Reference documentation for deal.II version Git 6d63218887 2020-10-30 17:17:53 -0400
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Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
MappingQ1Eulerian< dim, VectorType, spacedim > Class Template Reference

#include <deal.II/fe/mapping_q1_eulerian.h>

Inheritance diagram for MappingQ1Eulerian< dim, VectorType, spacedim >:
[legend]

Public Member Functions

 MappingQ1Eulerian (const DoFHandler< dim, spacedim > &euler_dof_handler, const VectorType &euler_vector)
 
virtual boost::container::small_vector< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell > get_vertices (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const override
 
virtual std::unique_ptr< Mapping< dim, spacedim > > clone () const override
 
virtual bool preserves_vertex_locations () const override
 
unsigned int get_degree () const
 
virtual Point< spacedim > get_center (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const bool map_center_of_reference_cell=true) const
 
virtual BoundingBox< spacedim > get_bounding_box (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
Mapping points between reference and real cells
virtual Point< spacedim > transform_unit_to_real_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< dim > &p) const override
 
virtual Point< dim > transform_real_to_unit_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p) const override
 
virtual void transform_points_real_to_unit_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< spacedim >> &real_points, const ArrayView< Point< dim >> &unit_points) const override
 
Functions to transform tensors from reference to real coordinates
virtual void transform (const ArrayView< const Tensor< 1, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 1, spacedim >> &output) const override
 
virtual void transform (const ArrayView< const DerivativeForm< 1, dim, spacedim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 2, spacedim >> &output) const override
 
virtual void transform (const ArrayView< const Tensor< 2, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 2, spacedim >> &output) const override
 
virtual void transform (const ArrayView< const DerivativeForm< 2, dim, spacedim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 3, spacedim >> &output) const override
 
virtual void transform (const ArrayView< const Tensor< 3, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 3, spacedim >> &output) const override
 
Interface with FEValues
virtual UpdateFlags requires_update_flags (const UpdateFlags update_flags) const override
 
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBaseget_data (const UpdateFlags, const Quadrature< dim > &quadrature) const override
 
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBaseget_face_data (const UpdateFlags flags, const Quadrature< dim - 1 > &quadrature) const override
 
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBaseget_subface_data (const UpdateFlags flags, const Quadrature< dim - 1 > &quadrature) const override
 
virtual CellSimilarity::Similarity fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
 
virtual void fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
 
virtual void fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const Quadrature< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
 
Mapping points between reference and real cells
Point< dim - 1 > project_real_point_to_unit_point_on_face (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Point< spacedim > &p) const
 
Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
unsigned int n_subscriptions () const
 
template<typename StreamType >
void list_subscribers (StreamType &stream) const
 
void list_subscribers () const
 

Static Public Member Functions

static ::ExceptionBaseExcInactiveCell ()
 
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 
Exceptions
static ::ExceptionBaseExcInvalidData ()
 
static ::ExceptionBaseExcTransformationFailed ()
 
static ::ExceptionBaseExcDistortedMappedCell (Point< spacedim > arg1, double arg2, int arg3)
 

Protected Member Functions

virtual CellSimilarity::Similarity fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
 
virtual std::vector< Point< spacedim > > compute_mapping_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const override
 
Point< dim > transform_real_to_unit_cell_internal (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p, const Point< dim > &initial_p_unit) const
 
template<>
Point< 1 > transform_real_to_unit_cell_internal (const Triangulation< 1, 1 >::cell_iterator &cell, const Point< 1 > &p, const Point< 1 > &initial_p_unit) const
 
template<>
Point< 2 > transform_real_to_unit_cell_internal (const Triangulation< 2, 2 >::cell_iterator &cell, const Point< 2 > &p, const Point< 2 > &initial_p_unit) const
 
template<>
Point< 3 > transform_real_to_unit_cell_internal (const Triangulation< 3, 3 >::cell_iterator &cell, const Point< 3 > &p, const Point< 3 > &initial_p_unit) const
 
template<>
Point< 1 > transform_real_to_unit_cell_internal (const Triangulation< 1, 2 >::cell_iterator &cell, const Point< 2 > &p, const Point< 1 > &initial_p_unit) const
 
template<>
Point< 2 > transform_real_to_unit_cell_internal (const Triangulation< 2, 3 >::cell_iterator &cell, const Point< 3 > &p, const Point< 2 > &initial_p_unit) const
 
template<>
Point< 1 > transform_real_to_unit_cell_internal (const Triangulation< 1, 3 >::cell_iterator &, const Point< 3 > &, const Point< 1 > &) const
 
virtual void add_line_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const
 
virtual void add_quad_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const
 
template<>
void add_quad_support_points (const Triangulation< 3, 3 >::cell_iterator &cell, std::vector< Point< 3 >> &a) const
 
template<>
void add_quad_support_points (const Triangulation< 2, 3 >::cell_iterator &cell, std::vector< Point< 3 >> &a) const
 

Protected Attributes

SmartPointer< const VectorType, MappingQ1Eulerian< dim, VectorType, spacedim > > euler_transform_vectors
 
SmartPointer< const DoFHandler< dim, spacedim >, MappingQ1Eulerian< dim, VectorType, spacedim > > shiftmap_dof_handler
 
const unsigned int polynomial_degree
 
const std::vector< Point< 1 > > line_support_points
 
const std::vector< Polynomials::Polynomial< double > > polynomials_1d
 
const std::vector< unsigned intrenumber_lexicographic_to_hierarchic
 
const std::vector< Point< dim > > unit_cell_support_points
 
const std::vector< Table< 2, double > > support_point_weights_perimeter_to_interior
 
const Table< 2, doublesupport_point_weights_cell
 

Detailed Description

template<int dim, typename VectorType = Vector<double>, int spacedim = dim>
class MappingQ1Eulerian< dim, VectorType, spacedim >

This class provides a mapping that adds to the location of each cell a \(d\)-linear displacement field. (The generalization to higher order polynomials is provided in the MappingQEulerian class.) Each cell is thus shifted in space by values given to the mapping through a finite element field.

