Classes
class	InverseQuadraticApproximation

Functions
template<int dim>
std::vector< Point< dim > >	unit_support_points (const std::vector< Point< 1 > > &line_support_points, const std::vector< unsigned int > &renumbering)

inline ::Table< 2, double >	compute_support_point_weights_on_quad (const unsigned int polynomial_degree)

inline ::Table< 2, double >	compute_support_point_weights_on_hex (const unsigned int polynomial_degree)

std::vector<::Table< 2, double > >	compute_support_point_weights_perimeter_to_interior (const unsigned int polynomial_degree, const unsigned int dim)

template<int dim>
inline ::Table< 2, double >	compute_support_point_weights_cell (const unsigned int polynomial_degree)

template<int dim, int spacedim>
Point< spacedim >	compute_mapped_location_of_point (const typename ::MappingQ< dim, spacedim >::InternalData &data)

template<int dim, int spacedim, typename Number >
Point< dim, Number >	do_transform_real_to_unit_cell_internal (const Point< spacedim, Number > &p, const Point< dim, Number > &initial_p_unit, const std::vector< Point< spacedim > > &points, const std::vector< Polynomials::Polynomial< double > > &polynomials_1d, const std::vector< unsigned int > &renumber, const bool print_iterations_to_deallog=false)

template<int dim>
Point< dim >	do_transform_real_to_unit_cell_internal_codim1 (const typename ::Triangulation< dim, dim+1 >::cell_iterator &cell, const Point< dim+1 > &p, const Point< dim > &initial_p_unit, typename ::MappingQ< dim, dim+1 >::InternalData &mdata)

template<int dim, int spacedim>
void	maybe_update_q_points_Jacobians_and_grads_tensor (const CellSimilarity::Similarity cell_similarity, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< Point< spacedim > > &quadrature_points, std::vector< DerivativeForm< 2, dim, spacedim > > &jacobian_grads)

template<int dim, int spacedim>
void	maybe_compute_q_points (const typename QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< Point< spacedim > > &quadrature_points)

template<int dim, int spacedim>
void	maybe_update_Jacobians (const CellSimilarity::Similarity cell_similarity, const typename ::QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data)

template<int dim, int spacedim>
void	maybe_update_jacobian_grads (const CellSimilarity::Similarity cell_similarity, const typename QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< DerivativeForm< 2, dim, spacedim > > &jacobian_grads)

template<int dim, int spacedim>
void	maybe_update_jacobian_pushed_forward_grads (const CellSimilarity::Similarity cell_similarity, const typename QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< Tensor< 3, spacedim > > &jacobian_pushed_forward_grads)

template<int dim, int spacedim>
void	maybe_update_jacobian_2nd_derivatives (const CellSimilarity::Similarity cell_similarity, const typename QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< DerivativeForm< 3, dim, spacedim > > &jacobian_2nd_derivatives)

template<int dim, int spacedim>
void	maybe_update_jacobian_pushed_forward_2nd_derivatives (const CellSimilarity::Similarity cell_similarity, const typename QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< Tensor< 4, spacedim > > &jacobian_pushed_forward_2nd_derivatives)

template<int dim, int spacedim>
void	maybe_update_jacobian_3rd_derivatives (const CellSimilarity::Similarity cell_similarity, const typename QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< DerivativeForm< 4, dim, spacedim > > &jacobian_3rd_derivatives)

template<int dim, int spacedim>
void	maybe_update_jacobian_pushed_forward_3rd_derivatives (const CellSimilarity::Similarity cell_similarity, const typename QProjector< dim >::DataSetDescriptor data_set, const typename ::MappingQ< dim, spacedim >::InternalData &data, std::vector< Tensor< 5, spacedim > > &jacobian_pushed_forward_3rd_derivatives)

template<int dim, int spacedim>
void	maybe_compute_face_data (const ::MappingQ< dim, spacedim > &mapping, const typename ::Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const unsigned int n_q_points, const std::vector< double > &weights, const typename ::MappingQ< dim, spacedim >::InternalData &data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data)

template<int dim, int spacedim>
void	do_fill_fe_face_values (const ::MappingQ< dim, spacedim > &mapping, const typename ::Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const typename QProjector< dim >::DataSetDescriptor data_set, const Quadrature< dim - 1 > &quadrature, const typename ::MappingQ< dim, spacedim >::InternalData &data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data)

