Classes | |
class | InternalData |
Public Types | |
typedef QProjector< dim > ::DataSetDescriptor | DataSetDescriptor |
Public Member Functions | |
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< Tensor< 2, dim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const |
virtual Mapping< dim, spacedim > * | clone () const |
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< Tensor< 2, spacedim > > &jacobians, std::vector< Tensor< 3, spacedim > > &jacobian_grads, std::vector< Tensor< 2, spacedim > > &inverse_jacobians, std::vector< Point< spacedim > > &cell_normal_vectors, enum CellSimilarity::Similarity &cell_similarity) 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< dim > > &quadrature_points, std::vector< double > &JxW_values, typename std::vector< Tensor< 1, dim > > &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< dim > > &quadrature_points, std::vector< double > &JxW_values, typename std::vector< Tensor< 1, dim > > &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 enum 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< dim > > &quadrature_points, std::vector< double > &JxW_values, std::vector< Tensor< 1, dim > > &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 |
void | transform_real_to_unit_cell_internal (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p, InternalData &mdata, Point< dim > &p_unit) const |
Private Member Functions | |
virtual UpdateFlags | update_once (const UpdateFlags flags) const |
virtual UpdateFlags | update_each (const UpdateFlags flags) const |
virtual Mapping< dim, spacedim > ::InternalDataBase * | get_data (const UpdateFlags, const Quadrature< dim > &quadrature) const |
virtual Mapping< dim, spacedim > ::InternalDataBase * | get_face_data (const UpdateFlags flags, const Quadrature< dim-1 > &quadrature) const |
virtual Mapping< dim, spacedim > ::InternalDataBase * | get_subface_data (const UpdateFlags flags, const Quadrature< dim-1 > &quadrature) const |
virtual void | compute_mapping_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim > > &a) const |
Static Private Attributes | |
static const unsigned int | n_shape_functions = GeometryInfo<dim>::vertices_per_cell |
Mapping of general quadrilateral/hexahedra by d-linear shape functions.
This function maps the unit cell to a general grid cell with straight lines in dimensions (remark that in 3D the surfaces may be curved, even if the edges are not). This is the well-known mapping for polyhedral domains.
Shape function for this mapping are the same as for the finite element FE_Q of order 1. Therefore, coupling these two yields an isoparametric element.
For more information about the spacedim
template parameter check the documentation of FiniteElement or the one of Triangulation.
typedef QProjector<dim>::DataSetDescriptor MappingQ1< dim, spacedim >::DataSetDescriptor |
Declare a convenience typedef for the class that describes offsets into quadrature formulas projected onto faces and subfaces.
Default constructor.
virtual Point<spacedim> MappingQ1< dim, spacedim >::transform_unit_to_real_cell | ( | const typename Triangulation< dim, spacedim >::cell_iterator & | cell, | |
const Point< dim > & | p | |||
) | const [virtual] |
Transforms the point p
on the unit cell to the point p_real
on the real cell cell
and returns p_real
.
Implements Mapping< dim, spacedim >.
Reimplemented in MappingQ< dim, spacedim >.
virtual Point<dim> MappingQ1< dim, spacedim >::transform_real_to_unit_cell | ( | const typename Triangulation< dim, spacedim >::cell_iterator & | cell, | |
const Point< spacedim > & | p | |||
) | const [virtual] |
Transforms the point p
on the real cell to the point p_unit
on the unit cell cell
and returns p_unit
.
Uses Newton iteration and the transform_unit_to_real_cell
function.
Implements Mapping< dim, spacedim >.
Reimplemented in MappingQ< dim, spacedim >.
virtual void MappingQ1< dim, spacedim >::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] |
Reimplemented in MappingQ< dim, spacedim >.
virtual void MappingQ1< dim, spacedim >::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] |
Reimplemented in MappingQ< dim, spacedim >.
virtual Mapping<dim,spacedim>* MappingQ1< dim, spacedim >::clone | ( | ) | const [virtual] |
Return a pointer to a copy of the present object. The caller of this copy then assumes ownership of it.
Implements Mapping< dim, spacedim >.