Usage

The constructor of this class takes two arguments: a reference to the vector that defines the mapping from the reference configuration to the current configuration and a reference to the DoFHandler. The vector should then represent a (flattened out version of a) vector valued field defined at nodes defined by the DoFHandler, where the number of components of the vector field equals the number of space dimensions. Thus, the DoFHandler shall operate on a finite element that has as many components as space dimensions. As an additional requirement, we impose that it have as many degree of freedom per vertex as there are space dimensions; since this object only evaluates the finite element field at the vertices, the values of all other degrees of freedom (not associated to vertices) are ignored. These requirements are met if the finite element which the given DoFHandler operates on is constructed as a system element (FESystem) from dim continuous FE_Q() objects.

In many cases, the shift vector will also be the solution vector of the problem under investigation. If this is not the case (i.e. the number of components of the solution variable is not equal to the space dimension, e.g. for scalar problems in dim>1 where the Eulerian coordinates only give a background field) or for coupled problems where more variables are computed than just the flow field), then a different DoFHandler has to be set up on the given triangulation, and the shift vector has then to be associated to it.

An example is shown below:

DoFHandler<dim> flowfield_dof_handler(triangulation);
flowfield_dof_handler.distribute_dofs(fe);
Vector<double> displacement_field(flowfield_dof_handler.n_dofs());
MappingQ1Eulerian<dim> mymapping(flowfield_dof_handler,
displacement_field);

Note that since the vector of shift values and the dof handler are only associated to this object at construction time, you have to make sure that whenever you use this object, the given objects still represent valid data.

To enable the use of the MappingQ1Eulerian class also in the context of parallel codes using the PETSc or Trilinos wrapper classes, the type of the vector can be specified as template parameter VectorType.

For more information about the spacedim template parameter check the documentation of FiniteElement or the one of Triangulation.

Definition at line 93 of file mapping_q1_eulerian.h.

Constructor & Destructor Documentation

◆ MappingQ1Eulerian()

template<int dim, class VectorType , int spacedim>
MappingQ1Eulerian< dim, VectorType, spacedim >::MappingQ1Eulerian ( const DoFHandler< dim, spacedim > &  euler_dof_handler,
const VectorType euler_vector 
)

Constructor.

Parameters
[in]euler_dof_handlerA DoFHandler object that defines a finite element space. This space needs to have exactly dim components and these will be considered displacements relative to the original positions of the cells of the triangulation. This DoFHandler must be based on a FESystem(FE_Q(1),dim) finite element.
[in]euler_vectorA finite element function in the space defined by the first argument. The dim components of this function will be interpreted as the displacement we use in defining the mapping, relative to the location of cells of the underlying triangulation.

Definition at line 42 of file mapping_q1_eulerian.cc.

Member Function Documentation

◆ get_vertices()

template<int dim, class VectorType , int spacedim>
boost::container::small_vector< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell > MappingQ1Eulerian< dim, VectorType, spacedim >::get_vertices ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell) const
overridevirtual

Return the mapped vertices of the cell. For the current class, this function does not use the support points from the geometry of the current cell but instead evaluates an externally given displacement field in addition to the geometry of the cell.

Reimplemented from Mapping< dim, spacedim >.

Definition at line 55 of file mapping_q1_eulerian.cc.

◆ clone()

template<int dim, class VectorType , int spacedim>
std::unique_ptr< Mapping< dim, spacedim > > MappingQ1Eulerian< dim, VectorType, spacedim >::clone ( ) const
overridevirtual

Return a pointer to a copy of the present object. The caller of this copy then assumes ownership of it.

Reimplemented from MappingQGeneric< dim, spacedim >.

Definition at line 124 of file mapping_q1_eulerian.cc.

◆ preserves_vertex_locations()

template<int dim, typename VectorType = Vector<double>, int spacedim = dim>
virtual bool MappingQ1Eulerian< dim, VectorType, spacedim >::preserves_vertex_locations ( ) const
overridevirtual

Always returns false because MappingQ1Eulerian does not in general preserve vertex locations (unless the translation vector happens to provide for zero displacements at vertex locations).

Reimplemented from MappingQGeneric< dim, spacedim >.

◆ fill_fe_values() [1/2]

template<int dim, class VectorType , int spacedim>
CellSimilarity::Similarity MappingQ1Eulerian< dim, VectorType, spacedim >::fill_fe_values ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const CellSimilarity::Similarity  cell_similarity,
const Quadrature< dim > &  quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase internal_data,
internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &  output_data 
) const
overrideprotectedvirtual

Compute mapping-related information for a cell. See the documentation of Mapping::fill_fe_values() for a discussion of purpose, arguments, and return value of this function.

This function overrides the function in the base class since we cannot use any cell similarity for this class.

Definition at line 133 of file mapping_q1_eulerian.cc.

◆ compute_mapping_support_points()

template<int dim, class VectorType , int spacedim>
std::vector< Point< spacedim > > MappingQ1Eulerian< dim, VectorType, spacedim >::compute_mapping_support_points ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell) const
overrideprotectedvirtual

Compute the support points of the mapping. For the current class, these are the vertices, as obtained by calling Mapping::get_vertices(). See the documentation of MappingQGeneric::compute_mapping_support_points() for more information.

Reimplemented from MappingQGeneric< dim, spacedim >.

Definition at line 108 of file mapping_q1_eulerian.cc.

◆ get_degree()

template<int dim, int spacedim>
unsigned int MappingQGeneric< dim, spacedim >::get_degree ( ) const
inherited

Return the degree of the mapping, i.e. the value which was passed to the constructor.

Definition at line 417 of file mapping_q_generic.cc.

◆ transform_unit_to_real_cell()

template<int dim, int spacedim>
Point< spacedim > MappingQGeneric< dim, spacedim >::transform_unit_to_real_cell ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const Point< dim > &  p 
) const
overridevirtualinherited

Map the point p on the unit cell to the corresponding point on the real cell cell.

Parameters
cellIterator to the cell that will be used to define the mapping.
pLocation of a point on the reference cell.
Returns
The location of the reference point mapped to real space using the mapping defined by the class derived from the current one that implements the mapping, and the coordinates of the cell identified by the first argument.

Implements Mapping< dim, spacedim >.

Definition at line 426 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell()

template<int dim, int spacedim>
Point< dim > MappingQGeneric< dim, spacedim >::transform_real_to_unit_cell ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const Point< spacedim > &  p 
) const
overridevirtualinherited

Map the point p on the real cell to the corresponding point on the unit cell, and return its coordinates. This function provides the inverse of the mapping provided by transform_unit_to_real_cell().

