Reference documentation for deal.II version 8.1.0
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MappingQ1Eulerian< dim, VECTOR, spacedim > Class Template Reference

#include <mapping_q1_eulerian.h>

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

Public Member Functions

 MappingQ1Eulerian (const VECTOR &euler_transform_vectors, const DoFHandler< dim, spacedim > &shiftmap_dof_handler)
 
virtual Mapping< dim, spacedim > * clone () const
 
bool preserves_vertex_locations () const
 
 DeclException0 (ExcInactiveCell)
 
- Public Member Functions inherited from MappingQ1< dim, spacedim >
 MappingQ1 ()
 
virtual Point< spacedim > transform_unit_to_real_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< dim > &p) const
 
virtual Point< dim > transform_real_to_unit_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p) const
 
virtual void transform (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const
 
virtual void transform (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const
 
virtual void transform (const VectorSlice< const std::vector< Tensor< 2, dim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) 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, typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, typename std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, typename std::vector< Tensor< 1, spacedim > > &boundary_form, typename std::vector< Point< spacedim > > &normal_vectors) const
 
virtual void fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, typename std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, typename std::vector< Tensor< 1, spacedim > > &boundary_form, typename std::vector< Point< spacedim > > &normal_vectors) const
 
void compute_shapes (const std::vector< Point< dim > > &unit_points, InternalData &data) const
 
void compute_data (const UpdateFlags flags, const Quadrature< dim > &quadrature, const unsigned int n_orig_q_points, InternalData &data) const
 
void compute_face_data (const UpdateFlags flags, const Quadrature< dim > &quadrature, const unsigned int n_orig_q_points, InternalData &data) const
 
void compute_fill (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int npts, const DataSetDescriptor data_set, const CellSimilarity::Similarity cell_similarity, InternalData &data, std::vector< Point< spacedim > > &quadrature_points) const
 
void compute_fill_face (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const unsigned int npts, const DataSetDescriptor data_set, const std::vector< double > &weights, InternalData &mapping_data, std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, std::vector< Tensor< 1, spacedim > > &boundary_form, std::vector< Point< spacedim > > &normal_vectors) const
 
virtual void compute_shapes_virtual (const std::vector< Point< dim > > &unit_points, InternalData &data) const
 
Point< spacedim > transform_unit_to_real_cell_internal (const InternalData &mdata) const
 
Point< dim > transform_real_to_unit_cell_internal (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p, const Point< dim > &initial_p_unit, InternalData &mdata) const
 
template<>
Point< 2 > transform_real_to_unit_cell_internal (const Triangulation< 2, 3 >::cell_iterator &cell, const Point< 3 > &p, const Point< 2 > &initial_p_unit, InternalData &mdata) const
 
template<>
Point< 1 > transform_real_to_unit_cell_internal (const Triangulation< 1, 2 >::cell_iterator &cell, const Point< 2 > &p, const Point< 1 > &initial_p_unit, InternalData &mdata) const
 
template<>
Point< 1 > transform_real_to_unit_cell_internal (const Triangulation< 1, 3 >::cell_iterator &cell, const Point< 3 > &p, const Point< 1 > &initial_p_unit, InternalData &mdata) const
 
- Public Member Functions inherited from Mapping< dim, spacedim >
virtual ~Mapping ()
 
virtual void transform (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const InternalDataBase &internal, const MappingType type) const =0
 
virtual void transform (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const InternalDataBase &internal, const MappingType type) const =0
 
virtual void transform (const VectorSlice< const std::vector< Tensor< 2, dim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const InternalDataBase &internal, const MappingType type) const =0
 
void transform_covariant (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, const unsigned int offset, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const InternalDataBase &internal) const DEAL_II_DEPRECATED
 
void transform_covariant (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, const unsigned int offset, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const InternalDataBase &internal) const DEAL_II_DEPRECATED
 
void transform_contravariant (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, const unsigned int offset, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const DEAL_II_DEPRECATED
 
void transform_contravariant (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, const unsigned int offset, const VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const DEAL_II_DEPRECATED
 
const Point< spacedim > & support_point_value (const unsigned int index, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const
 
const Tensor< 2, spacedim > & support_point_gradient (const unsigned int index, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const
 
const Tensor< 2, spacedim > & support_point_inverse_gradient (const unsigned int index, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const
 
 DeclException0 (ExcInvalidData)
 
 DeclException0 (ExcTransformationFailed)
 
 DeclException3 (ExcDistortedMappedCell, Point< spacedim >, double, int,<< "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<< ".")
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
 DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Protected Member Functions

virtual void fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Quadrature< dim > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, typename std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, std::vector< DerivativeForm< 1, dim, spacedim > > &jacobians, std::vector< DerivativeForm< 2, dim, spacedim > > &jacobian_grads, std::vector< DerivativeForm< 1, spacedim, dim > > &inverse_jacobians, std::vector< Point< spacedim > > &cell_normal_vectors, CellSimilarity::Similarity &cell_similarity) const
 
