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deal.II version GIT relicensing-2055-gd703fda1ad 2024-10-30 20:00:00+00:00
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deal.II version GIT relicensing-2055-gd703fda1ad 2024-10-30 20:00:00+00:00
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#include <deal.II/fe/mapping_fe_field.h>
Classes | |
| class | InternalData |
Public Member Functions | |
| MappingFEField (const DoFHandler< dim, spacedim > &euler_dof_handler, const VectorType &euler_vector, const ComponentMask &mask={}) | |
| MappingFEField (const DoFHandler< dim, spacedim > &euler_dof_handler, const std::vector< VectorType > &euler_vector, const ComponentMask &mask={}) | |
| MappingFEField (const DoFHandler< dim, spacedim > &euler_dof_handler, const MGLevelObject< VectorType > &euler_vector, const ComponentMask &mask={}) | |
| MappingFEField (const MappingFEField< dim, spacedim, VectorType > &mapping) | |
| virtual std::unique_ptr< Mapping< dim, spacedim > > | clone () const override |
| virtual bool | preserves_vertex_locations () const override |
| virtual bool | is_compatible_with (const ReferenceCell &reference_cell) const override |
| virtual boost::container::small_vector< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell > | get_vertices (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const override |
| unsigned int | get_degree () const |
| ComponentMask | get_component_mask () const |
| boost::container::small_vector< Point< spacedim >, GeometryInfo< dim >::vertices_per_face > | get_vertices (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no) const |
| virtual Point< spacedim > | get_center (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const bool map_barycenter_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 |
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 |
Mapping points between reference and real cells | |
| 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 |
| 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 |
EnableObserverPointer functionality | |
Classes derived from EnableObserverPointer provide a facility to subscribe to this object. This is mostly used by the ObserverPointer 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 ::ExceptionBase & | ExcInactiveCell () |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Exceptions | |
| static ::ExceptionBase & | ExcInvalidData () |
| static ::ExceptionBase & | ExcTransformationFailed () |
| static ::ExceptionBase & | ExcDistortedMappedCell (Point< spacedim > arg1, double arg2, int arg3) |
Protected Member Functions | |
Interface with FEValues | |
| virtual std::unique_ptr< InternalDataBase > | get_face_data (const UpdateFlags update_flags, const Quadrature< dim - 1 > &quadrature) const |
| 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 |
Protected Attributes | |
| ReferenceCell | reference_cell |
| const bool | uses_level_dofs |
| std::vector< ObserverPointer< const VectorType, MappingFEField< dim, spacedim, VectorType > > > | euler_vector |
| ObserverPointer< const DoFHandler< dim, spacedim >, MappingFEField< dim, spacedim, VectorType > > | euler_dof_handler |
Private Types | |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
Private Member Functions | |
| Point< spacedim > | do_transform_unit_to_real_cell (const InternalData &mdata) const |
| Point< dim > | do_transform_real_to_unit_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p, const Point< dim > &starting_guess, InternalData &mdata) const |
| void | update_internal_dofs (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const typename MappingFEField< dim, spacedim, VectorType >::InternalData &data) const |
| void | compute_face_data (const unsigned int n_original_q_points, InternalData &data) const |
| void | check_no_subscribers () const noexcept |
Private Attributes | |
| const ComponentMask | fe_mask |
| std::vector< unsigned int > | fe_to_real |
| FEValues< dim, spacedim > | fe_values |
| Threads::Mutex | fe_values_mutex |
| std::atomic< unsigned int > | counter |
| std::map< std::string, unsigned int > | counter_map |
| std::vector< std::atomic< bool > * > | validity_pointers |
| const std::type_info * | object_info |
Static Private Attributes | |
| static std::mutex | mutex |
Friends | |
| template<int , int , class > | |
| class | MappingFEField |
Interface with FEValues | |
| 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 |
The MappingFEField is a generalization of the MappingQEulerian class, for arbitrary vector finite elements. The two main differences are that this class uses a vector of absolute positions instead of a vector of displacements, and it allows for arbitrary FiniteElement types, instead of only FE_Q.
This class effectively decouples the topology from the geometry, by relegating all geometrical information to some components of a FiniteElement vector field. The components that are used for the geometry can be arbitrarily selected at construction time.
The idea is to consider the Triangulation as a parameter configuration space, on which we construct an arbitrary geometrical mapping, using the instruments of the deal.II library: a vector of degrees of freedom, a DoFHandler associated to the geometry of the problem and a ComponentMask that tells us which components of the FiniteElement to use for the mapping.