In the codimension one case, this function returns the normal projection of the real point p on the curve or surface identified by the cell.

Note
Polynomial mappings from the reference (unit) cell coordinates to the coordinate system of a real cell are not always invertible if the point for which the inverse mapping is to be computed lies outside the cell's boundaries. In such cases, the current function may fail to compute a point on the reference cell whose image under the mapping equals the given point p. If this is the case then this function throws an exception of type Mapping::ExcTransformationFailed . Whether the given point p lies outside the cell can therefore be determined by checking whether the returned reference coordinates lie inside or outside the reference cell (e.g., using GeometryInfo::is_inside_unit_cell()) or whether the exception mentioned above has been thrown.
Parameters
cellIterator to the cell that will be used to define the mapping.
pLocation of a point on the given cell.
Returns
The reference cell location of the point that when mapped to real space equals the coordinates given by the second argument. This mapping uses the mapping defined by the class derived from the current one that implements the mapping, and the coordinates of the cell identified by the first argument.

Implements Mapping< dim, spacedim >.

Definition at line 604 of file mapping_q_generic.cc.

◆ transform_points_real_to_unit_cell()

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::transform_points_real_to_unit_cell ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const ArrayView< const Point< spacedim >> &  real_points,
const ArrayView< Point< dim >> &  unit_points 
) const
overridevirtualinherited

Map multiple points from the real point locations to points in reference locations. The functionality is essentially the same as looping over all points and calling the Mapping::transform_real_to_unit_cell() function for each point individually, but it can be much faster for certain mappings that implement a more specialized version such as MappingQGeneric. The only difference in behavior is that this function will never throw an ExcTransformationFailed() exception. If the transformation fails for real_points[i], the returned unit_points[i] contains std::numeric_limits<double>::infinity() as the first entry.

Reimplemented from Mapping< dim, spacedim >.

Definition at line 725 of file mapping_q_generic.cc.

◆ transform() [1/5]

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::transform ( const ArrayView< const Tensor< 1, dim >> &  input,
const MappingKind  kind,
const typename Mapping< dim, spacedim >::InternalDataBase internal,
const ArrayView< Tensor< 1, spacedim >> &  output 
) const
overridevirtualinherited

Transform a field of vectors or 1-differential forms according to the selected MappingKind.

Note
Normally, this function is called by a finite element, filling FEValues objects. For this finite element, there should be an alias MappingKind like mapping_bdm, mapping_nedelec, etc. This alias should be preferred to using the kinds below.

The mapping kinds currently implemented by derived classes are:

  • mapping_contravariant: maps a vector field on the reference cell to the physical cell through the Jacobian:

    \[ \mathbf u(\mathbf x) = J(\hat{\mathbf x})\hat{\mathbf u}(\hat{\mathbf x}). \]

    In physics, this is usually referred to as the contravariant transformation. Mathematically, it is the push forward of a vector field.

  • mapping_covariant: maps a field of one-forms on the reference cell to a field of one-forms on the physical cell. (Theoretically this would refer to a DerivativeForm<1,dim,1> but we canonically identify this type with a Tensor<1,dim>). Mathematically, it is the pull back of the differential form

    \[ \mathbf u(\mathbf x) = J(\hat{\mathbf x})(J(\hat{\mathbf x})^{T} J(\hat{\mathbf x}))^{-1}\hat{\mathbf u}(\hat{\mathbf x}). \]

    Gradients of scalar differentiable functions are transformed this way.

    In the case when dim=spacedim the previous formula reduces to

    \[ \mathbf u(\mathbf x) = J(\hat{\mathbf x})^{-T}\hat{\mathbf u}(\hat{\mathbf x}) \]

    because we assume that the mapping \(\mathbf F_K\) is always invertible, and consequently its Jacobian \(J\) is an invertible matrix.

  • mapping_piola: A field of dim-1-forms on the reference cell is also represented by a vector field, but again transforms differently, namely by the Piola transform

    \[ \mathbf u(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J(\hat{\mathbf x}) \hat{\mathbf u}(\hat{\mathbf x}). \]

Parameters
[in]inputAn array (or part of an array) of input objects that should be mapped.
[in]kindThe kind of mapping to be applied.
[in]internalA pointer to an object of type Mapping::InternalDataBase that contains information previously stored by the mapping. The object pointed to was created by the get_data(), get_face_data(), or get_subface_data() function, and will have been updated as part of a call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() for the current cell, before calling the current function. In other words, this object also represents with respect to which cell the transformation should be applied to.
[out]outputAn array (or part of an array) into which the transformed objects should be placed. (Note that the array view is const, but the tensors it points to are not.)

Implements Mapping< dim, spacedim >.

Definition at line 1236 of file mapping_q_generic.cc.

◆ transform() [2/5]

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::transform ( const ArrayView< const DerivativeForm< 1, dim, spacedim >> &  input,
const MappingKind  kind,
const typename Mapping< dim, spacedim >::InternalDataBase internal,
const ArrayView< Tensor< 2, spacedim >> &  output 
) const
overridevirtualinherited

Transform a field of differential forms from the reference cell to the physical cell. It is useful to think of \(\mathbf{T} = \nabla \mathbf u\) and \(\hat{\mathbf T} = \hat \nabla \hat{\mathbf u}\), with \(\mathbf u\) a vector field. The mapping kinds currently implemented by derived classes are:

  • mapping_covariant: maps a field of forms on the reference cell to a field of forms on the physical cell. Mathematically, it is the pull back of the differential form

    \[ \mathbf T(\mathbf x) = \hat{\mathbf T}(\hat{\mathbf x}) J(\hat{\mathbf x})(J(\hat{\mathbf x})^{T} J(\hat{\mathbf x}))^{-1}. \]

    Jacobians of spacedim-vector valued differentiable functions are transformed this way.

    In the case when dim=spacedim the previous formula reduces to

    \[ \mathbf T(\mathbf x) = \hat{\mathbf u}(\hat{\mathbf x}) J(\hat{\mathbf x})^{-1}. \]

Note
It would have been more reasonable to make this transform a template function with the rank in DerivativeForm<1, dim, rank>. Unfortunately C++ does not allow templatized virtual functions. This is why we identify DerivativeForm<1, dim, 1> with a Tensor<1,dim> when using mapping_covariant() in the function transform() above this one.
Parameters
[in]inputAn array (or part of an array) of input objects that should be mapped.
[in]kindThe kind of mapping to be applied.
[in]internalA pointer to an object of type Mapping::InternalDataBase that contains information previously stored by the mapping. The object pointed to was created by the get_data(), get_face_data(), or get_subface_data() function, and will have been updated as part of a call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() for the current cell, before calling the current function. In other words, this object also represents with respect to which cell the transformation should be applied to.
[out]outputAn array (or part of an array) into which the transformed objects should be placed. (Note that the array view is const, but the tensors it points to are not.)