Reimplemented in MappingC1< dim, spacedim >, MappingQ< dim, spacedim >, MappingQ1Eulerian< dim, EulerVectorType, spacedim >, and MappingQEulerian< dim, EulerVectorType, spacedim >.
virtual void MappingQ1< dim, 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< Tensor< 2, spacedim > > & | jacobians, | |||
std::vector< Tensor< 3, spacedim > > & | jacobian_grads, | |||
std::vector< Tensor< 2, spacedim > > & | inverse_jacobians, | |||
std::vector< Point< spacedim > > & | cell_normal_vectors, | |||
enum CellSimilarity::Similarity & | cell_similarity | |||
) | const [virtual] |
Implementation of the interface in Mapping.
Reimplemented in MappingQ< dim, spacedim >, MappingQ1Eulerian< dim, EulerVectorType, spacedim >, and MappingQEulerian< dim, EulerVectorType, spacedim >.
virtual void MappingQ1< dim, spacedim >::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< dim > > & | quadrature_points, | |||
std::vector< double > & | JxW_values, | |||
typename std::vector< Tensor< 1, dim > > & | boundary_form, | |||
typename std::vector< Point< spacedim > > & | normal_vectors | |||
) | const [virtual] |
Implementation of the interface in Mapping.
virtual void MappingQ1< dim, spacedim >::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< dim > > & | quadrature_points, | |||
std::vector< double > & | JxW_values, | |||
typename std::vector< Tensor< 1, dim > > & | boundary_form, | |||
typename std::vector< Point< spacedim > > & | normal_vectors | |||
) | const [virtual] |
Implementation of the interface in Mapping.
void MappingQ1< dim, spacedim >::compute_shapes | ( | const std::vector< Point< dim > > & | unit_points, | |
InternalData & | data | |||
) | const |
Compute shape values and/or derivatives.
Calls either the compute_shapes_virtual
of this class or that of the derived class, depending on whether data.is_mapping_q1_data
equals true
or false
.
void MappingQ1< dim, spacedim >::compute_data | ( | const UpdateFlags | flags, | |
const Quadrature< dim > & | quadrature, | |||
const unsigned int | n_orig_q_points, | |||
InternalData & | data | |||
) | const |
Do the computations for the get_data
functions. Here, the data vectors of InternalData
are reinitialized to proper size and shape values are computed.
void MappingQ1< dim, spacedim >::compute_face_data | ( | const UpdateFlags | flags, | |
const Quadrature< dim > & | quadrature, | |||
const unsigned int | n_orig_q_points, | |||
InternalData & | data | |||
) | const |
Do the computations for the get_face_data
functions. Here, the data vectors of InternalData
are reinitialized to proper size and shape values and derivatives are computed. Furthermore unit_tangential
vectors of the face are computed.
void MappingQ1< dim, spacedim >::compute_fill | ( | const typename Triangulation< dim, spacedim >::cell_iterator & | cell, | |
const unsigned int | npts, | |||
const DataSetDescriptor | data_set, | |||
const enum CellSimilarity::Similarity | cell_similarity, | |||
InternalData & | data, | |||
std::vector< Point< spacedim > > & | quadrature_points | |||
) | const |
Do the computation for the fill_*
functions.
void MappingQ1< dim, spacedim >::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< dim > > & | quadrature_points, | |||
std::vector< double > & | JxW_values, | |||
std::vector< Tensor< 1, dim > > & | boundary_form, | |||
std::vector< Point< spacedim > > & | normal_vectors | |||
) | const |
Do the computation for the fill_*
functions.
virtual void MappingQ1< dim, spacedim >::compute_shapes_virtual | ( | const std::vector< Point< dim > > & | unit_points, | |
InternalData & | data | |||
) | const [virtual] |
Compute shape values and/or derivatives.