Typically, the DoFHandler operates on a finite element that is constructed as a system element (FESystem()) from continuous FE_Q() (for iso-parametric discretizations) or FE_Bernstein() (for iso-geometric discretizations) objects. An example is shown below:
Definition at line 79 of file mapping_fe_field.h.
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privateinherited |
The data type used in counter_map.
Definition at line 238 of file enable_observer_pointer.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 243 of file enable_observer_pointer.h.
| MappingFEField< dim, spacedim, VectorType >::MappingFEField | ( | const DoFHandler< dim, spacedim > & | euler_dof_handler, |
| const VectorType & | euler_vector, | ||
| const ComponentMask & | mask = {} |
||
| ) |
Constructor. The first argument is a VectorType that specifies the transformation of the domain from the reference to the current configuration.
In general this class decouples geometry from topology, allowing users to define geometries which are only topologically equivalent to the underlying Triangulation, but which may otherwise be arbitrary. Differently from what happens in MappingQEulerian, the FiniteElement field which is passed to the constructor is interpreted as an absolute geometrical configuration, therefore one has to make sure that the euler_vector actually represents a valid geometry (i.e., one with no inverted cells, or with no zero-volume cells).
If the underlying FiniteElement is a system of FE_Q(), and euler_vector is initialized using VectorTools::get_position_vector(), then this class is in all respects identical to MappingQ().
The optional ComponentMask argument can be used to specify what components of the FiniteElement to use for the geometrical transformation. If no mask is specified at construction time, then a default one is used, which makes this class works in the same way of MappingQEulerian(), i.e., the first spacedim components of the FiniteElement are assumed to represent the geometry of the problem.
Notice that if a mask is specified, it has to match in size the underlying FiniteElement, and it has to have exactly spacedim non-zero elements, indicating the components (in order) of the FiniteElement which will be used for the geometry.
If an incompatible mask is passed, an exception is thrown.
Definition at line 276 of file mapping_fe_field.cc.
| MappingFEField< dim, spacedim, VectorType >::MappingFEField | ( | const DoFHandler< dim, spacedim > & | euler_dof_handler, |
| const std::vector< VectorType > & | euler_vector, | ||
| const ComponentMask & | mask = {} |
||
| ) |
Constructor taking vectors on the multigrid levels rather than the active cells only. The vector of vectors is expected to have as many entries as there are global levels in the triangulation and provide valid data on each level, i.e., be of compatible length DoFHandler::n_dofs(level). A prerequisite of this constructor is that DoFHandler::distribute_mg_dofs() has been called. Apart from the level vectors, the same arguments as in the other constructor need to be provided.
Definition at line 307 of file mapping_fe_field.cc.
| MappingFEField< dim, spacedim, VectorType >::MappingFEField | ( | const DoFHandler< dim, spacedim > & | euler_dof_handler, |
| const MGLevelObject< VectorType > & | euler_vector, | ||
| const ComponentMask & | mask = {} |
||
| ) |
Constructor with MGLevelObject instead of std::vector, otherwise the same as above. It is required that euler_vector.max_level()+1 equals the global number of levels in the triangulation. The minimum level may be zero or more — it only needs to be consistent between what is set here and later used for evaluation of the mapping.
Definition at line 350 of file mapping_fe_field.cc.
| MappingFEField< dim, spacedim, VectorType >::MappingFEField | ( | const MappingFEField< dim, spacedim, VectorType > & | mapping | ) |
Copy constructor.
Definition at line 395 of file mapping_fe_field.cc.
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overridevirtual |
Return a pointer to a copy of the present object. The caller of this copy then assumes ownership of it.
Implements Mapping< dim, spacedim >.
Definition at line 2407 of file mapping_fe_field.cc.
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overridevirtual |
See the documentation of Mapping::preserves_vertex_locations() for the purpose of this function. The implementation in this class always returns false.
Implements Mapping< dim, spacedim >.
Definition at line 424 of file mapping_fe_field.cc.
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overridevirtual |
Returns if this instance of Mapping is compatible with the type of cell in reference_cell.
Implements Mapping< dim, spacedim >.
Definition at line 433 of file mapping_fe_field.cc.
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overridevirtual |
Return the mapped vertices of a cell.
This mapping ignores the vertices of the Triangulation it is associated to, and constructs the position of the vertices according to the euler_vector that was passed at construction time.
Reimplemented from Mapping< dim, spacedim >.
Definition at line 451 of file mapping_fe_field.cc.
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overridevirtual |
Map the point p on the unit cell to the corresponding point on the real cell cell.
| cell | Iterator to the cell that will be used to define the mapping. |
| p | Location of a point on the reference cell. |
Implements Mapping< dim, spacedim >.
Definition at line 2194 of file mapping_fe_field.cc.
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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.