Implements Mapping< dim, spacedim >.

Definition at line 1252 of file mapping_q_generic.cc.

◆ transform() [3/5]

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::transform ( const ArrayView< const Tensor< 2, dim >> &  input,
const MappingKind  kind,
const typename Mapping< dim, spacedim >::InternalDataBase internal,
const ArrayView< Tensor< 2, spacedim >> &  output 
) const
overridevirtualinherited

Transform a tensor field from the reference cell to the physical cell. These tensors are usually the Jacobians in the reference cell of vector fields that have been pulled back from the physical cell. The mapping kinds currently implemented by derived classes are:

  • mapping_contravariant_gradient: it assumes \(\mathbf u(\mathbf x) = J \hat{\mathbf u}\) so that

    \[ \mathbf T(\mathbf x) = J(\hat{\mathbf x}) \hat{\mathbf T}(\hat{\mathbf x}) J(\hat{\mathbf x})^{-1}. \]

  • mapping_covariant_gradient: it assumes \(\mathbf u(\mathbf x) = J^{-T} \hat{\mathbf u}\) so that

    \[ \mathbf T(\mathbf x) = J(\hat{\mathbf x})^{-T} \hat{\mathbf T}(\hat{\mathbf x}) J(\hat{\mathbf x})^{-1}. \]

  • mapping_piola_gradient: it assumes \(\mathbf u(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J(\hat{\mathbf x}) \hat{\mathbf u}(\hat{\mathbf x})\) so that

    \[ \mathbf T(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J(\hat{\mathbf x}) \hat{\mathbf T}(\hat{\mathbf x}) J(\hat{\mathbf x})^{-1}. \]

Todo:
The formulas for mapping_covariant_gradient, mapping_contravariant_gradient and mapping_piola_gradient are only true as stated for linear mappings. If, for example, the mapping is bilinear (or has a higher order polynomial degree) then there is a missing term associated with the derivative of \(J\).
Parameters
[in]inputAn array (or part of an array) of input objects that should be mapped.
[in]kindThe kind of mapping to be applied.
[in]internalA pointer to an object of type Mapping::InternalDataBase that contains information previously stored by the mapping. The object pointed to was created by the get_data(), get_face_data(), or get_subface_data() function, and will have been updated as part of a call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() for the current cell, before calling the current function. In other words, this object also represents with respect to which cell the transformation should be applied to.
[out]outputAn array (or part of an array) into which the transformed objects should be placed. (Note that the array view is const, but the tensors it points to are not.)

Implements Mapping< dim, spacedim >.

Definition at line 1266 of file mapping_q_generic.cc.

◆ transform() [4/5]

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::transform ( const ArrayView< const DerivativeForm< 2, dim, spacedim >> &  input,
const MappingKind  kind,
const typename Mapping< dim, spacedim >::InternalDataBase internal,
const ArrayView< Tensor< 3, spacedim >> &  output 
) const
overridevirtualinherited

Transform a tensor field from the reference cell to the physical cell. This tensors are most of times the hessians in the reference cell of vector fields that have been pulled back from the physical cell.

The mapping kinds currently implemented by derived classes are:

  • mapping_covariant_gradient: maps a field of forms on the reference cell to a field of forms on the physical cell. Mathematically, it is the pull back of the differential form

    \[ \mathbf T_{ijk}(\mathbf x) = \hat{\mathbf T}_{iJK}(\hat{\mathbf x}) J_{jJ}^{\dagger} J_{kK}^{\dagger}\]

    ,

    where

    \[ J^{\dagger} = J(\hat{\mathbf x})(J(\hat{\mathbf x})^{T} J(\hat{\mathbf x}))^{-1}. \]

Hessians of spacedim-vector valued differentiable functions are transformed this way (After subtraction of the product of the derivative with the Jacobian gradient).

In the case when dim=spacedim the previous formula reduces to

\[J^{\dagger} = J^{-1}\]

Parameters
[in]inputAn array (or part of an array) of input objects that should be mapped.
[in]kindThe kind of mapping to be applied.
[in]internalA pointer to an object of type Mapping::InternalDataBase that contains information previously stored by the mapping. The object pointed to was created by the get_data(), get_face_data(), or get_subface_data() function, and will have been updated as part of a call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() for the current cell, before calling the current function. In other words, this object also represents with respect to which cell the transformation should be applied to.
[out]outputAn array (or part of an array) into which the transformed objects should be placed. (Note that the array view is const, but the tensors it points to are not.)

Implements Mapping< dim, spacedim >.

Definition at line 1296 of file mapping_q_generic.cc.

◆ transform() [5/5]

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::transform ( const ArrayView< const Tensor< 3, dim >> &  input,
const MappingKind  kind,
const typename Mapping< dim, spacedim >::InternalDataBase internal,
const ArrayView< Tensor< 3, spacedim >> &  output 
) const
overridevirtualinherited

Transform a field of 3-differential forms from the reference cell to the physical cell. It is useful to think of \(\mathbf{T}_{ijk} = D^2_{jk} \mathbf u_i\) and \(\mathbf{\hat T}_{IJK} = \hat D^2_{JK} \mathbf{\hat u}_I\), with \(\mathbf u_i\) a vector field.