- Protected Member Functions inherited from MappingQ1< dim, spacedim >
template<int rank>
void transform_fields (const VectorSlice< const std::vector< Tensor< rank, dim > > > input, VectorSlice< std::vector< Tensor< rank, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const
 
template<int rank>
void transform_gradients (const VectorSlice< const std::vector< Tensor< rank, dim > > > input, VectorSlice< std::vector< Tensor< rank, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const
 
template<int rank>
void transform_differential_forms (const VectorSlice< const std::vector< DerivativeForm< rank, dim, spacedim > > > input, VectorSlice< std::vector< DerivativeForm< rank, spacedim, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const
 
template<int dim_>
Point< dim_ > transform_real_to_unit_cell_internal_codim1 (const typename Triangulation< dim_, dim_+1 >::cell_iterator &cell, const Point< dim_+1 > &p, const Point< dim_ > &initial_p_unit, InternalData &mdata) const
 
Point< dim > transform_real_to_unit_cell_initial_guess (const std::vector< Point< spacedim > > &vertex, const Point< spacedim > &p) const
 

Protected Attributes

SmartPointer< const VECTOR,
MappingQ1Eulerian< dim, VECTOR,
spacedim > > 
euler_transform_vectors
 
SmartPointer< const DoFHandler
< dim, spacedim >
, MappingQ1Eulerian< dim,
VECTOR, spacedim > > 
shiftmap_dof_handler
 

Private Member Functions

virtual void compute_mapping_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim > > &a) const
 

Additional Inherited Members

- Public Types inherited from MappingQ1< dim, spacedim >
typedef QProjector< dim >
::DataSetDescriptor 
DataSetDescriptor
 

Detailed Description

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

Eulerian mapping of general unit cells by d-linear shape functions. Each cell is thus shifted in space by values given to the mapping through a finite element field.

Usage

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

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

An example is shown below:

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

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

To enable the use of the MappingQ1Eulerian class also in the context of parallel codes using the PETSc wrapper classes, the type of the vector can be specified as template parameter EulerVectorType Not specifying this template argument in applications using the PETSc vector classes leads to the construction of a copy of the vector which is not acccessible afterwards!

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

Author
Michael Stadler, 2001

Definition at line 92 of file mapping_q1_eulerian.h.

Constructor & Destructor Documentation

template<int dim, class VECTOR = Vector<double>, int spacedim = dim>
MappingQ1Eulerian< dim, VECTOR, spacedim >::MappingQ1Eulerian ( const VECTOR &  euler_transform_vectors,
const DoFHandler< dim, spacedim > &  shiftmap_dof_handler 
)

Constructor. It takes a Vector<double> & as its first argument to specify the transformation of the whole problem from the reference to the current configuration. The organization of the elements in the Vector must follow the concept how deal.II stores solutions that are associated to a triangulation. This is automatically the case if the Vector represents the solution of the previous step of a nonlinear problem. Alternatively, the Vector can be initialized by DoFAccessor::set_dof_values().

Member Function Documentation

template<int dim, class VECTOR = Vector<double>, int spacedim = dim>
virtual Mapping<dim,spacedim>* MappingQ1Eulerian< dim, VECTOR, spacedim >::clone ( ) const
virtual

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

Reimplemented from MappingQ1< dim, spacedim >.

template<int dim, class VECTOR = Vector<double>, int spacedim = dim>
bool MappingQ1Eulerian< dim, VECTOR, spacedim >::preserves_vertex_locations ( ) const
virtual

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

Reimplemented from MappingQ1< dim, spacedim >.

template<int dim, class VECTOR = Vector<double>, int spacedim = dim>
MappingQ1Eulerian< dim, VECTOR, spacedim >::DeclException0 ( ExcInactiveCell  )

Exception.

template<int dim, class VECTOR = Vector<double>, int spacedim = dim>
virtual void MappingQ1Eulerian< dim, VECTOR, spacedim >::fill_fe_values ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const Quadrature< dim > &  quadrature,
typename Mapping< dim, spacedim >::InternalDataBase mapping_data,
typename std::vector< Point< spacedim > > &  quadrature_points,
std::vector< double > &  JxW_values,
std::vector< DerivativeForm< 1, dim, spacedim > > &  jacobians,
std::vector< DerivativeForm< 2, dim, spacedim > > &  jacobian_grads,
std::vector< DerivativeForm< 1, spacedim, dim > > &  inverse_jacobians,
std::vector< Point< spacedim > > &  cell_normal_vectors,
CellSimilarity::Similarity &  cell_similarity 
) const
protectedvirtual

Implementation of the interface in MappingQ1. Overrides the function in the base class, since we cannot use any cell similarity for this class.

Reimplemented from MappingQ1< dim, spacedim >.

template<int dim, class VECTOR = Vector<double>, int spacedim = dim>
virtual void MappingQ1Eulerian< dim, VECTOR, spacedim >::compute_mapping_support_points ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
std::vector< Point< spacedim > > &  a 
) const
privatevirtual

Computes the support points of the mapping. For MappingQ1Eulerian these are the vertices.

Reimplemented from MappingQ1< dim, spacedim >.

Member Data Documentation

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

Reference to the vector of shifts.

Definition at line 168 of file mapping_q1_eulerian.h.

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

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

Definition at line 175 of file mapping_q1_eulerian.h.


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