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.| cell | Iterator to the cell that will be used to define the mapping. |
| p | Location of a point on the given cell. |
Implements Mapping< dim, spacedim >.
Definition at line 2236 of file mapping_fe_field.cc.
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overridevirtual |
Transform a field of vectors or 1-differential forms according to the selected MappingKind.
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 \[ \mathbf u(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J(\hat{\mathbf x}) \hat{\mathbf u}(\hat{\mathbf x}). \]
| [in] | input | An array (or part of an array) of input objects that should be mapped. |
| [in] | kind | The kind of mapping to be applied. |
| [in] | internal | A 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] | output | An 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 2072 of file mapping_fe_field.cc.
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overridevirtual |
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
\[ \mathbf T(\mathbf x) = \hat{\mathbf u}(\hat{\mathbf x}) J(\hat{\mathbf x})^{-1}. \]
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.| [in] | input | An array (or part of an array) of input objects that should be mapped. |
| [in] | kind | The kind of mapping to be applied. |
| [in] | internal | A 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] | output | An 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 2091 of file mapping_fe_field.cc.
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overridevirtual |
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 \[ \mathbf T(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J(\hat{\mathbf x}) \hat{\mathbf T}(\hat{\mathbf x}) J(\hat{\mathbf x})^{-1}. \]
| [in] | input | An array (or part of an array) of input objects that should be mapped. |
| [in] | kind | The kind of mapping to be applied. |
| [in] | internal | A 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] | output | An 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 2110 of file mapping_fe_field.cc.
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overridevirtual |
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
\[J^{\dagger} = J^{-1}\]
| [in] | input | An array (or part of an array) of input objects that should be mapped. |
| [in] | kind | The kind of mapping to be applied. |
| [in] | internal | A 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] | output | An 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 2128 of file mapping_fe_field.cc.
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overridevirtual |
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 \[ \mathbf T_{ijk}(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} J_{iI}(\hat{\mathbf x}) \hat{\mathbf T}_{IJK}(\hat{\mathbf x}) J_{jJ}(\hat{\mathbf x})^{-1} J_{kK}(\hat{\mathbf x})^{-1}. \]
| [in] | input | An array (or part of an array) of input objects that should be mapped. |
| [in] | kind | The kind of mapping to be applied. |
| [in] | internal | A 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] | output | An array (or part of an array) into which the transformed objects should be placed. |
Implements Mapping< dim, spacedim >.
Definition at line 2176 of file mapping_fe_field.cc.
| unsigned int MappingFEField< dim, spacedim, VectorType >::get_degree | ( | ) | const |
Return the degree of the mapping, i.e. the value which was passed to the constructor.
Definition at line 2390 of file mapping_fe_field.cc.
| ComponentMask MappingFEField< dim, spacedim, VectorType >::get_component_mask | ( | ) | const |
Return the ComponentMask of the mapping, i.e. which components to use for the mapping.
Definition at line 2399 of file mapping_fe_field.cc.
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overrideprivatevirtual |
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.
Implements Mapping< dim, spacedim >.
Definition at line 513 of file mapping_fe_field.cc.
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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.
| update_flags | A 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. |
| quadrature | The quadrature object for which mapping information will have to be computed. This includes the locations and weights of quadrature points. |
Implements Mapping< dim, spacedim >.
Definition at line 619 of file mapping_fe_field.cc.
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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.
| update_flags | A 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. |
| quadrature | The quadrature object for which mapping information will have to be computed. This includes the locations and weights of quadrature points. |
Reimplemented from Mapping< dim, spacedim >.
Definition at line 634 of file mapping_fe_field.cc.
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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.
| update_flags | A 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. |
| quadrature | The quadrature object for which mapping information will have to be computed. This includes the locations and weights of quadrature points. |
Implements Mapping< dim, spacedim >.
Definition at line 655 of file mapping_fe_field.cc.
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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:
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.
| [in] | cell | The cell of the triangulation for which this function is to compute a mapping from the reference cell to. |
| [in] | cell_similarity | Whether 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] | quadrature | A 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_data | A 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_data | A 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. |
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.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 1497 of file mapping_fe_field.cc.
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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().
| [in] | cell | The cell of the triangulation for which this function is to compute a mapping from the reference cell to. |
| [in] | face_no | The number of the face of the given cell for which information is requested. |
| [in] | quadrature | A 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_data | A 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_data | A 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 from Mapping< dim, spacedim >.
Definition at line 1701 of file mapping_fe_field.cc.
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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().
| [in] | cell | The cell of the triangulation for which this function is to compute a mapping from the reference cell to. |
| [in] | face_no | The number of the face of the given cell for which information is requested. |
| [in] | subface_no | The number of the child of a face of the given cell for which information is requested. |
| [in] | quadrature | A 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_data | A 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_data | A 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 1740 of file mapping_fe_field.cc.
