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Reference documentation for deal.II version 9.6.0
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#include <deal.II/fe/fe_interface_values.h>
Public Member Functions | |
FEInterfaceValues (const Mapping< dim, spacedim > &mapping, const FiniteElement< dim, spacedim > &fe, const Quadrature< dim - 1 > &quadrature, const UpdateFlags update_flags) | |
FEInterfaceValues (const Mapping< dim, spacedim > &mapping, const FiniteElement< dim, spacedim > &fe, const hp::QCollection< dim - 1 > &quadrature, const UpdateFlags update_flags) | |
FEInterfaceValues (const FiniteElement< dim, spacedim > &fe, const Quadrature< dim - 1 > &quadrature, const UpdateFlags update_flags) | |
FEInterfaceValues (const hp::MappingCollection< dim, spacedim > &mapping_collection, const hp::FECollection< dim, spacedim > &fe_collection, const hp::QCollection< dim - 1 > &quadrature_collection, const UpdateFlags update_flags) | |
FEInterfaceValues (const hp::FECollection< dim, spacedim > &fe_collection, const hp::QCollection< dim - 1 > &quadrature_collection, const UpdateFlags update_flags) | |
template<typename CellIteratorType , typename CellNeighborIteratorType > | |
void | reinit (const CellIteratorType &cell, const unsigned int face_no, const unsigned int sub_face_no, const CellNeighborIteratorType &cell_neighbor, const unsigned int face_no_neighbor, const unsigned int sub_face_no_neighbor, const unsigned int q_index=numbers::invalid_unsigned_int, const unsigned int mapping_index=numbers::invalid_unsigned_int, const unsigned int fe_index=numbers::invalid_unsigned_int, const unsigned int fe_index_neighbor=numbers::invalid_unsigned_int) |
template<typename CellIteratorType > | |
void | reinit (const CellIteratorType &cell, const unsigned int face_no, const unsigned int q_index=numbers::invalid_unsigned_int, const unsigned int mapping_index=numbers::invalid_unsigned_int, const unsigned int fe_index=numbers::invalid_unsigned_int) |
const FEFaceValuesBase< dim, spacedim > & | get_fe_face_values (const unsigned int cell_index) const |
const Mapping< dim, spacedim > & | get_mapping () const |
const FiniteElement< dim, spacedim > & | get_fe () const |
const Quadrature< dim - 1 > & | get_quadrature () const |
const hp::MappingCollection< dim, spacedim > & | get_mapping_collection () const |
const hp::FECollection< dim, spacedim > & | get_fe_collection () const |
const hp::QCollection< dim - 1 > & | get_quadrature_collection () const |
bool | has_hp_capabilities () const |
UpdateFlags | get_update_flags () const |
Triangulation< dim, spacedim >::cell_iterator | get_cell (const unsigned int cell_index) const |
unsigned int | get_face_number (const unsigned int cell_index) const |
Functions to query information on a given interface | |
bool | at_boundary () const |
double | JxW (const unsigned int quadrature_point) const |
const std::vector< double > & | get_JxW_values () const |
const std::vector< Tensor< 1, spacedim > > & | get_normal_vectors () const |
std_cxx20::ranges::iota_view< unsigned int, unsigned int > | quadrature_point_indices () const |
const std::vector< Point< spacedim > > & | get_quadrature_points () const |
unsigned | n_current_interface_dofs () const |
std_cxx20::ranges::iota_view< unsigned int, unsigned int > | dof_indices () const |
std::vector< types::global_dof_index > | get_interface_dof_indices () const |
std::array< unsigned int, 2 > | interface_dof_to_dof_indices (const unsigned int interface_dof_index) const |
Tensor< 1, spacedim > | normal (const unsigned int q_point_index) const |
Access to shape functions | |
double | shape_value (const bool here_or_there, const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Access to jumps in shape function values and their derivatives | |
double | jump_in_shape_values (const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Tensor< 1, spacedim > | jump_in_shape_gradients (const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Tensor< 2, spacedim > | jump_in_shape_hessians (const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Tensor< 3, spacedim > | jump_in_shape_3rd_derivatives (const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Access to the average of shape function values and their derivatives | |
double | average_of_shape_values (const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Tensor< 1, spacedim > | average_of_shape_gradients (const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Tensor< 2, spacedim > | average_of_shape_hessians (const unsigned int interface_dof_index, const unsigned int q_point, const unsigned int component=0) const |
