Reference documentation for deal.II version 9.6.2
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MappingQ< 3, 4 > Class Referenceabstract
Inheritance diagram for MappingQ< 3, 4 >:

Public Member Functions

 MappingQ (const unsigned int polynomial_degree)
virtual std::unique_ptr< Mapping< dim, spacedim > > clone () const override
unsigned int get_degree () const
virtual bool preserves_vertex_locations () const override
virtual BoundingBox< spacedim > get_bounding_box (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const override
virtual bool is_compatible_with (const ReferenceCell &reference_cell) const override
void fill_mapping_data_for_generic_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< dim > > &unit_points, const UpdateFlags update_flags, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const
void fill_mapping_data_for_face_quadrature (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_number, const Quadrature< dim - 1 > &face_quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const
virtual boost::container::small_vector< Point< spacedim >, GeometryInfo< dim >::vertices_per_cellget_vertices (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const
virtual Point< spacedim > get_center (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const bool map_barycenter_of_reference_cell=true) const
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
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
void list_subscribers (StreamType &stream) const
void list_subscribers () const
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=0

Static Public Member Functions

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

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
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
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
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
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
Point< 1 > transform_real_to_unit_cell_internal (const Triangulation< 1, 3 >::cell_iterator &, const Point< 3 > &, const Point< 1 > &) const
void add_quad_support_points (const Triangulation< 3, 3 >::cell_iterator &cell, std::vector< Point< 3 > > &a) const
void add_quad_support_points (const Triangulation< 2, 3 >::cell_iterator &cell, std::vector< Point< 3 > > &a) const
virtual std::vector< Point< spacedim > > compute_mapping_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const
virtual void add_line_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim > > &a) const
Interface with FEValues and friends
virtual UpdateFlags requires_update_flags (const UpdateFlags update_flags) const override
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_data (const UpdateFlags, const Quadrature< dim > &quadrature) const override
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_face_data (const UpdateFlags flags, const hp::QCollection< dim - 1 > &quadrature) const override
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_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 hp::QCollection< 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
virtual void fill_fe_immersed_surface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const NonMatching::ImmersedSurfaceQuadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
Interface with FEValues
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=0
virtual void fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const hp::QCollection< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const
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=0

Protected Attributes

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, double > support_point_weights_cell

Private Types

using map_value_type
using map_iterator

Private Member Functions

void check_no_subscribers () const noexcept

Private Attributes

std::atomic< unsigned intcounter
std::map< std::string, unsigned intcounter_map
std::vector< std::atomic< bool > * > validity_pointers
const std::type_info * object_info

Static Private Attributes

static std::mutex mutex

Friends

class MappingQCache

Detailed Description

Definition at line 315 of file mapping_q.cc.

Member Typedef Documentation

◆ map_value_type

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

◆ map_iterator

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.h.

Constructor & Destructor Documentation

◆ MappingQ()

MappingQ< dim, spacedim >::MappingQ ( const unsigned int polynomial_degree)

Constructor. polynomial_degree denotes the polynomial degree of the polynomials that are used to map cells from the reference to the real cell.

Definition at line 117 of file mapping_q.cc.

Member Function Documentation

◆ transform_real_to_unit_cell_internal() [1/6]

Point< 1 > MappingQ< 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
protected

Definition at line 342 of file mapping_q.cc.

◆ transform_real_to_unit_cell_internal() [2/6]

Point< 2 > MappingQ< 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
protected

Definition at line 374 of file mapping_q.cc.

◆ transform_real_to_unit_cell_internal() [3/6]

Point< 3 > MappingQ< 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
protected

Definition at line 404 of file mapping_q.cc.

◆ transform_real_to_unit_cell_internal() [4/6]

Point< 1 > MappingQ< 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
protected

Definition at line 434 of file mapping_q.cc.

◆ transform_real_to_unit_cell_internal() [5/6]

Point< 2 > MappingQ< 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
protected

Definition at line 467 of file mapping_q.cc.