Point<spacedim> MappingQ1< dim, spacedim >::transform_unit_to_real_cell_internal | ( | const InternalData & | mdata | ) | const |
Transforms 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 multiply (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.
void MappingQ1< dim, spacedim >::transform_real_to_unit_cell_internal | ( | const typename Triangulation< dim, spacedim >::cell_iterator & | cell, | |
const Point< spacedim > & | p, | |||
InternalData & | mdata, | |||
Point< dim > & | p_unit | |||
) | const |
Transforms the point p
on the real cell to the point p_unit
on the unit cell cell
by a 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 including the given point p_unit
. Hence this function assumes that mdata
already includes the transformation shape values and gradients computed at p_unit
.
These assumptions should be fulfilled by the calling function. That is up to now only the function transform_real_to_unit_cell
and its overloaded versions. mdata
will be changed by this function.
virtual UpdateFlags MappingQ1< dim, spacedim >::update_once | ( | const UpdateFlags | flags | ) | const [private, virtual] |
Implementation of the interface in Mapping.
Description of effects:
update_quadrature_points
is required, the output will contain update_transformation_values
. This computes the values of the transformation basis polynomials at the unit cell quadrature points. update_covariant_transformation
, update_contravariant_transformation
, update_JxW_values
, update_boundary_forms
, update_normal_vectors
is required, the output will contain update_transformation_gradients
to compute derivatives of the transformation basis polynomials. Implements Mapping< dim, spacedim >.
virtual UpdateFlags MappingQ1< dim, spacedim >::update_each | ( | const UpdateFlags | flags | ) | const [private, virtual] |
Implementation of the interface in Mapping.
Description of effects if flags
contains:
update_quadrature_points
is copied to the output to compute the quadrature points on the real cell. update_JxW_values
is copied and requires update_boundary_forms
on faces. The latter, because the surface element is just the norm of the boundary form. update_normal_vectors
is copied and requires update_boundary_forms
. The latter, because the normal vector is the normalized boundary form. update_covariant_transformation
is copied and requires update_contravariant_transformation
, since it is computed as the inverse of the latter. update_JxW_values
is copied and requires update_contravariant_transformation
, since it is computed as one over determinant of the latter. update_boundary_forms
is copied and requires update_contravariant_transformation
, since the boundary form is computed as the contravariant image of the normal vector to the unit cell. Implements Mapping< dim, spacedim >.
virtual Mapping<dim,spacedim>::InternalDataBase* MappingQ1< dim, spacedim >::get_data | ( | const | UpdateFlags, | |
const Quadrature< dim > & | quadrature | |||
) | const [private, virtual] |
Prepare internal data structures and fill in values independent of the cell.
Implements Mapping< dim, spacedim >.
Reimplemented in MappingQ< dim, spacedim >.
virtual Mapping<dim,spacedim>::InternalDataBase* MappingQ1< dim, spacedim >::get_face_data | ( | const UpdateFlags | flags, | |
const Quadrature< dim-1 > & | quadrature | |||
) | const [private, virtual] |
Prepare internal data structure for transformation of faces and fill in values independent of the cell.
Implements Mapping< dim, spacedim >.
Reimplemented in MappingQ< dim, spacedim >.
virtual Mapping<dim,spacedim>::InternalDataBase* MappingQ1< dim, spacedim >::get_subface_data | ( | const UpdateFlags | flags, | |
const Quadrature< dim-1 > & | quadrature | |||
) | const [private, virtual] |
Prepare internal data structure for transformation of children of faces and fill in values independent of the cell.
Implements Mapping< dim, spacedim >.
Reimplemented in MappingQ< dim, spacedim >.
virtual void MappingQ1< dim, spacedim >::compute_mapping_support_points | ( | const typename Triangulation< dim, spacedim >::cell_iterator & | cell, | |
std::vector< Point< spacedim > > & | a | |||
) | const [private, virtual] |
Computes the support points of the mapping. For MappingQ1
these are the vertices. However, other classes may override this function. In particular, the MappingQ1Eulerian class does exactly this by not computing the support points from the geometry of the current cell but instead evaluating an externally given displacement field in addition to the geometry of the cell.
const unsigned int MappingQ1< dim, spacedim >::n_shape_functions = GeometryInfo<dim>::vertices_per_cell [static, private] |
Number of shape functions. Is simply the number of vertices per cell for the Q1 mapping.
Reimplemented in MappingQ< dim, spacedim >.