MappingQEulerian< dim, VectorType, spacedim > Class Template Reference

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

Inheritance diagram for MappingQEulerian< dim, VectorType, spacedim >:

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, dim >
	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 bool	preserves_vertex_locations () const override
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 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
virtual std::unique_ptr< Mapping< dim, spacedim > >	clone () const override

Static Public Member Functions
static ::ExceptionBase &	ExcInactiveCell ()

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, dim >
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 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, dim >
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

Detailed Description

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

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.

Usage

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:

FESystem<dim> fe(FE_Q<dim>(2), dim, FE_Q<dim>(1), 1);
DoFHandler<dim> dof_handler(triangulation);
dof_handler.distribute_dofs(fe);
Vector<double> displacement_field(dof_handler.n_dofs());
// ... compute displacement field somehow...
MappingQEulerian<dim> q2_mapping(2, dof_handler, displacement_field);

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.

Author

Joshua White, 2008

Definition at line 95 of file mapping_q_eulerian.h.

Constructor & Destructor Documentation

MappingQEulerian()

template<int dim, class VectorType , int spacedim>

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
	)

Constructor.

Parameters

[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 62 of file mapping_q_eulerian.cc.

Member Function Documentation

get_vertices()

template<int dim, class VectorType , int spacedim>

std::array< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell > MappingQEulerian< dim, VectorType, spacedim >::get_vertices ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell ) const

overridevirtual

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

Definition at line 124 of file mapping_q_eulerian.cc.

clone()

template<int dim, class VectorType , int spacedim>

std::unique_ptr< Mapping< dim, spacedim > > MappingQEulerian< dim, VectorType, spacedim >::clone

overridevirtual

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

Definition at line 87 of file mapping_q_eulerian.cc.

preserves_vertex_locations()

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

virtual bool MappingQEulerian< dim, VectorType, spacedim >::preserves_vertex_locations ( ) const

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).

fill_fe_values()

template<int dim, class VectorType , int spacedim>

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

overrideprotectedvirtual

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

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

Reimplemented from MappingQ< dim, dim >.

Definition at line 248 of file mapping_q_eulerian.cc.

Member Data Documentation

euler_vector

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

SmartPointer<const VectorType, MappingQEulerian<dim, VectorType, spacedim> > MappingQEulerian< dim, VectorType, spacedim >::euler_vector

protected

Reference to the vector of shifts.

Definition at line 172 of file mapping_q_eulerian.h.

euler_dof_handler

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

SmartPointer<const DoFHandler<dim, spacedim>, MappingQEulerian<dim, VectorType, spacedim> > MappingQEulerian< dim, VectorType, spacedim >::euler_dof_handler

protected

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

Definition at line 179 of file mapping_q_eulerian.h.

level

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

const unsigned int MappingQEulerian< dim, VectorType, spacedim >::level

private

Multigrid level at which the mapping is to be used.

Definition at line 186 of file mapping_q_eulerian.h.

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

• include/deal.II/fe/mapping_q_eulerian.h
• source/fe/mapping_q_eulerian.cc