◆ transform_real_to_unit_cell_internal() [6/6]

Point< 1 > MappingQ< 1, 3 >::transform_real_to_unit_cell_internal ( const Triangulation< 1, 3 >::cell_iterator & ,
const Point< 3 > & ,
const Point< 1 > &  ) const
protected

Definition at line 500 of file mapping_q.cc.

◆ add_quad_support_points() [1/2]

void MappingQ< 3, 3 >::add_quad_support_points ( const Triangulation< 3, 3 >::cell_iterator & cell,
std::vector< Point< 3 > > & a ) const
protected

Definition at line 1626 of file mapping_q.cc.

◆ add_quad_support_points() [2/2]

void MappingQ< 2, 3 >::add_quad_support_points ( const Triangulation< 2, 3 >::cell_iterator & cell,
std::vector< Point< 3 > > & a ) const
protected

Definition at line 1695 of file mapping_q.cc.

◆ clone()

std::unique_ptr< Mapping< dim, spacedim > > MappingQ< dim, spacedim >::clone ( ) const
overridevirtual

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

The function is declared abstract virtual in this base class, and derived classes will have to implement it.

This function is mainly used by the hp::MappingCollection class.

Implements Mapping< dim, spacedim >.

Definition at line 135 of file mapping_q.cc.

◆ get_degree()

unsigned int MappingQ< dim, spacedim >::get_degree ( ) const

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

Definition at line 142 of file mapping_q.cc.

◆ preserves_vertex_locations()

virtual bool MappingQ< dim, spacedim >::preserves_vertex_locations ( ) const
overridevirtual

Always returns true because the default implementation of functions in this class preserves vertex locations.

Implements Mapping< dim, spacedim >.

◆ get_bounding_box()

BoundingBox< spacedim > MappingQ< dim, spacedim >::get_bounding_box ( const typename Triangulation< dim, spacedim >::cell_iterator & cell) const
overridevirtual

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.

For linear mappings, this function returns the bounding box containing all the vertices of the cell, as returned by the get_vertices() method. For higher order mappings defined through support points, the bounding box is only guaranteed to contain all the support points, and it is, in general, only an approximation of the true bounding box, which may be larger.

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

Reimplemented from Mapping< dim, spacedim >.

Definition at line 153 of file mapping_q.cc.

◆ is_compatible_with()

bool MappingQ< dim, spacedim >::is_compatible_with ( const ReferenceCell & reference_cell) const
overridevirtual

Returns if this instance of Mapping is compatible with the type of cell in reference_cell.

Implements Mapping< dim, spacedim >.

Definition at line 157 of file mapping_q.cc.

◆ transform_unit_to_real_cell()

Point< spacedim > MappingQ< dim, spacedim >::transform_unit_to_real_cell ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const Point< dim > & p ) const
overridevirtual

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 166 of file mapping_q.cc.

◆ transform_real_to_unit_cell()

Point< dim > MappingQ< dim, spacedim >::transform_real_to_unit_cell ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const Point< spacedim > & p ) const
overridevirtual

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 172 of file mapping_q.cc.

◆ transform_points_real_to_unit_cell()

void MappingQ< 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
overridevirtual

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 MappingQ. 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 178 of file mapping_q.cc.

◆ transform() [1/2]

void MappingQ< 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
overridevirtual

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.)

Definition at line 194 of file mapping_q.cc.

◆ fill_mapping_data_for_generic_points()

void MappingQ< dim, spacedim >::fill_mapping_data_for_generic_points ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const ArrayView< const Point< dim > > & unit_points,
const UpdateFlags update_flags,
internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > & output_data ) const

As opposed to the other fill_fe_values() and fill_fe_face_values() functions that rely on pre-computed information of InternalDataBase, this function chooses the flexible evaluation path on the cell and points passed in to the current function.

Parameters
[in]cellThe cell where to evaluate the mapping
[in]unit_pointsThe points in reference coordinates where the transformation (Jacobians, positions) should be computed.
[in]update_flagsThe kind of information that should be computed.
[out]output_dataA struct containing the evaluated quantities such as the Jacobian resulting from application of the mapping on the given cell with its underlying manifolds.