The mapping kinds currently implemented by derived classes are:

  • mapping_contravariant_hessian: it assumes \(\mathbf u_i(\mathbf x) = J_{iI} \hat{\mathbf u}_I\) so that

    \[ \mathbf T_{ijk}(\mathbf x) = J_{iI}(\hat{\mathbf x}) \hat{\mathbf T}_{IJK}(\hat{\mathbf x}) J_{jJ}(\hat{\mathbf x})^{-1} J_{kK}(\hat{\mathbf x})^{-1}. \]

  • mapping_covariant_hessian: it assumes \(\mathbf u_i(\mathbf x) = J_{iI}^{-T} \hat{\mathbf u}_I\) so that

    \[ \mathbf T_{ijk}(\mathbf x) = J_iI(\hat{\mathbf x})^{-1} \hat{\mathbf T}_{IJK}(\hat{\mathbf x}) J_{jJ}(\hat{\mathbf x})^{-1} J_{kK}(\hat{\mathbf x})^{-1}. \]

  • mapping_piola_hessian: it assumes \(\mathbf u_i(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J_{iI}(\hat{\mathbf x}) \hat{\mathbf u}(\hat{\mathbf x})\) so that

    \[ \mathbf T_{ijk}(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J_{iI}(\hat{\mathbf x}) \hat{\mathbf T}_{IJK}(\hat{\mathbf x}) J_{jJ}(\hat{\mathbf x})^{-1} J_{kK}(\hat{\mathbf x})^{-1}. \]

Parameters
[in]inputAn array (or part of an array) of input objects that should be mapped.
[in]kindThe kind of mapping to be applied.
[in]internalA pointer to an object of type Mapping::InternalDataBase that contains information previously stored by the mapping. The object pointed to was created by the get_data(), get_face_data(), or get_subface_data() function, and will have been updated as part of a call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() for the current cell, before calling the current function. In other words, this object also represents with respect to which cell the transformation should be applied to.
[out]outputAn array (or part of an array) into which the transformed objects should be placed.

Implements Mapping< dim, spacedim >.

Definition at line 1345 of file mapping_q_generic.cc.

◆ requires_update_flags()

template<int dim, int spacedim>
UpdateFlags MappingQGeneric< dim, spacedim >::requires_update_flags ( const UpdateFlags  update_flags) const
overridevirtualinherited

Given a set of update flags, compute which other quantities also need to be computed in order to satisfy the request by the given flags. Then return the combination of the original set of flags and those just computed.

As an example, if update_flags contains update_JxW_values (i.e., the product of the determinant of the Jacobian and the weights provided by the quadrature formula), a mapping may require the computation of the full Jacobian matrix in order to compute its determinant. They would then return not just update_JxW_values, but also update_jacobians. (This is not how it is actually done internally in the derived classes that compute the JxW values – they set update_contravariant_transformation instead, from which the determinant can also be computed – but this does not take away from the instructiveness of the example.)

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

See also
UpdateFlags

Implements Mapping< dim, spacedim >.

Definition at line 808 of file mapping_q_generic.cc.

◆ get_data()

template<int dim, int spacedim>
std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > MappingQGeneric< dim, spacedim >::get_data ( const UpdateFlags  update_flags,
const Quadrature< dim > &  quadrature 
) const
overridevirtualinherited

Create and return a pointer to an object into which mappings can store data that only needs to be computed once but that can then be used whenever the mapping is applied to a concrete cell (e.g., in the various transform() functions, as well as in the fill_fe_values(), fill_fe_face_values() and fill_fe_subface_values() that form the interface of mappings with the FEValues class).

Derived classes will return pointers to objects of a type derived from Mapping::InternalDataBase (see there for more information) and may pre- compute some information already (in accordance with what will be asked of the mapping in the future, as specified by the update flags) and for the given quadrature object. Subsequent calls to transform() or fill_fe_values() and friends will then receive back the object created here (with the same set of update flags and for the same quadrature object). Derived classes can therefore pre-compute some information in their get_data() function and store it in the internal data object.

The mapping classes do not keep track of the objects created by this function. Ownership will therefore rest with the caller.

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

Parameters
update_flagsA set of flags that define what is expected of the mapping class in future calls to transform() or the fill_fe_values() group of functions. This set of flags may contain flags that mappings do not know how to deal with (e.g., for information that is in fact computed by the finite element classes, such as UpdateFlags::update_values). Derived classes will need to store these flags, or at least that subset of flags that will require the mapping to perform any actions in fill_fe_values(), in InternalDataBase::update_each.
quadratureThe quadrature object for which mapping information will have to be computed. This includes the locations and weights of quadrature points.
Returns
A pointer to a newly created object of type InternalDataBase (or a derived class). Ownership of this object passes to the calling function.
Note
C++ allows that virtual functions in derived classes may return pointers to objects not of type InternalDataBase but in fact pointers to objects of classes derived from InternalDataBase. (This feature is called "covariant return types".) This is useful in some contexts where the calling is within the derived class and will immediately make use of the returned object, knowing its real (derived) type.

Implements Mapping< dim, spacedim >.

Definition at line 865 of file mapping_q_generic.cc.

◆ get_face_data()

template<int dim, int spacedim>
std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > MappingQGeneric< dim, spacedim >::get_face_data ( const UpdateFlags  update_flags,
const Quadrature< dim - 1 > &  quadrature 
) const
overridevirtualinherited

Like get_data(), but in preparation for later calls to transform() or fill_fe_face_values() that will need information about mappings from the reference face to a face of a concrete cell.

Parameters
update_flagsA set of flags that define what is expected of the mapping class in future calls to transform() or the fill_fe_values() group of functions. This set of flags may contain flags that mappings do not know how to deal with (e.g., for information that is in fact computed by the finite element classes, such as UpdateFlags::update_values). Derived classes will need to store these flags, or at least that subset of flags that will require the mapping to perform any actions in fill_fe_values(), in InternalDataBase::update_each.
quadratureThe quadrature object for which mapping information will have to be computed. This includes the locations and weights of quadrature points.
Returns
A pointer to a newly created object of type InternalDataBase (or a derived class). Ownership of this object passes to the calling function.
Note
C++ allows that virtual functions in derived classes may return pointers to objects not of type InternalDataBase but in fact pointers to objects of classes derived from InternalDataBase. (This feature is called "covariant return types".) This is useful in some contexts where the calling is within the derived class and will immediately make use of the returned object, knowing its real (derived) type.

Implements Mapping< dim, spacedim >.

Definition at line 880 of file mapping_q_generic.cc.

◆ get_subface_data()

template<int dim, int spacedim>
std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > MappingQGeneric< dim, spacedim >::get_subface_data ( const UpdateFlags  update_flags,
const Quadrature< dim - 1 > &  quadrature 
) const
overridevirtualinherited

Like get_data() and get_face_data(), but in preparation for later calls to transform() or fill_fe_subface_values() that will need information about mappings from the reference face to a child of a face (i.e., subface) of a concrete cell.