Access to jumps in the function values and derivatives | |
template<class InputVector > | |
void | get_jump_in_function_values (const InputVector &fe_function, std::vector< typename InputVector::value_type > &values) const |
template<class InputVector > | |
void | get_jump_in_function_gradients (const InputVector &fe_function, std::vector< Tensor< 1, spacedim, typename InputVector::value_type > > &gradients) const |
template<class InputVector > | |
void | get_jump_in_function_hessians (const InputVector &fe_function, std::vector< Tensor< 2, spacedim, typename InputVector::value_type > > &hessians) const |
template<class InputVector > | |
void | get_jump_in_function_third_derivatives (const InputVector &fe_function, std::vector< Tensor< 3, spacedim, typename InputVector::value_type > > &third_derivatives) const |
Access to the average of the function values and derivatives | |
template<class InputVector > | |
void | get_average_of_function_values (const InputVector &fe_function, std::vector< typename InputVector::value_type > &values) const |
template<class InputVector > | |
void | get_average_of_function_gradients (const InputVector &fe_function, std::vector< Tensor< 1, spacedim, typename InputVector::value_type > > &gradients) const |
template<class InputVector > | |
void | get_average_of_function_hessians (const InputVector &fe_function, std::vector< Tensor< 2, spacedim, typename InputVector::value_type > > &hessians) const |
Extractors Methods to extract individual components | |
FEInterfaceViews::Scalar< dim, spacedim > | operator[] (const FEValuesExtractors::Scalar &scalar) const |
FEInterfaceViews::Vector< dim, spacedim > | operator[] (const FEValuesExtractors::Vector &vector) const |
Public Attributes | |
const unsigned int | n_quadrature_points |
Private Attributes | |
std::vector< types::global_dof_index > | interface_dof_indices |
std::vector< std::array< unsigned int, 2 > > | dofmap |
FEFaceValuesBase< dim, spacedim > * | fe_face_values |
FEFaceValuesBase< dim, spacedim > * | fe_face_values_neighbor |
Data that supports the standard FE implementation | |
std::unique_ptr< FEFaceValues< dim, spacedim > > | internal_fe_face_values |
std::unique_ptr< FESubfaceValues< dim, spacedim > > | internal_fe_subface_values |
std::unique_ptr< FEFaceValues< dim, spacedim > > | internal_fe_face_values_neighbor |
std::unique_ptr< FESubfaceValues< dim, spacedim > > | internal_fe_subface_values_neighbor |
Friends | |
template<int , int > | |
class | FEInterfaceViews::Scalar |
template<int , int > | |
class | FEInterfaceViews::Vector |
Data that supports the hp-FE implementation | |
std::unique_ptr< hp::FEFaceValues< dim, spacedim > > | internal_hp_fe_face_values |
std::unique_ptr< hp::FESubfaceValues< dim, spacedim > > | internal_hp_fe_subface_values |
std::unique_ptr< hp::FEFaceValues< dim, spacedim > > | internal_hp_fe_face_values_neighbor |
std::unique_ptr< hp::FESubfaceValues< dim, spacedim > > | internal_hp_fe_subface_values_neighbor |
static ::ExceptionBase & | ExcOnlyAvailableWithoutHP () |
static ::ExceptionBase & | ExcOnlyAvailableWithHP () |
FEInterfaceValues is a data structure to access and assemble finite element data on interfaces between two cells of a mesh.
It provides a way to access averages, jump terms, and similar operations used in Discontinuous Galerkin methods on a face between two neighboring cells. This allows the computation of typical mesh-dependent linear or bilinear forms in a similar way as FEValues does for cells and FEFaceValues does for faces. In the literature, the faces between neighboring cells are called "inner interfaces" or "facets".
Internally, this class provides an abstraction for two FEFaceValues objects (or FESubfaceValues when using adaptive refinement). The class introduces a new "interface dof index" that walks over the union of the dof indices of the two FEFaceValues objects. Helper functions allow translating between the new "interface dof index" and the corresponding "cell index" (0 for the first cell, 1 for the second cell) and "dof index" within that cell.
The class is made to be used inside MeshWorker::mesh_loop(). It is intended to be a low level replacement for MeshWorker and LocalIntegrators and a higher level abstraction compared to assembling face terms manually.
Definition at line 1276 of file fe_interface_values.h.