Definition at line 249 of file mapping_q.cc.

◆ fill_mapping_data_for_face_quadrature()

void MappingQ< dim, spacedim >::fill_mapping_data_for_face_quadrature ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const unsigned int face_number,
const Quadrature< dim - 1 > & face_quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase & internal_data,
internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > & output_data ) const

As opposed to the fill_fe_face_values() function that relies on pre-computed information of InternalDataBase, this function chooses the flexible evaluation path on the cell and points passed in to the current function.

Parameters
[in]cellThe cell where to evaluate the mapping.
[in]face_numberThe face number where to evaluate the mapping.
[in]face_quadratureThe quadrature points where the transformation (Jacobians, positions) should be computed.
[in]internal_dataA reference to an object previously created 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 struct containing the evaluated quantities such as the Jacobian resulting from application of the mapping on the given cell with its underlying manifolds.

Definition at line 279 of file mapping_q.cc.

◆ requires_update_flags()

UpdateFlags MappingQ< dim, spacedim >::requires_update_flags ( const UpdateFlags update_flags) const
overrideprotectedvirtual

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 topic.

See also
UpdateFlags

Implements Mapping< dim, spacedim >.

Definition at line 456 of file mapping_q.cc.

◆ get_data()

std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > MappingQ< dim, spacedim >::get_data ( const UpdateFlags update_flags,
const Quadrature< dim > & quadrature ) const
overrideprotectedvirtual

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 topic.

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 460 of file mapping_q.cc.

◆ get_face_data()

std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > MappingQ< dim, spacedim >::get_face_data ( const UpdateFlags flags,
const hp::QCollection< dim - 1 > & quadrature ) const
overrideprotectedvirtual

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.

Reimplemented from Mapping< dim, spacedim >.

Definition at line 466 of file mapping_q.cc.

◆ get_subface_data()

std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > MappingQ< dim, spacedim >::get_subface_data ( const UpdateFlags flags,
const Quadrature< dim - 1 > & quadrature ) const
overrideprotectedvirtual

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 471 of file mapping_q.cc.

◆ fill_fe_values() [1/2]

CellSimilarity::Similarity MappingQ< 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
overrideprotectedvirtual

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 topic.

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.

Definition at line 476 of file mapping_q.cc.

◆ fill_fe_face_values() [1/2]

void MappingQ< dim, spacedim >::fill_fe_face_values ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const unsigned int face_no,
const hp::QCollection< dim - 1 > & quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase & internal_data,
internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > & output_data ) const
overrideprotectedvirtual

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.

Definition at line 488 of file mapping_q.cc.

◆ fill_fe_subface_values() [1/2]

void MappingQ< 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
overrideprotectedvirtual

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.

Definition at line 498 of file mapping_q.cc.

◆ fill_fe_immersed_surface_values()

void MappingQ< dim, spacedim >::fill_fe_immersed_surface_values ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const NonMatching::ImmersedSurfaceQuadrature< dim > & quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase & internal_data,
internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > & output_data ) const
overrideprotectedvirtual

The equivalent of Mapping::fill_fe_values(), but for the case that the quadrature is an ImmersedSurfaceQuadrature. See there for a comprehensive description of the input parameters. This function is called by FEImmersedSurfaceValues::reinit().

Reimplemented from Mapping< dim, spacedim >.

Definition at line 509 of file mapping_q.cc.

◆ compute_mapping_support_points()

std::vector< Point< spacedim > > MappingQ< dim, spacedim >::compute_mapping_support_points ( const typename Triangulation< dim, spacedim >::cell_iterator & cell) const
protectedvirtual

Return the locations of support points for the mapping. For example, for $Q_1$ mappings these are the vertices, and for higher order polynomial mappings they are the vertices plus interior points on edges, faces, and the cell interior that are placed in consultation with the Manifold description of the domain and its boundary. However, other classes may override this function differently. In particular, the MappingQ1Eulerian class does exactly this by not computing the support points from the geometry of the current cell but instead evaluating an externally given displacement field in addition to the geometry of the cell.

The default implementation of this function is appropriate for most cases. It takes the locations of support points on the boundary of the cell from the underlying manifold. Interior support points (ie. support points in quads for 2d, in hexes for 3d) are then computed using an interpolation from the lower-dimensional entities (lines, quads) in order to make the transformation as smooth as possible without introducing additional boundary layers within the cells due to the placement of support points.

The function works its way from the vertices (which it takes from the given cell) via the support points on the line (for which it calls the add_line_support_points() function) and the support points on the quad faces (in 3d, for which it calls the add_quad_support_points() function). It then adds interior support points that are either computed by interpolation from the surrounding points using weights for transfinite interpolation, or if dim<spacedim, it asks the underlying manifold for the locations of interior points.

Definition at line 628 of file mapping_q.cc.

◆ add_line_support_points()

void MappingQ< dim, spacedim >::add_line_support_points ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
std::vector< Point< spacedim > > & a ) const
protectedvirtual

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 655 of file mapping_q.cc.

◆ get_vertices()

virtual boost::container::small_vector< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell > Mapping< dim, spacedim >::get_vertices ( const typename Triangulation< dim, spacedim >::cell_iterator & cell) const
virtual

Return the mapped vertices of a cell.

Most of the time, these values will simply be the coordinates of the vertices of a cell as returned by cell->vertex(v) for vertex v, i.e., information stored by the triangulation. However, there are also mappings that add displacements or choose completely different locations, e.g., MappingQEulerian, MappingQ1Eulerian, or MappingFEField.

The default implementation of this function simply returns the information stored by the triangulation, i.e., cell->vertex(v).

◆ get_center()

virtual Point< spacedim > Mapping< dim, spacedim >::get_center ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const bool map_barycenter_of_reference_cell = true ) const
virtual

Return one of two possible mapped centers 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 barycenter of the reference cell. If the parameter map_barycenter_of_reference_cell is set to false, then the returned 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_barycenter_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.

◆ project_real_point_to_unit_point_on_face()

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

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.

◆ ExcInvalidData()

::ExceptionBase & Mapping< dim, spacedim >::ExcInvalidData ( )
static

Exception

◆ ExcTransformationFailed()

::ExceptionBase & Mapping< dim, spacedim >::ExcTransformationFailed ( )
static

Computing the mapping between a real space point and a point in reference space failed, typically because the given point lies outside the cell where the inverse mapping is not unique.

Note
The message that will be printed by this exception reads:
"Computing the mapping between a real space point and a point in reference " "space failed, typically because the given point lies outside the cell " "where the inverse mapping is not unique."

◆ ExcDistortedMappedCell()

::ExceptionBase & Mapping< dim, spacedim >::ExcDistortedMappedCell ( Point< spacedim > arg1,
double arg2,
int arg3 )
static

deal.II assumes the Jacobian determinant to be positive. When the cell geometry is distorted under the image of the mapping, the mapping becomes invalid and this exception is thrown.

Note
The message that will be printed by this exception reads:
<< "The image of the mapping applied to cell with center [" << arg1 << "] is distorted. The cell geometry or the " << "mapping are invalid, giving a non-positive volume " << "fraction of " << arg2 << " in quadrature point " << arg3 << '.'

◆ subscribe()

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

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

Definition at line 116 of file subscriptor.cc.

◆ unsubscribe()

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

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 126 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const
inline

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 135 of file subscriptor.h.

◆ list_subscribers() [1/2]

void Subscriptor::list_subscribers ( StreamType & stream) const
inline

List the subscribers to the input stream.

Definition at line 142 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

List the subscribers to deallog.

Definition at line 148 of file subscriptor.cc.

◆ ExcInUse()

::ExceptionBase & Subscriptor::ExcInUse ( int arg1,
std::string arg2,
std::string arg3 )
static

Exception: Object may not be deleted, since it is used.

Note
The message that will be printed by this exception reads:
<< "Object of class " << arg2 << " is still used by " << arg1 << " other objects." << "\n\n" << "(Additional information: " << arg3 << ")\n\n" << "See the entry in the Frequently Asked Questions of " << "deal.II (linked to from http://www.dealii.org/) for " << "a lot more information on what this error means and " << "how to fix programs in which it happens."

◆ ExcNoSubscriber()

::ExceptionBase & Subscriptor::ExcNoSubscriber ( std::string arg1,
std::string arg2 )
static

A subscriber with the identification string given to Subscriptor::unsubscribe() did not subscribe to the object.

Note
The message that will be printed by this exception reads:
<< "No subscriber with identifier <" << arg2 << "> subscribes to this object of class " << arg1 << ". Consequently, it cannot be unsubscribed."

◆ serialize()

void Subscriptor::serialize ( Archive & ar,
const unsigned int version )
inline

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

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 200 of file subscriptor.h.

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const
privatenoexcept

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note
Since this function is just a consistency check it does nothing in release mode.
If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 264 of file subscriptor.cc.

◆ fill_fe_values() [2/2]

virtual CellSimilarity::Similarity Mapping< 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
protectedpure virtualinherited

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 topic.

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.

Implemented in MappingManifold< 3, 4 >, MappingQ1Eulerian< dim, VectorType, spacedim >, MappingQ< dim, spacedim >, and MappingQEulerian< dim, VectorType, spacedim >.

◆ fill_fe_face_values() [2/2]

virtual void Mapping< dim, spacedim >::fill_fe_face_values ( const typename Triangulation< dim, spacedim >::cell_iterator & cell,
const unsigned int face_no,
const hp::QCollection< dim - 1 > & quadrature,
const typename Mapping< dim, spacedim >::InternalDataBase & internal_data,
internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > & output_data ) const
protectedvirtualinherited

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.

Reimplemented in MappingManifold< 3, 4 >, and MappingQ< dim, spacedim >.

◆ fill_fe_subface_values() [2/2]

virtual void Mapping< 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
protectedpure virtualinherited

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.

Implemented in MappingManifold< 3, 4 >, and MappingQ< dim, spacedim >.

◆ transform() [2/2]

virtual void Mapping< 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
pure virtualinherited

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.)

Implemented in MappingManifold< 3, 4 >, and MappingQ< dim, spacedim >.

◆ MappingQCache

friend class MappingQCache
friend

Definition at line 681 of file mapping_q.h.

Member Data Documentation

◆ polynomial_degree

const unsigned int MappingQ< dim, spacedim >::polynomial_degree
protected

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

Definition at line 524 of file mapping_q.h.

◆ line_support_points

const std::vector<Point<1> > MappingQ< dim, spacedim >::line_support_points
protected

Definition at line 534 of file mapping_q.h.

◆ polynomials_1d

const std::vector<Polynomials::Polynomial<double> > MappingQ< dim, spacedim >::polynomials_1d
protected

Definition at line 541 of file mapping_q.h.

◆ renumber_lexicographic_to_hierarchic

const std::vector<unsigned int> MappingQ< dim, spacedim >::renumber_lexicographic_to_hierarchic
protected

Definition at line 548 of file mapping_q.h.

◆ unit_cell_support_points

const std::vector<Point<dim> > MappingQ< dim, spacedim >::unit_cell_support_points
protected

Definition at line 560 of file mapping_q.h.

◆ support_point_weights_perimeter_to_interior

const std::vector<Table<2, double> > MappingQ< dim, spacedim >::support_point_weights_perimeter_to_interior
protected

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 582 of file mapping_q.h.

◆ support_point_weights_cell

const Table<2, double> MappingQ< dim, spacedim >::support_point_weights_cell
protected

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 596 of file mapping_q.h.

◆ counter

std::atomic<unsigned int> Subscriptor::counter
mutableprivate

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 218 of file subscriptor.h.

◆ counter_map

std::map<std::string, unsigned int> Subscriptor::counter_map
mutableprivate

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 224 of file subscriptor.h.

◆ validity_pointers

std::vector<std::atomic<bool> *> Subscriptor::validity_pointers
mutableprivate

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 240 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info
mutableprivate

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 248 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex
staticprivate

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.


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