Parameters
update_flagsA set of flags that define what is expected of the mapping class in future calls to transform() or the fill_fe_values() group of functions. This set of flags may contain flags that mappings do not know how to deal with (e.g., for information that is in fact computed by the finite element classes, such as UpdateFlags::update_values). Derived classes will need to store these flags, or at least that subset of flags that will require the mapping to perform any actions in fill_fe_values(), in InternalDataBase::update_each.
quadratureThe quadrature object for which mapping information will have to be computed. This includes the locations and weights of quadrature points.
Returns
A pointer to a newly created object of type InternalDataBase (or a derived class). Ownership of this object passes to the calling function.
Note
C++ allows that virtual functions in derived classes may return pointers to objects not of type InternalDataBase but in fact pointers to objects of classes derived from InternalDataBase. (This feature is called "covariant return types".) This is useful in some contexts where the calling is within the derived class and will immediately make use of the returned object, knowing its real (derived) type.

Implements Mapping< dim, spacedim >.

Definition at line 899 of file mapping_q_generic.cc.

◆ fill_fe_values() [2/2]

template<int dim, int spacedim = dim>
CellSimilarity::Similarity MappingQGeneric< dim, spacedim >::fill_fe_values ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const CellSimilarity::Similarity  cell_similarity,
const Quadrature< dim > &  quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase internal_data,
::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &  output_data 
) const
overridevirtualinherited

Compute information about the mapping from the reference cell to the real cell indicated by the first argument to this function. Derived classes will have to implement this function based on the kind of mapping they represent. It is called by FEValues::reinit().

Conceptually, this function's represents the application of the mapping \(\mathbf x=\mathbf F_K(\hat {\mathbf x})\) from reference coordinates \(\mathbf\in [0,1]^d\) to real space coordinates \(\mathbf x\) for a given cell \(K\). Its purpose is to compute the following kinds of data:

  • Data that results from the application of the mapping itself, e.g., computing the location \(\mathbf x_q = \mathbf F_K(\hat{\mathbf x}_q)\) of quadrature points on the real cell, and that is directly useful to users of FEValues, for example during assembly.
  • Data that is necessary for finite element implementations to compute their shape functions on the real cell. To this end, the FEValues::reinit() function calls FiniteElement::fill_fe_values() after the current function, and the output of this function serves as input to FiniteElement::fill_fe_values(). Examples of information that needs to be computed here for use by the finite element classes is the Jacobian of the mapping, \(\hat\nabla \mathbf F_K(\hat{\mathbf x})\) or its inverse, for example to transform the gradients of shape functions on the reference cell to the gradients of shape functions on the real cell.

The information computed by this function is used to fill the various member variables of the output argument of this function. Which of the member variables of that structure should be filled is determined by the update flags stored in the Mapping::InternalDataBase object passed to this function.

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

Parameters
[in]cellThe cell of the triangulation for which this function is to compute a mapping from the reference cell to.
[in]cell_similarityWhether or not the cell given as first argument is simply a translation, rotation, etc of the cell for which this function was called the most recent time. This information is computed simply by matching the vertices (as stored by the Triangulation) between the previous and the current cell. The value passed here may be modified by implementations of this function and should then be returned (see the discussion of the return value of this function).
[in]quadratureA reference to the quadrature formula in use for the current evaluation. This quadrature object is the same as the one used when creating the internal_data object. The object is used both to map the location of quadrature points, as well as to compute the JxW values for each quadrature point (which involves the quadrature weights).
[in]internal_dataA reference to an object previously created by get_data() and that may be used to store information the mapping can compute once on the reference cell. See the documentation of the Mapping::InternalDataBase class for an extensive description of the purpose of these objects.
[out]output_dataA reference to an object whose member variables should be computed. Not all of the members of this argument need to be filled; which ones need to be filled is determined by the update flags stored inside the internal_data object.
Returns
An updated value of the cell_similarity argument to this function. The returned value will be used for the corresponding argument when FEValues::reinit() calls FiniteElement::fill_fe_values(). In most cases, derived classes will simply want to return the value passed for cell_similarity. However, implementations of this function may downgrade the level of cell similarity. This is, for example, the case for classes that take not only into account the locations of the vertices of a cell (as reported by the Triangulation), but also other information specific to the mapping. The purpose is that FEValues::reinit() can compute whether a cell is similar to the previous one only based on the cell's vertices, whereas the mapping may also consider displacement fields (e.g., in the MappingQ1Eulerian and MappingFEField classes). In such cases, the mapping may conclude that the previously computed cell similarity is too optimistic, and invalidate it for subsequent use in FiniteElement::fill_fe_values() by returning a less optimistic cell similarity value.
Note
FEValues ensures that this function is always called with the same pair of internal_data and output_data objects. In other words, if an implementation of this function knows that it has written a piece of data into the output argument in a previous call, then there is no need to copy it there again in a later call if the implementation knows that this is the same value.

Implements Mapping< dim, spacedim >.

Definition at line 918 of file mapping_q_generic.cc.

◆ fill_fe_face_values()

template<int dim, int spacedim = dim>
void MappingQGeneric< dim, spacedim >::fill_fe_face_values ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const unsigned int  face_no,
const Quadrature< dim - 1 > &  quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase internal_data,
::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &  output_data 
) const
overridevirtualinherited

This function is the equivalent to Mapping::fill_fe_values(), but for faces of cells. See there for an extensive discussion of its purpose. It is called by FEFaceValues::reinit().

Parameters
[in]cellThe cell of the triangulation for which this function is to compute a mapping from the reference cell to.
[in]face_noThe number of the face of the given cell for which information is requested.
[in]quadratureA reference to the quadrature formula in use for the current evaluation. This quadrature object is the same as the one used when creating the internal_data object. The object is used both to map the location of quadrature points, as well as to compute the JxW values for each quadrature point (which involves the quadrature weights).
[in]internal_dataA reference to an object previously created by get_data() and that may be used to store information the mapping can compute once on the reference cell. See the documentation of the Mapping::InternalDataBase class for an extensive description of the purpose of these objects.
[out]output_dataA reference to an object whose member variables should be computed. Not all of the members of this argument need to be filled; which ones need to be filled is determined by the update flags stored inside the internal_data object.

Implements Mapping< dim, spacedim >.

Definition at line 1140 of file mapping_q_generic.cc.