template<int dim, int spacedim, int rank>
void	transform_fields (const ArrayView< const Tensor< rank, dim > > &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< rank, spacedim > > &output)

template<int dim, int spacedim, int rank>
void	transform_gradients (const ArrayView< const Tensor< rank, dim > > &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< rank, spacedim > > &output)

template<int dim, int spacedim>
void	transform_hessians (const ArrayView< const Tensor< 3, dim > > &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< 3, spacedim > > &output)

template<int dim, int spacedim, int rank>
void	transform_differential_forms (const ArrayView< const DerivativeForm< rank, dim, spacedim > > &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< rank+1, spacedim > > &output)

Detailed Description

Internal namespace to implement methods of MappingQ, such as the evaluation of the mapping and the transformation between real and unit cell.

Function Documentation

◆ unit_support_points()

template<int dim>

std::vector< Point< dim > > internal::MappingQImplementation::unit_support_points	(	const std::vector< Point< 1 > > &	line_support_points,
		const std::vector< unsigned int > &	renumbering
	)

This function generates the reference cell support points from the 1d support points by expanding the tensor product.

Definition at line 217 of file mapping_q_internal.h.

◆ compute_support_point_weights_on_quad()

inline ::Table< 2, double > internal::MappingQImplementation::compute_support_point_weights_on_quad ( const unsigned int polynomial_degree )

This function is needed by the constructor of MappingQ<dim,spacedim> for dim= 2 and 3.

For the definition of the support_point_weights_on_quad please refer to the description of TransfiniteInterpolationManifold.

Definition at line 247 of file mapping_q_internal.h.

◆ compute_support_point_weights_on_hex()

inline ::Table< 2, double > internal::MappingQImplementation::compute_support_point_weights_on_hex ( const unsigned int polynomial_degree )

This function is needed by the constructor of MappingQ<3>.

For the definition of the support_point_weights_on_quad please refer to the description of TransfiniteInterpolationManifold.

Definition at line 299 of file mapping_q_internal.h.

◆ compute_support_point_weights_perimeter_to_interior()

std::vector<::Table< 2, double > > internal::MappingQImplementation::compute_support_point_weights_perimeter_to_interior	(	const unsigned int	polynomial_degree,
		const unsigned int	dim
	)

inline

This function collects the output of compute_support_point_weights_on_{quad,hex} in a single data structure.

Definition at line 388 of file mapping_q_internal.h.

◆ compute_support_point_weights_cell()

template<int dim>

inline ::Table< 2, double > internal::MappingQImplementation::compute_support_point_weights_cell ( const unsigned int polynomial_degree )

Collects all interior points for the various dimensions.

Definition at line 423 of file mapping_q_internal.h.

◆ compute_mapped_location_of_point()

template<int dim, int spacedim>

Point< spacedim > internal::MappingQImplementation::compute_mapped_location_of_point ( const typename ::MappingQ< dim, spacedim >::InternalData & data )

inline

Using the relative weights of the shape functions evaluated at one point on the reference cell (and stored in data.shape_values and accessed via data.shape(0,i)) and the locations of mapping support points (stored in data.mapping_support_points), compute the mapped location of that point in real space.

Definition at line 455 of file mapping_q_internal.h.

◆ do_transform_real_to_unit_cell_internal()

template<int dim, int spacedim, typename Number >

Point< dim, Number > internal::MappingQImplementation::do_transform_real_to_unit_cell_internal	(	const Point< spacedim, Number > &	p,
		const Point< dim, Number > &	initial_p_unit,
		const std::vector< Point< spacedim > > &	points,
		const std::vector< Polynomials::Polynomial< double > > &	polynomials_1d,
		const std::vector< unsigned int > &	renumber,
		const bool	print_iterations_to_deallog = `false`
	)

inline

Implementation of transform_real_to_unit_cell for either type double or VectorizedArray<double>

Definition at line 477 of file mapping_q_internal.h.

