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Reference documentation for deal.II version 9.0.0
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Reference documentation for deal.II version 9.0.0
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#include <deal.II/fe/mapping_q_eulerian.h>
Classes | |
| class | MappingQEulerianGeneric |
Public Member Functions | |
| MappingQEulerian (const unsigned int degree, const DoFHandler< dim, spacedim > &euler_dof_handler, const VectorType &euler_vector, const unsigned int level=numbers::invalid_unsigned_int) | |
| virtual std::array< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell > | get_vertices (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const override |
| virtual std::unique_ptr< Mapping< dim, spacedim > > | clone () const override |
| virtual bool | preserves_vertex_locations () const override |
 Public Member Functions inherited from MappingQ< dim, spacedim > | |
| MappingQ (const unsigned int polynomial_degree, const bool use_mapping_q_on_all_cells=false) | |
| MappingQ (const MappingQ< dim, spacedim > &mapping) | |
| unsigned int | get_degree () const |
| 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 (const ArrayView< const Tensor< 1, dim > > &input, const MappingType type, 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 MappingType type, 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 MappingType type, 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 MappingType type, 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 MappingType type, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 3, spacedim > > &output) const override |
| Public Member Functions inherited from Mapping< dim, spacedim > | |
| virtual | ~Mapping () override=default |
| 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 |
| Public Member Functions inherited from Subscriptor | |
| Subscriptor () | |
| Subscriptor (const Subscriptor &) | |
| Subscriptor (Subscriptor &&) noexcept | |
| virtual | ~Subscriptor () |
| Subscriptor & | operator= (const Subscriptor &) |
| Subscriptor & | operator= (Subscriptor &&) noexcept |
| void | subscribe (const char *identifier=nullptr) const |
| void | unsubscribe (const char *identifier=nullptr) const |
| unsigned int | n_subscriptions () const |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
Static Public Member Functions | |
| static ::ExceptionBase & | ExcInactiveCell () |
| Static Public Member Functions inherited from Mapping< dim, spacedim > | |
| static ::ExceptionBase & | ExcInvalidData () |
| static ::ExceptionBase & | ExcTransformationFailed () |
| static ::ExceptionBase & | ExcDistortedMappedCell (Point< spacedim > arg1, double arg2, int arg3) |
| Static Public Member Functions inherited from Subscriptor | |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Protected Member Functions | |
| virtual CellSimilarity::Similarity | fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override |
| Protected Member Functions inherited from MappingQ< dim, spacedim > | |
| 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 Quadrature< 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 void | fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override |
| virtual void | fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const Quadrature< dim-1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override |
| Protected Member Functions inherited from Mapping< dim, spacedim > | |
| 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 Quadrature< dim-1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const =0 |
| 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 | |
| SmartPointer< const VectorType, MappingQEulerian< dim, VectorType, spacedim > > | euler_vector |
| SmartPointer< const DoFHandler< dim, spacedim >, MappingQEulerian< dim, VectorType, spacedim > > | euler_dof_handler |
| Protected Attributes inherited from MappingQ< dim, spacedim > | |
| const unsigned int | polynomial_degree |
| const bool | use_mapping_q_on_all_cells |
| std::shared_ptr< const MappingQGeneric< dim, spacedim > > | q1_mapping |
| std::shared_ptr< const MappingQGeneric< dim, spacedim > > | qp_mapping |
Private Attributes | |
| const unsigned int | level |
This class is an extension of the MappingQ1Eulerian class to higher order \(Q_p\) mappings. It is useful when one wants to calculate shape function information on a domain that is deforming as the computation proceeds.
The constructor of this class takes three arguments: the polynomial degree of the desired Qp mapping, a reference to the vector that defines the mapping from the initial configuration to the current configuration, and a reference to the DoFHandler. The most common case is to use the solution vector for the problem under consideration as the shift vector. The key requirement is that the number of components of the given vector field must be equal to (or possibly greater than) the number of space dimensions. If there are more components than space dimensions (for example, if one is working with a coupled problem where there are additional solution variables), the first dim components are assumed to represent the displacement field, and the remaining components are ignored. If this assumption does not hold one may need to set up a separate DoFHandler on the triangulation and associate the desired shift vector to it.
Typically, the DoFHandler operates on a finite element that is constructed as a system element (FESystem) from continuous FE_Q objects. An example is shown below:
In this example, our element consists of (dim+1) components. Only the first dim components will be used, however, to define the Q2 mapping. The remaining components are ignored.
Note that it is essential to call the distribute_dofs(...) function before constructing a mapping object.
Also note that since the vector of shift values and the dof handler are only associated to this object at construction time, you have to make sure that whenever you use this object, the given objects still represent valid data.
To enable the use of the MappingQEulerian class also in the context of parallel codes using the PETSc or Trilinos wrapper classes, the type of the vector can be specified as template parameter VectorType.
Definition at line 90 of file mapping_q_eulerian.h.
| MappingQEulerian< dim, VectorType, spacedim >::MappingQEulerian | ( | const unsigned int | degree, |
| const DoFHandler< dim, spacedim > & | euler_dof_handler, | ||
| const VectorType & | euler_vector, | ||
| const unsigned int | level = numbers::invalid_unsigned_int |
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| ) |
Constructor.
| [in] | degree | The polynomial degree of the desired \(Q_p\) mapping. |
| [in] | euler_dof_handler | A DoFHandler object that defines a finite element space. This space needs to have at least dim components and the first dim components of the space will be considered displacements relative to the original positions of the cells of the triangulation. |
| [in] | euler_vector | A finite element function in the space defined by the second argument. The first dim components of this function will be interpreted as the displacement we use in defining the mapping, relative to the location of cells of the underlying triangulation. |
| [in] | level | The multi-grid level at which the mapping will be used. It is mainly used to check if the size of the euler_vector is consistent with the euler_dof_handler . |
Definition at line 60 of file mapping_q_eulerian.cc.
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overridevirtual |
Return the mapped vertices of the cell. For the current class, this function does not use the support points from the geometry of the current cell but instead evaluates an externally given displacement field in addition to the geometry of the cell.
Reimplemented from Mapping< dim, spacedim >.
Definition at line 131 of file mapping_q_eulerian.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.
Reimplemented from MappingQ< dim, spacedim >.
Definition at line 84 of file mapping_q_eulerian.cc.
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overridevirtual |
Always return false because MappingQEulerian does not in general preserve vertex locations (unless the translation vector happens to provide zero displacements at vertex locations).
Reimplemented from MappingQ< dim, spacedim >.
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overrideprotectedvirtual |
Compute mapping-related information for a cell. See the documentation of Mapping::fill_fe_values() for a discussion of purpose, arguments, and return value of this function.
This function overrides the function in the base class since we cannot use any cell similarity for this class.
Reimplemented from MappingQ< dim, spacedim >.
Definition at line 246 of file mapping_q_eulerian.cc.
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protected |
Reference to the vector of shifts.
Definition at line 165 of file mapping_q_eulerian.h.
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protected |
Pointer to the DoFHandler to which the mapping vector is associated.
Definition at line 170 of file mapping_q_eulerian.h.
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private |
Multigrid level at which the mapping is to be used.
Definition at line 178 of file mapping_q_eulerian.h.
1.8.14