FEInterfaceValues< dim, spacedim >::FEInterfaceValues | ( | const Mapping< dim, spacedim > & | mapping, |
const FiniteElement< dim, spacedim > & | fe, | ||
const Quadrature< dim - 1 > & | quadrature, | ||
const UpdateFlags | update_flags ) |
Construct the FEInterfaceValues with a single FiniteElement (same on both sides of the facet). The FEFaceValues objects will be initialized with the given mapping
, quadrature
, and update_flags
.
FEInterfaceValues< dim, spacedim >::FEInterfaceValues | ( | const Mapping< dim, spacedim > & | mapping, |
const FiniteElement< dim, spacedim > & | fe, | ||
const hp::QCollection< dim - 1 > & | quadrature, | ||
const UpdateFlags | update_flags ) |
The same as above but taking a collection of quadrature rules so that different quadrature rules can be assigned to different faces.
FEInterfaceValues< dim, spacedim >::FEInterfaceValues | ( | const FiniteElement< dim, spacedim > & | fe, |
const Quadrature< dim - 1 > & | quadrature, | ||
const UpdateFlags | update_flags ) |
Construct the FEInterfaceValues with a single FiniteElement and a Q1 Mapping.
See the constructor above.
FEInterfaceValues< dim, spacedim >::FEInterfaceValues | ( | const hp::MappingCollection< dim, spacedim > & | mapping_collection, |
const hp::FECollection< dim, spacedim > & | fe_collection, | ||
const hp::QCollection< dim - 1 > & | quadrature_collection, | ||
const UpdateFlags | update_flags ) |
Construct the FEInterfaceValues object with different FiniteElements assigned to different faces.
FEInterfaceValues< dim, spacedim >::FEInterfaceValues | ( | const hp::FECollection< dim, spacedim > & | fe_collection, |
const hp::QCollection< dim - 1 > & | quadrature_collection, | ||
const UpdateFlags | update_flags ) |
Same as above, but using the default linear mapping.
void FEInterfaceValues< dim, spacedim >::reinit | ( | const CellIteratorType & | cell, |
const unsigned int | face_no, | ||
const unsigned int | sub_face_no, | ||
const CellNeighborIteratorType & | cell_neighbor, | ||
const unsigned int | face_no_neighbor, | ||
const unsigned int | sub_face_no_neighbor, | ||
const unsigned int | q_index = numbers::invalid_unsigned_int, | ||
const unsigned int | mapping_index = numbers::invalid_unsigned_int, | ||
const unsigned int | fe_index = numbers::invalid_unsigned_int, | ||
const unsigned int | fe_index_neighbor = numbers::invalid_unsigned_int ) |
Re-initialize this object to be used on a new interface given by two faces of two neighboring cells. The cell
and cell_neighbor
cells will be referred to through cell_index
zero and one after this call in all places where one needs to identify the two cells adjacent to the interface.
Use numbers::invalid_unsigned_int for sub_face_no
or sub_face_no_neighbor
to indicate that you want to work on the entire face, not a sub-face.
The arguments (including their order) are identical to the face_worker
arguments in MeshWorker::mesh_loop().
In order to do integration on a face or sub-face, this object will have to choose what quadrature formula to use. This is simple if you initialized the current FEInterfaceValues object with just a single FiniteElement and a single (face) Quadrature object, because in that case there is only one element and quadrature that will be used for all interfaces. But it is not so simple in the hp case where there may be different elements used on different cells, and different quadrature formulas should be used on different faces; one may also want to use a different mapping for different faces. As a consequence, you would have initialized the current object with a hp::FECollection, hp::QCollection, and possible an hp::MappingCollection object. The question then is: For a given face or subface, which quadrature and mapping should be used? The following decision tree will then be used:
q_index
and mapping_index
arguments to this function are explicitly specified (rather than leaving them at their default values), then these indices will be used to select which element of the hp::QCollection and hp::MappingCollection passed to the constructor should serve as the quadrature and mapping to be used.active_fe_index
values of the two adjacent cells are identical (i.e., have quadrature points at the same locations, and have the same weights). If this is so, then it does not matter which one of the two we take, and we choose one or the other.q_index
and mapping_index
arguments to this function.[in] | cell | An iterator to the first cell adjacent to the interface. |
[in] | face_no | An integer identifying which face of the first cell the interface is on. |
[in] | sub_face_no | An integer identifying the subface (child) of the face (identified by the previous two arguments) that the interface corresponds to. If equal to numbers::invalid_unsigned_int, then the interface is considered to be the entire face. |