◆ do_transform_real_to_unit_cell_internal_codim1()

template<int dim>

Point< dim > internal::MappingQImplementation::do_transform_real_to_unit_cell_internal_codim1	(	const typename ::Triangulation< dim, dim+1 >::cell_iterator &	cell,
		const Point< dim+1 > &	p,
		const Point< dim > &	initial_p_unit,
		typename ::MappingQ< dim, dim+1 >::InternalData &	mdata
	)

inline

Implementation of transform_real_to_unit_cell for dim==spacedim-1

Definition at line 734 of file mapping_q_internal.h.

◆ maybe_update_q_points_Jacobians_and_grads_tensor()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_q_points_Jacobians_and_grads_tensor	(	const CellSimilarity::Similarity	cell_similarity,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< Point< spacedim > > &	quadrature_points,
		std::vector< DerivativeForm< 2, dim, spacedim > > &	jacobian_grads
	)

inline

In case the quadrature formula is a tensor product, this is a replacement for maybe_compute_q_points(), maybe_update_Jacobians() and maybe_update_jacobian_grads()

Definition at line 1114 of file mapping_q_internal.h.

◆ maybe_compute_q_points()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_compute_q_points	(	const typename QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< Point< spacedim > > &	quadrature_points
	)

inline

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 data argument indicate so.

Definition at line 1296 of file mapping_q_internal.h.

◆ maybe_update_Jacobians()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_Jacobians	(	const CellSimilarity::Similarity	cell_similarity,
		const typename ::QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data
	)

inline

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 data argument indicate so.

Skip the computation if possible as indicated by the first argument.

Definition at line 1328 of file mapping_q_internal.h.

◆ maybe_update_jacobian_grads()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_jacobian_grads	(	const CellSimilarity::Similarity	cell_similarity,
		const typename QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< DerivativeForm< 2, dim, spacedim > > &	jacobian_grads
	)

inline

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.

Definition at line 1407 of file mapping_q_internal.h.

◆ maybe_update_jacobian_pushed_forward_grads()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_jacobian_pushed_forward_grads	(	const CellSimilarity::Similarity	cell_similarity,
		const typename QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< Tensor< 3, spacedim > > &	jacobian_pushed_forward_grads
	)

inline

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.

Definition at line 1454 of file mapping_q_internal.h.

◆ maybe_update_jacobian_2nd_derivatives()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_jacobian_2nd_derivatives	(	const CellSimilarity::Similarity	cell_similarity,
		const typename QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< DerivativeForm< 3, dim, spacedim > > &	jacobian_2nd_derivatives
	)

inline

Update the third derivatives of the transformation from unit to real cell, the Jacobian hessians.

Skip the computation if possible as indicated by the first argument.

Definition at line 1528 of file mapping_q_internal.h.

◆ maybe_update_jacobian_pushed_forward_2nd_derivatives()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_jacobian_pushed_forward_2nd_derivatives	(	const CellSimilarity::Similarity	cell_similarity,
		const typename QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< Tensor< 4, spacedim > > &	jacobian_pushed_forward_2nd_derivatives
	)

inline

Update the Hessian of the Hessian of the transformation from unit to real cell, the Jacobian Hessian gradients, pushed forward to the real cell coordinates.

Skip the computation if possible as indicated by the first argument.

Definition at line 1584 of file mapping_q_internal.h.

◆ maybe_update_jacobian_3rd_derivatives()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_jacobian_3rd_derivatives	(	const CellSimilarity::Similarity	cell_similarity,
		const typename QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< DerivativeForm< 4, dim, spacedim > > &	jacobian_3rd_derivatives
	)

inline

Update the fourth derivatives of the transformation from unit to real cell, the Jacobian hessian gradients.

Skip the computation if possible as indicated by the first argument.

Definition at line 1685 of file mapping_q_internal.h.

◆ maybe_update_jacobian_pushed_forward_3rd_derivatives()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_update_jacobian_pushed_forward_3rd_derivatives	(	const CellSimilarity::Similarity	cell_similarity,
		const typename QProjector< dim >::DataSetDescriptor	data_set,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		std::vector< Tensor< 5, spacedim > > &	jacobian_pushed_forward_3rd_derivatives
	)

inline

Update the Hessian gradient 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.

Definition at line 1744 of file mapping_q_internal.h.