◆ fill_fe_subface_values()

template<int dim, int spacedim = dim>
void MappingQGeneric< dim, spacedim >::fill_fe_subface_values ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const unsigned int  face_no,
const unsigned int  subface_no,
const Quadrature< dim - 1 > &  quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase internal_data,
::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &  output_data 
) const
overridevirtualinherited

This function is the equivalent to Mapping::fill_fe_values(), but for subfaces (i.e., children of faces) of cells. See there for an extensive discussion of its purpose. It is called by FESubfaceValues::reinit().

Parameters
[in]cellThe cell of the triangulation for which this function is to compute a mapping from the reference cell to.
[in]face_noThe number of the face of the given cell for which information is requested.
[in]subface_noThe number of the child of a face of the given cell for which information is requested.
[in]quadratureA reference to the quadrature formula in use for the current evaluation. This quadrature object is the same as the one used when creating the internal_data object. The object is used both to map the location of quadrature points, as well as to compute the JxW values for each quadrature point (which involves the quadrature weights).
[in]internal_dataA reference to an object previously created by get_data() and that may be used to store information the mapping can compute once on the reference cell. See the documentation of the Mapping::InternalDataBase class for an extensive description of the purpose of these objects.
[out]output_dataA reference to an object whose member variables should be computed. Not all of the members of this argument need to be filled; which ones need to be filled is determined by the update flags stored inside the internal_data object.

Implements Mapping< dim, spacedim >.

Definition at line 1186 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell_internal() [1/7]

template<int dim, int spacedim>
Point< dim > MappingQGeneric< dim, spacedim >::transform_real_to_unit_cell_internal ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const Point< spacedim > &  p,
const Point< dim > &  initial_p_unit 
) const
protectedinherited

Transform the point p on the real cell to the corresponding point on the unit cell cell by a Newton iteration.

Definition at line 461 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell_internal() [2/7]

template<>
Point< 1 > MappingQGeneric< 1, 1 >::transform_real_to_unit_cell_internal ( const Triangulation< 1, 1 >::cell_iterator &  cell,
const Point< 1 > &  p,
const Point< 1 > &  initial_p_unit 
) const
protectedinherited

Definition at line 475 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell_internal() [3/7]

template<>
Point< 2 > MappingQGeneric< 2, 2 >::transform_real_to_unit_cell_internal ( const Triangulation< 2, 2 >::cell_iterator &  cell,
const Point< 2 > &  p,
const Point< 2 > &  initial_p_unit 
) const
protectedinherited

Definition at line 495 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell_internal() [4/7]

template<>
Point< 3 > MappingQGeneric< 3, 3 >::transform_real_to_unit_cell_internal ( const Triangulation< 3, 3 >::cell_iterator &  cell,
const Point< 3 > &  p,
const Point< 3 > &  initial_p_unit 
) const
protectedinherited

Definition at line 513 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell_internal() [5/7]

template<>
Point< 1 > MappingQGeneric< 1, 2 >::transform_real_to_unit_cell_internal ( const Triangulation< 1, 2 >::cell_iterator &  cell,
const Point< 2 > &  p,
const Point< 1 > &  initial_p_unit 
) const
protectedinherited

Definition at line 531 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell_internal() [6/7]

template<>
Point< 2 > MappingQGeneric< 2, 3 >::transform_real_to_unit_cell_internal ( const Triangulation< 2, 3 >::cell_iterator &  cell,
const Point< 3 > &  p,
const Point< 2 > &  initial_p_unit 
) const
protectedinherited

Definition at line 562 of file mapping_q_generic.cc.

◆ transform_real_to_unit_cell_internal() [7/7]

template<>
Point< 1 > MappingQGeneric< 1, 3 >::transform_real_to_unit_cell_internal ( const Triangulation< 1, 3 >::cell_iterator &  ,
const Point< 3 > &  ,
const Point< 1 > &   
) const
protectedinherited

Definition at line 591 of file mapping_q_generic.cc.

◆ add_line_support_points()

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::add_line_support_points ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
std::vector< Point< spacedim >> &  a 
) const
protectedvirtualinherited

Append the support points of all shape functions located on bounding lines of the given cell to the vector a. Points located on the vertices of a line are not included.

This function uses the underlying manifold object of the line (or, if none is set, of the cell) for the location of the requested points. This function is usually called by compute_mapping_support_points() function.

This function is made virtual in order to allow derived classes to choose shape function support points differently than the present class, which chooses the points as interpolation points on the boundary.

Definition at line 1368 of file mapping_q_generic.cc.

◆ add_quad_support_points() [1/3]

template<int dim, int spacedim>
void MappingQGeneric< dim, spacedim >::add_quad_support_points ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
std::vector< Point< spacedim >> &  a 
) const
protectedvirtualinherited

Append the support points of all shape functions located on bounding faces (quads in 3d) of the given cell to the vector a. This function is only defined for dim=3. Points located on the vertices or lines of a quad are not included.

This function uses the underlying manifold object of the quad (or, if none is set, of the cell) for the location of the requested points. This function is usually called by compute_mapping_support_points().

This function is made virtual in order to allow derived classes to choose shape function support points differently than the present class, which chooses the points as interpolation points on the boundary.

Definition at line 1534 of file mapping_q_generic.cc.

◆ add_quad_support_points() [2/3]

template<>
void MappingQGeneric< 3, 3 >::add_quad_support_points ( const Triangulation< 3, 3 >::cell_iterator &  cell,
std::vector< Point< 3 >> &  a 
) const
protectedinherited

Definition at line 1435 of file mapping_q_generic.cc.

◆ add_quad_support_points() [3/3]

template<>
void MappingQGeneric< 2, 3 >::add_quad_support_points ( const Triangulation< 2, 3 >::cell_iterator &  cell,
std::vector< Point< 3 >> &  a 
) const
protectedinherited

Definition at line 1504 of file mapping_q_generic.cc.

◆ get_center()

template<int dim, int spacedim>
Point< spacedim > Mapping< dim, spacedim >::get_center ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const bool  map_center_of_reference_cell = true 
) const
virtualinherited

Return the mapped center of a cell.

If you are using a (bi-,tri-)linear mapping that preserves vertex locations, this function simply returns the value also produced by cell->center(). However, there are also mappings that add displacements or choose completely different locations, e.g., MappingQEulerian, MappingQ1Eulerian, or MappingFEField, and mappings based on high order polynomials, for which the center may not coincide with the average of the vertex locations.