[in] | cell_neighbor | An iterator to the second cell adjacent to the interface. The type of this iterator does not have to equal that of cell , but must be convertible to it. This allows using an active cell iterator for cell , and cell->neighbor(f) for cell_neighbor , since the return type of cell->neighbor(f) is simply a cell iterator (not necessarily an active cell iterator). |
[in] | face_no_neighbor | Like face_no , just for the neighboring cell. |
[in] | sub_face_no_neighbor | Like sub_face_no , just for the neighboring cell. |
[in] | q_index | The index of the quadrature object within the hp::QCollection passed to the constructor to use on the current interface. See the documentation above what happens if this argument is not explicitly provided but left at its default value. |
[in] | mapping_index | The index of the mapping object within the hp::MappingCollection passed to the constructor to use on the current interface. See the documentation above what happens if this argument is not explicitly provided but left at its default value. |
[in] | fe_index | If left at its default, use the finite element within the hp::FECollection passed to the constructor as given by the dominating finite element across the interface (only used if the FEInterface object is initialized with an hp::FECollection, an hp::QCollection, and possibly an hp::MappingCollection). |
[in] | fe_index_neighbor | Active fe index of neighboring cell. Useful if hp capabilities are used and for non-DoFHandler iterators. |
void FEInterfaceValues< dim, spacedim >::reinit | ( | const CellIteratorType & | cell, |
const unsigned int | face_no, | ||
const unsigned int | q_index = numbers::invalid_unsigned_int, | ||
const unsigned int | mapping_index = numbers::invalid_unsigned_int, | ||
const unsigned int | fe_index = numbers::invalid_unsigned_int ) |
Re-initialize this object to be used on an interface given by a single face face_no
of the cell cell
. This is useful to use FEInterfaceValues on boundaries of the domain.
As a consequence, members like jump() will assume a value of zero for the values on the "other" side. Note that no sub_face_number is needed as a boundary face can not neighbor a finer cell.
After calling this function at_boundary() will return true.
[in] | cell | An iterator to the first cell adjacent to the interface. |
[in] | face_no | An integer identifying which face of the first cell the interface is on. |
[in] | q_index | This argument selects which quadrature formula to use See the discussion in the documentation of the other reinit() function for what happens when this argument is left at its default value. |
[in] | mapping_index | This argument selects which mapping to use See the discussion in the documentation of the other reinit() function for what happens when this argument is left at its default value. |
[in] | fe_index | If left at its default, use the finite element within the hp::FECollection passed to the constructor as given by the dominating finite element across the interface (only used if the FEInterface object is initialized with an hp::FECollection, an hp::QCollection, and possibly an hp::MappingCollection). |
const FEFaceValuesBase< dim, spacedim > & FEInterfaceValues< dim, spacedim >::get_fe_face_values | ( | const unsigned int | cell_index | ) | const |
Return a reference to the FEFaceValues or FESubfaceValues object of the specified cell of the interface.
The cell_index
is either 0 or 1 and corresponds to the cell index returned by interface_dof_to_cell_and_dof_index().
const Mapping< dim, spacedim > & FEInterfaceValues< dim, spacedim >::get_mapping | ( | ) | const |
Constant reference to the selected mapping object.
const FiniteElement< dim, spacedim > & FEInterfaceValues< dim, spacedim >::get_fe | ( | ) | const |
Constant reference to the selected finite element object.
const Quadrature< dim - 1 > & FEInterfaceValues< dim, spacedim >::get_quadrature | ( | ) | const |
Return a reference to the quadrature object in use.
const hp::MappingCollection< dim, spacedim > & FEInterfaceValues< dim, spacedim >::get_mapping_collection | ( | ) | const |
Return a reference to the used mapping.
const hp::FECollection< dim, spacedim > & FEInterfaceValues< dim, spacedim >::get_fe_collection | ( | ) | const |
Return a reference to the selected finite element object.
const hp::QCollection< dim - 1 > & FEInterfaceValues< dim, spacedim >::get_quadrature_collection | ( | ) | const |
Return a reference to the face quadrature object in use.
bool FEInterfaceValues< dim, spacedim >::has_hp_capabilities | ( | ) | const |
Returns a boolean indicating whether or not this FEInterfaceValues object has hp-capabilities enabled.
UpdateFlags FEInterfaceValues< dim, spacedim >::get_update_flags | ( | ) | const |
Return the update flags set.
Triangulation< dim, spacedim >::cell_iterator FEInterfaceValues< dim, spacedim >::get_cell | ( | const unsigned int | cell_index | ) | const |
Return a triangulation iterator to the current cell of the interface.
The cell_index
is either 0 or 1 and corresponds to the cell index returned by interface_dof_to_cell_and_dof_index().
unsigned int FEInterfaceValues< dim, spacedim >::get_face_number | ( | const unsigned int | cell_index | ) | const |
Return the number of the face on the interface selected the last time the reinit() function was called.
The cell_index
is either 0 or 1 and corresponds to the cell index returned by interface_dof_to_cell_and_dof_index().
bool FEInterfaceValues< dim, spacedim >::at_boundary | ( | ) | const |
Return if the current interface is a boundary face or an internal face with two adjacent cells.
See the corresponding reinit() functions for details.
double FEInterfaceValues< dim, spacedim >::JxW | ( | const unsigned int | quadrature_point | ) | const |
Mapped quadrature weight. This value equals the mapped surface element times the weight of the quadrature point.
You can think of the quantity returned by this function as the surface element \(ds\) in the integral that we implement here by quadrature.
update_JxW_values
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. const std::vector< double > & FEInterfaceValues< dim, spacedim >::get_JxW_values | ( | ) | const |
Return the vector of JxW values for each quadrature point.
update_JxW_values
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. const std::vector< Tensor< 1, spacedim > > & FEInterfaceValues< dim, spacedim >::get_normal_vectors | ( | ) | const |
Return the normal vector of the interface in each quadrature point.
The return value is identical to get_fe_face_values(0).get_normal_vectors() and therefore, are outside normal vectors from the perspective of the first cell of this interface.
update_normal_vectors
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. std_cxx20::ranges::iota_view< unsigned int, unsigned int > FEInterfaceValues< dim, spacedim >::quadrature_point_indices | ( | ) | const |
Return an object that can be thought of as an array containing all indices from zero to n_quadrature_points
. This allows to write code using range-based for
loops.
const std::vector< Point< spacedim > > & FEInterfaceValues< dim, spacedim >::get_quadrature_points | ( | ) | const |
Return a reference to the quadrature points in real space.
update_quadrature_points
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. unsigned FEInterfaceValues< dim, spacedim >::n_current_interface_dofs | ( | ) | const |
Return the number of DoFs (or shape functions) on the current interface.
std_cxx20::ranges::iota_view< unsigned int, unsigned int > FEInterfaceValues< dim, spacedim >::dof_indices | ( | ) | const |
Return an object that can be thought of as an array containing all indices from zero (inclusive) to n_current_interface_dofs()
(exclusive). This allows one to write code using range-based for
loops of the following kind:
Here, we are looping over all degrees of freedom on all cell interfaces, with i
and j
taking on all valid indices for interface degrees of freedom, as defined by the finite element passed to fe_iv
.
std::vector< types::global_dof_index > FEInterfaceValues< dim, spacedim >::get_interface_dof_indices | ( | ) | const |
Return the set of joint DoF indices. This includes indices from both cells. If reinit was called with an active cell iterator, the indices are based on the active indices (returned by DoFCellAccessor::get_dof_indices()
), in case of level cell (that is, if is_level_cell() return true ) the mg dof indices are returned.
std::array< unsigned int, 2 > FEInterfaceValues< dim, spacedim >::interface_dof_to_dof_indices | ( | const unsigned int | interface_dof_index | ) | const |
Convert an interface dof index into the corresponding local DoF indices of the two cells. If an interface DoF is only active on one of the cells, the other index will be numbers::invalid_unsigned_int.
For discontinuous finite elements, each interface dof is located on exactly one side of the interface and, consequently, only one of the two values returned is valid (i.e., different from numbers::invalid_unsigned_int).
Tensor< 1, spacedim > FEInterfaceValues< dim, spacedim >::normal | ( | const unsigned int | q_point_index | ) | const |
Return the normal in a given quadrature point.
The normal points in outwards direction as seen from the first cell of this interface.
update_normal_vectors
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. double FEInterfaceValues< dim, spacedim >::shape_value | ( | const bool | here_or_there, |
const unsigned int | interface_dof_index, | ||
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return component component
of the value of the shape function with interface dof index interface_dof_index
in quadrature point q_point
.