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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 1782 of file mapping_fe_field.cc.
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private |
Transform a point p on the unit cell to the point p_real on the real cell cell and returns p_real.
This function is called by transform_unit_to_real_cell and multiple times (through the Newton iteration) by transform_real_to_unit_cell_internal.
Takes a reference to an InternalData that must already include the shape values at point p and the mapping support points of the cell.
This InternalData argument avoids multiple computations of the shape values at point p and especially multiple computations of the mapping support points.
Definition at line 2215 of file mapping_fe_field.cc.
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private |
Transform the point p on the real cell to the corresponding point on the unit cell cell by a Newton iteration. starting_guess is a guess for the position on the unit cell at which this function will start its Newton iteration.
Takes a reference to an InternalData that is assumed to be previously created by the get_data function with UpdateFlags including update_transformation_values and update_transformation_gradients and a one point Quadrature that includes the given initial guess specified through the given starting_guess.
mdata will be changed by this function.
Definition at line 2278 of file mapping_fe_field.cc.
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private |
Update internal degrees of freedom.
Definition at line 2415 of file mapping_fe_field.cc.
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private |
Definition at line 567 of file mapping_fe_field.cc.
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inherited |
Return the mapped vertices of a face.
Same as above but working on a given face of a cell.
| [in] | cell | The cell containing the face. |
| [in] | face_no | The number of the face within the cell. |
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virtualinherited |
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.
| [in] | cell | The cell for which you want to compute the center |
| [in] | map_barycenter_of_reference_cell | A 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. |
|
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.
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.
| [in] | cell | The cell for which you want to compute the bounding box |
Reimplemented in MappingFE< dim, spacedim >, MappingQ< dim, spacedim >, and MappingQ< dim, dim >.
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virtualinherited |
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 in MappingCartesian< dim, spacedim >, MappingQ< dim, spacedim >, and MappingQ< dim, dim >.
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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.
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protectedvirtualinherited |
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protectedvirtualinherited |
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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 131 of file enable_observer_pointer.cc.
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inherited |
Unsubscribes a user from the object.
identifier and the validity pointer must be the same as the one supplied to subscribe(). Definition at line 151 of file enable_observer_pointer.cc.
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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 322 of file enable_observer_pointer.h.
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inlineinherited |
List the subscribers to the input stream.
Definition at line 339 of file enable_observer_pointer.h.
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inherited |
List the subscribers to deallog.
Definition at line 199 of file enable_observer_pointer.cc.
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inlineinherited |
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 331 of file enable_observer_pointer.h.
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privatenoexceptinherited |
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.
Definition at line 53 of file enable_observer_pointer.cc.
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friend |
Definition at line 666 of file mapping_fe_field.h.
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protected |
Reference cell over which the mapping is defined. This class does not yet support mixed meshes.
Definition at line 562 of file mapping_fe_field.h.
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protected |
Specifies whether we access unknowns on the active dofs (with a single Euler vector) or on the level dofs (via a vector of Euler vectors).
Definition at line 568 of file mapping_fe_field.h.
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protected |
Reference to the vector of shifts.
Definition at line 575 of file mapping_fe_field.h.
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protected |
Pointer to the DoFHandler to which the mapping vector is associated.
Definition at line 582 of file mapping_fe_field.h.
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private |
Definition at line 636 of file mapping_fe_field.h.
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private |
Mapping between indices in the FE space and the real space. This vector contains one index for each component of the finite element space. If the index is one for which the ComponentMask which is used to construct this element is false, then numbers::invalid_unsigned_int is returned, otherwise the component in real space is returned. For example, if we construct the mapping using ComponentMask(spacedim, true), then this vector contains {0,1,2} in spacedim = 3.
Definition at line 647 of file mapping_fe_field.h.
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mutableprivate |
FEValues object used to query the given finite element field at the support points in the reference configuration.
Definition at line 653 of file mapping_fe_field.h.
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mutableprivate |
A variable to guard access to the fe_values variable.
Definition at line 658 of file mapping_fe_field.h.
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mutableprivateinherited |
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 227 of file enable_observer_pointer.h.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 233 of file enable_observer_pointer.h.
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mutableprivateinherited |
In this vector, we store pointers to the validity bool in the ObserverPointer objects that subscribe to this class.
Definition at line 249 of file enable_observer_pointer.h.
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mutableprivateinherited |
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 257 of file enable_observer_pointer.h.
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staticprivateinherited |
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 280 of file enable_observer_pointer.h.
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