◆ maybe_compute_face_data()

template<int dim, int spacedim>

void internal::MappingQImplementation::maybe_compute_face_data	(	const ::MappingQ< dim, spacedim > &	mapping,
		const typename ::Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const unsigned int	subface_no,
		const unsigned int	n_q_points,
		const std::vector< double > &	weights,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	output_data
	)

inline

Depending on what information is called for in the update flags of the data object, compute the various pieces of information that is required by the fill_fe_face_values() and fill_fe_subface_values() functions. This function simply unifies the work that would be done by those two functions.

The resulting data is put into the output_data argument.

Definition at line 1871 of file mapping_q_internal.h.

◆ do_fill_fe_face_values()

template<int dim, int spacedim>

void internal::MappingQImplementation::do_fill_fe_face_values	(	const ::MappingQ< dim, spacedim > &	mapping,
		const typename ::Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const unsigned int	subface_no,
		const typename QProjector< dim >::DataSetDescriptor	data_set,
		const Quadrature< dim - 1 > &	quadrature,
		const typename ::MappingQ< dim, spacedim >::InternalData &	data,
		internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	output_data
	)

inline

Do the work of MappingQ::fill_fe_face_values() and MappingQ::fill_fe_subface_values() in a generic way, using the 'data_set' to differentiate whether we will work on a face (and if so, which one) or subface.

Definition at line 2035 of file mapping_q_internal.h.

◆ transform_fields()

template<int dim, int spacedim, int rank>

void internal::MappingQImplementation::transform_fields	(	const ArrayView< const Tensor< rank, dim > > &	input,
		const MappingKind	mapping_kind,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_data,
		const ArrayView< Tensor< rank, spacedim > > &	output
	)

inline

Implementation of MappingQ::transform() for generic tensors.

Definition at line 2108 of file mapping_q_internal.h.

◆ transform_gradients()

template<int dim, int spacedim, int rank>

void internal::MappingQImplementation::transform_gradients	(	const ArrayView< const Tensor< rank, dim > > &	input,
		const MappingKind	mapping_kind,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_data,
		const ArrayView< Tensor< rank, spacedim > > &	output
	)

inline

Implementation of MappingQ::transform() for gradients.

Definition at line 2186 of file mapping_q_internal.h.

◆ transform_hessians()

template<int dim, int spacedim>

void internal::MappingQImplementation::transform_hessians	(	const ArrayView< const Tensor< 3, dim > > &	input,
		const MappingKind	mapping_kind,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_data,
		const ArrayView< Tensor< 3, spacedim > > &	output
	)

inline

Implementation of MappingQ::transform() for hessians.

Definition at line 2284 of file mapping_q_internal.h.

◆ transform_differential_forms()

template<int dim, int spacedim, int rank>

void internal::MappingQImplementation::transform_differential_forms	(	const ArrayView< const DerivativeForm< rank, dim, spacedim > > &	input,
		const MappingKind	mapping_kind,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_data,
		const ArrayView< Tensor< rank+1, spacedim > > &	output
	)

inline

Implementation of MappingQ::transform() for DerivativeForm arguments.

Definition at line 2451 of file mapping_q_internal.h.

Classes

Functions

Detailed Description

Function Documentation

◆ unit_support_points()

◆ compute_support_point_weights_on_quad()

◆ compute_support_point_weights_on_hex()

◆ compute_support_point_weights_perimeter_to_interior()

◆ compute_support_point_weights_cell()

◆ compute_mapped_location_of_point()

◆ do_transform_real_to_unit_cell_internal()

◆ do_transform_real_to_unit_cell_internal_codim1()

◆ maybe_update_q_points_Jacobians_and_grads_tensor()

◆ maybe_compute_q_points()

◆ maybe_update_Jacobians()

◆ maybe_update_jacobian_grads()

◆ maybe_update_jacobian_pushed_forward_grads()

◆ maybe_update_jacobian_2nd_derivatives()

◆ maybe_update_jacobian_pushed_forward_2nd_derivatives()

◆ maybe_update_jacobian_3rd_derivatives()

◆ maybe_update_jacobian_pushed_forward_3rd_derivatives()

◆ maybe_compute_face_data()

◆ do_fill_fe_face_values()

◆ transform_fields()

◆ transform_gradients()

◆ transform_hessians()

◆ transform_differential_forms()