By default, this function returns the push forward of the center of the reference cell. If the parameter map_center_of_reference_cell is set to false, than the return value will be the average of the vertex locations, as returned by the get_vertices() method.

Parameters
[in]cellThe cell for which you want to compute the center
[in]map_center_of_reference_cellA flag that switches the algorithm for the computation of the cell center from transform_unit_to_real_cell() applied to the center of the reference cell to computing the vertex averages.

Definition at line 45 of file mapping.cc.

◆ get_bounding_box()

template<int dim, int spacedim>
BoundingBox< spacedim > Mapping< dim, spacedim >::get_bounding_box ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell) const
virtualinherited

Return the bounding box of a mapped cell.

If you are using a (bi-,tri-)linear mapping that preserves vertex locations, this function simply returns the value also produced by cell->bounding_box(). However, there are also mappings that add displacements or choose completely different locations, e.g., MappingQEulerian, MappingQ1Eulerian, or MappingFEField.

This function returns the bounding box containing all the vertices of the cell, as returned by the get_vertices() method. Beware of the fact that for higher order mappings this bounding box is only an approximation of the true bounding box, since it does not take into account curved faces, and it may be smaller than the true bounding box.

Parameters
[in]cellThe cell for which you want to compute the bounding box

Definition at line 70 of file mapping.cc.

◆ project_real_point_to_unit_point_on_face()

template<int dim, int spacedim>
Point< dim - 1 > Mapping< dim, spacedim >::project_real_point_to_unit_point_on_face ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const unsigned int  face_no,
const Point< spacedim > &  p 
) const
inherited

Transform the point p on the real cell to the corresponding point on the reference cell, and then project this point to a (dim-1)-dimensional point in the coordinate system of the face with the given face number face_no. Ideally the point p is near the face face_no, but any point in the cell can technically be projected.

This function does not make physical sense when dim=1, so it throws an exception in this case.

Definition at line 107 of file mapping.cc.

◆ subscribe()

void Subscriptor::subscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

◆ unsubscribe()

void Subscriptor::unsubscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const
inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >
void Subscriptor::list_subscribers ( StreamType &  stream) const
inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

◆ serialize()

template<class Archive >
void Subscriptor::serialize ( Archive &  ar,
const unsigned int  version 
)
inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 309 of file subscriptor.h.

Member Data Documentation

◆ euler_transform_vectors

template<int dim, typename VectorType = Vector<double>, int spacedim = dim>
SmartPointer<const VectorType, MappingQ1Eulerian<dim, VectorType, spacedim> > MappingQ1Eulerian< dim, VectorType, spacedim >::euler_transform_vectors
protected

Reference to the vector of shifts.

Definition at line 179 of file mapping_q1_eulerian.h.

◆ shiftmap_dof_handler

template<int dim, typename VectorType = Vector<double>, int spacedim = dim>
SmartPointer<const DoFHandler<dim, spacedim>, MappingQ1Eulerian<dim, VectorType, spacedim> > MappingQ1Eulerian< dim, VectorType, spacedim >::shiftmap_dof_handler
protected

Pointer to the DoFHandler to which the mapping vector is associated.

Definition at line 186 of file mapping_q1_eulerian.h.

◆ polynomial_degree

template<int dim, int spacedim = dim>
const unsigned int MappingQGeneric< dim, spacedim >::polynomial_degree
protectedinherited

The degree of the polynomials used as shape functions for the mapping of cells.

Definition at line 604 of file mapping_q_generic.h.

◆ line_support_points

template<int dim, int spacedim = dim>
const std::vector<Point<1> > MappingQGeneric< dim, spacedim >::line_support_points
protectedinherited

Definition at line 614 of file mapping_q_generic.h.

◆ polynomials_1d

template<int dim, int spacedim = dim>
const std::vector<Polynomials::Polynomial<double> > MappingQGeneric< dim, spacedim >::polynomials_1d
protectedinherited

Definition at line 621 of file mapping_q_generic.h.

◆ renumber_lexicographic_to_hierarchic

template<int dim, int spacedim = dim>
const std::vector<unsigned int> MappingQGeneric< dim, spacedim >::renumber_lexicographic_to_hierarchic
protectedinherited

Definition at line 628 of file mapping_q_generic.h.

◆ unit_cell_support_points

template<int dim, int spacedim = dim>
const std::vector<Point<dim> > MappingQGeneric< dim, spacedim >::unit_cell_support_points
protectedinherited

Definition at line 640 of file mapping_q_generic.h.

◆ support_point_weights_perimeter_to_interior

template<int dim, int spacedim = dim>
const std::vector<Table<2, double> > MappingQGeneric< dim, spacedim >::support_point_weights_perimeter_to_interior
protectedinherited

A vector of tables of weights by which we multiply the locations of the support points on the perimeter of an object (line, quad, hex) to get the location of interior support points.

Access into this table is by [structdim-1], i.e., use 0 to access the support point weights on a line (i.e., the interior points of the GaussLobatto quadrature), use 1 to access the support point weights from to perimeter to the interior of a quad, and use 2 to access the support point weights from the perimeter to the interior of a hex.

The table itself contains as many columns as there are surrounding points to a particular object (2 for a line, 4 + 4*(degree-1) for a quad, 8 + 12*(degree-1) + 6*(degree-1)*(degree-1) for a hex) and as many rows as there are strictly interior points.

For the definition of this table see equation (8) of the `mapping' report.

Definition at line 662 of file mapping_q_generic.h.

◆ support_point_weights_cell

template<int dim, int spacedim = dim>
const Table<2, double> MappingQGeneric< dim, spacedim >::support_point_weights_cell
protectedinherited

A table of weights by which we multiply the locations of the vertex points of the cell to get the location of all additional support points, both on lines, quads, and hexes (as appropriate). This data structure is used when we fill all support points at once, which is the case if the same manifold is attached to all sub-entities of a cell. This way, we can avoid some of the overhead in transforming data for mappings.

The table has as many rows as there are vertices to the cell (2 in 1D, 4 in 2D, 8 in 3D), and as many rows as there are additional support points in the mapping, i.e., (degree+1)^dim - 2^dim.

Definition at line 676 of file mapping_q_generic.h.


The documentation for this class was generated from the following files: