int spacedim,
typename VectorType,
typename DoFHandlerType>
void
maybe_update_jacobian_grads(
const CellSimilarity::Similarity cell_similarity,
const typename dealii::QProjector<dim>::DataSetDescriptor data_set,
const typename dealii::
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
InternalData & data,
const FiniteElement<dim, spacedim> & fe,
const ComponentMask & fe_mask,
const std::vector<unsigned int> & fe_to_real,
std::vector<DerivativeForm<2, dim, spacedim>> &jacobian_grads)
{
const UpdateFlags update_flags = data.update_each;
if (update_flags & update_jacobian_grads)
{
const unsigned int n_q_points = jacobian_grads.size();
if (cell_similarity != CellSimilarity::translation)
{
for (unsigned int point = 0; point < n_q_points; ++point)
{
const Tensor<2, dim> *second =
&data.second_derivative(point + data_set, 0);
DerivativeForm<2, dim, spacedim> result;
for (unsigned int k = 0; k < data.n_shape_functions; ++k)
{
unsigned int comp_k =
fe.system_to_component_index(k).first;
if (fe_mask[comp_k])
for (unsigned int j = 0; j < dim; ++j)
for (unsigned int l = 0; l < dim; ++l)
result[fe_to_real[comp_k]][j][l] +=
(second[k][j][l] * data.local_dof_values[k]);
}
// never touch any data for j=dim in case dim<spacedim, so
// it will always be zero as it was initialized
for (unsigned int i = 0; i < spacedim; ++i)
for (unsigned int j = 0; j < dim; ++j)
for (unsigned int l = 0; l < dim; ++l)
jacobian_grads[point][i][j][l] = result[i][j][l];
}
}
}
}
/**
* Update the Hessian of the transformation from unit to real cell, the
* Jacobian gradients, pushed forward to the real cell coordinates.
*
* Skip the computation if possible as indicated by the first argument.
*/
template <int dim,
int spacedim,
typename VectorType,
typename DoFHandlerType>
void
maybe_update_jacobian_pushed_forward_grads(
const CellSimilarity::Similarity cell_similarity,
const typename dealii::QProjector<dim>::DataSetDescriptor data_set,
const typename dealii::
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
InternalData & data,
const FiniteElement<dim, spacedim> &fe,
const ComponentMask & fe_mask,
const std::vector<unsigned int> & fe_to_real,
std::vector<Tensor<3, spacedim>> & jacobian_pushed_forward_grads)
{
const UpdateFlags update_flags = data.update_each;
if (update_flags & update_jacobian_pushed_forward_grads)
{
const unsigned int n_q_points =
jacobian_pushed_forward_grads.size();
if (cell_similarity != CellSimilarity::translation)
{
double tmp[spacedim][spacedim][spacedim];
for (unsigned int point = 0; point < n_q_points; ++point)
{
const Tensor<2, dim> *second =
&data.second_derivative(point + data_set, 0);
DerivativeForm<2, dim, spacedim> result;
for (unsigned int k = 0; k < data.n_shape_functions; ++k)
{
unsigned int comp_k =
fe.system_to_component_index(k).first;
if (fe_mask[comp_k])
for (unsigned int j = 0; j < dim; ++j)
for (unsigned int l = 0; l < dim; ++l)
result[fe_to_real[comp_k]][j][l] +=
(second[k][j][l] * data.local_dof_values[k]);
}
// first push forward the j-components
for (unsigned int i = 0; i < spacedim; ++i)
for (unsigned int j = 0; j < spacedim; ++j)
for (unsigned int l = 0; l < dim; ++l)
{
tmp[i][j][l] =
result[i][0][l] * data.covariant[point][j][0];
for (unsigned int jr = 1; jr < dim; ++jr)
{
tmp[i][j][l] += result[i][jr][l] *
data.covariant[point][j][jr];
}
}
// now, pushing forward the l-components
for (unsigned int i = 0; i < spacedim; ++i)
for (unsigned int j = 0; j < spacedim; ++j)
for (unsigned int l = 0; l < spacedim; ++l)
{
jacobian_pushed_forward_grads[point][i][j][l] =
tmp[i][j][0] * data.covariant[point][l][0];
for (unsigned int lr = 1; lr < dim; ++lr)
{
jacobian_pushed_forward_grads[point][i][j][l] +=
tmp[i][j][lr] * data.covariant[point][l][lr];
}
}
}
}
}
}
/**
* Update the third derivative of the transformation from unit to real
* cell, the Jacobian hessians.
*
* Skip the computation if possible as indicated by the first argument.
*/
template <int dim,
int spacedim,
typename VectorType,
typename DoFHandlerType>
void
maybe_update_jacobian_2nd_derivatives(
const CellSimilarity::Similarity cell_similarity,
const typename dealii::QProjector<dim>::DataSetDescriptor data_set,
const typename dealii::
MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
InternalData & data,
const FiniteElement<dim, spacedim> & fe,
const ComponentMask & fe_mask,
const std::vector<unsigned int> & fe_to_real,
std::vector<DerivativeForm<3, dim, spacedim>> &jacobian_2nd_derivatives)
{
const UpdateFlags update_flags = data.update_each;
if (update_flags & update_jacobian_2nd_derivatives)
{
const unsigned int n_q_points = jacobian_2nd_derivatives.size();
if (cell_similarity != CellSimilarity::translation)
{
for (unsigned int point = 0; point < n_q_points; ++point)
{
const Tensor<3, dim> *third =
&data.third_derivative(point + data_set, 0);
DerivativeForm<3, dim, spacedim> result;
for (unsigned int k = 0; k < data.n_shape_functions; ++k)
{
unsigned int comp_k =
fe.system_to_component_index(k).first;
if (fe_mask[comp_k])
for (unsigned int j = 0; j < dim; ++j)
for (unsigned int l = 0; l < dim; ++l)
for (unsigned int m = 0; m < dim; ++m)
result[fe_to_real[comp_k]][j][l][m] +=
(third[k][j][l][m] *
data.local_dof_values[k]);
}
// never touch any data for j=dim in case dim<spacedim, so
// it will always be zero as it was initialized
for (unsigned int i = 0; i < spacedim; ++i)
for (unsigned int j = 0; j < dim; ++j)
for (unsigned int l = 0; l < dim; ++l)
for (unsigned int m = 0; m < dim; ++m)
jacobian_2nd_derivatives[point][i][j][l][m] =
result[i][j][l][m];
}
}
}
}
/**
* Update the third derivative of the transformation from unit to real
* cell, the Jacobian hessians, pushed forward to the real cell
* coordinates.
*
* Skip the computation if possible as indicated by the first argument.
*/
template <int dim,
int spacedim,
typename VectorType,
typename DoFHandlerType>
void