The argument here_or_there
selects between the value on cell 0 (here, true
) and cell 1 (there, false
). You can also interpret it as "upstream" (true
) and "downstream" (false
) as defined by the direction of the normal vector in this quadrature point. If here_or_there
is true, the shape functions from the first cell of the interface is used.
In other words, this function returns the limit of the value of the shape function in the given quadrature point when approaching it from one of the two cells of the interface.
(direction * normal)>0
as the first argument of this function. double FEInterfaceValues< dim, spacedim >::jump_in_shape_values | ( | const unsigned int | interface_dof_index, |
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return the jump \(\jump{u}=u_{\text{cell0}} - u_{\text{cell1}}\) on the interface for the shape function interface_dof_index
at the quadrature point q_point
of component component
.
Note that one can define the jump in different ways (the value "there" minus the value "here", or the other way around; both are used in the finite element literature). The definition here uses "value here minus value there", as seen from the first cell.
If this is a boundary face (at_boundary() returns true), then \(\jump{u}=u_{\text{cell0}}\), that is "the value here (minus zero)".
Tensor< 1, spacedim > FEInterfaceValues< dim, spacedim >::jump_in_shape_gradients | ( | const unsigned int | interface_dof_index, |
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return the jump in the gradient \(\jump{\nabla u}=\nabla u_{\text{cell0}} -
\nabla u_{\text{cell1}}\) on the interface for the shape function interface_dof_index
at the quadrature point q_point
of component component
.
If this is a boundary face (at_boundary() returns true), then \(\jump{\nabla u}=\nabla u_{\text{cell0}}\).
Tensor< 2, spacedim > FEInterfaceValues< dim, spacedim >::jump_in_shape_hessians | ( | const unsigned int | interface_dof_index, |
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return the jump in the Hessian \(\jump{\nabla^2 u} = \nabla^2
u_{\text{cell0}} - \nabla^2 u_{\text{cell1}}\) on the interface for the shape function interface_dof_index
at the quadrature point q_point
of component component
.
If this is a boundary face (at_boundary() returns true), then \(\jump{\nabla^2 u} = \nabla^2 u_{\text{cell0}}\).
Tensor< 3, spacedim > FEInterfaceValues< dim, spacedim >::jump_in_shape_3rd_derivatives | ( | const unsigned int | interface_dof_index, |
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return the jump in the third derivative \(\jump{\nabla^3 u} = \nabla^3
u_{\text{cell0}} - \nabla^3 u_{\text{cell1}}\) on the interface for the shape function interface_dof_index
at the quadrature point q_point
of component component
.
If this is a boundary face (at_boundary() returns true), then \(\jump{\nabla^3 u} = \nabla^3 u_{\text{cell0}}\).
double FEInterfaceValues< dim, spacedim >::average_of_shape_values | ( | const unsigned int | interface_dof_index, |
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return the average \(\average{u}=\frac{1}{2}u_{\text{cell0}} +
\frac{1}{2}u_{\text{cell1}}\) on the interface for the shape function interface_dof_index
at the quadrature point q_point
of component component
.
If this is a boundary face (at_boundary() returns true), then \(\average{u}=u_{\text{cell0}}\).
Tensor< 1, spacedim > FEInterfaceValues< dim, spacedim >::average_of_shape_gradients | ( | const unsigned int | interface_dof_index, |
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return the average of the gradient \(\average{\nabla u} = \frac{1}{2}\nabla
u_{\text{cell0}} + \frac{1}{2} \nabla u_{\text{cell1}}\) on the interface for the shape function interface_dof_index
at the quadrature point q_point
of component component
.
If this is a boundary face (at_boundary() returns true), then \(\average{\nabla u}=\nabla u_{\text{cell0}}\).
Tensor< 2, spacedim > FEInterfaceValues< dim, spacedim >::average_of_shape_hessians | ( | const unsigned int | interface_dof_index, |
const unsigned int | q_point, | ||
const unsigned int | component = 0 ) const |
Return the average of the Hessian \(\average{\nabla^2 u} =
\frac{1}{2}\nabla^2 u_{\text{cell0}} + \frac{1}{2} \nabla^2
u_{\text{cell1}}\) on the interface for the shape function interface_dof_index
at the quadrature point q_point
of component component
.
If this is a boundary face (at_boundary() returns true), then \(\average{\nabla^2 u}=\nabla^2 u_{\text{cell0}}\).
void FEInterfaceValues< dim, spacedim >::get_jump_in_function_values | ( | const InputVector & | fe_function, |
std::vector< typename InputVector::value_type > & | values ) const |
Return the jump in the values of the finite element function characterized by fe_function
at the quadrature points of the cell interface selected the last time the reinit
function of the FEInterfaceValues object was called.
update_values
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. void FEInterfaceValues< dim, spacedim >::get_jump_in_function_gradients | ( | const InputVector & | fe_function, |
std::vector< Tensor< 1, spacedim, typename InputVector::value_type > > & | gradients ) const |
Return the jump in the gradients of the finite element function characterized by fe_function
at the quadrature points of the cell interface selected the last time the reinit
function of the FEInterfaceValues object was called.
update_gradients
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. void FEInterfaceValues< dim, spacedim >::get_jump_in_function_hessians | ( | const InputVector & | fe_function, |
std::vector< Tensor< 2, spacedim, typename InputVector::value_type > > & | hessians ) const |
Return the jump in the Hessians of the finite element function characterized by fe_function
at the quadrature points of the cell interface selected the last time the reinit
function of the FEInterfaceValues object was called.
update_hessians
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. void FEInterfaceValues< dim, spacedim >::get_jump_in_function_third_derivatives | ( | const InputVector & | fe_function, |
std::vector< Tensor< 3, spacedim, typename InputVector::value_type > > & | third_derivatives ) const |
Return the jump in the third derivatives of the finite element function characterized by fe_function
at the quadrature points of the cell interface selected the last time the reinit
function of the FEInterfaceValues object was called.
update_third_derivatives
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. void FEInterfaceValues< dim, spacedim >::get_average_of_function_values | ( | const InputVector & | fe_function, |
std::vector< typename InputVector::value_type > & | values ) const |
Return the average of the values of the finite element function characterized by fe_function
at the quadrature points of the cell interface selected the last time the reinit
function of the FEInterfaceValues object was called.
update_values
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. void FEInterfaceValues< dim, spacedim >::get_average_of_function_gradients | ( | const InputVector & | fe_function, |
std::vector< Tensor< 1, spacedim, typename InputVector::value_type > > & | gradients ) const |
Return the average of the gradients of the finite element function characterized by fe_function
at the quadrature points of the cell interface selected the last time the reinit
function of the FEInterfaceValues object was called.
update_gradients
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. void FEInterfaceValues< dim, spacedim >::get_average_of_function_hessians | ( | const InputVector & | fe_function, |
std::vector< Tensor< 2, spacedim, typename InputVector::value_type > > & | hessians ) const |
Return the average of the Hessians of the finite element function characterized by fe_function
at the quadrature points of the cell interface selected the last time the reinit
function of the FEInterfaceValues object was called.
update_hessians
flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. FEInterfaceViews::Scalar< dim, spacedim > FEInterfaceValues< dim, spacedim >::operator[] | ( | const FEValuesExtractors::Scalar & | scalar | ) | const |
Create a view of the current FEInterfaceValues object that represents a particular scalar component of the possibly vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews.
FEInterfaceViews::Vector< dim, spacedim > FEInterfaceValues< dim, spacedim >::operator[] | ( | const FEValuesExtractors::Vector & | vector | ) | const |
Create a view of the current FEInterfaceValues object that represents a set of dim
scalar components (i.e. a vector) of the vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews.
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Definition at line 2171 of file fe_interface_values.h.
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Definition at line 2173 of file fe_interface_values.h.
const unsigned int FEInterfaceValues< dim, spacedim >::n_quadrature_points |
Number of quadrature points.
Definition at line 1282 of file fe_interface_values.h.
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The list of DoF indices for the current interface, filled in reinit().
Definition at line 2062 of file fe_interface_values.h.
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The mapping from interface dof to the two local dof indices of the FEFaceValues objects. If an interface DoF is only active on one of the cells, the other one will have numbers::invalid_unsigned_int.
Definition at line 2069 of file fe_interface_values.h.
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Pointer to internal_fe_face_values or internal_fe_subface_values, respectively as determined in reinit().
Definition at line 2075 of file fe_interface_values.h.
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Pointer to internal_fe_face_values_neighbor, internal_fe_subface_values_neighbor, or nullptr, respectively as determined in reinit().
Definition at line 2082 of file fe_interface_values.h.
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The FEFaceValues object for the current cell.
Definition at line 2092 of file fe_interface_values.h.
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The FEFaceValues object for the current cell if the cell is refined.
Definition at line 2097 of file fe_interface_values.h.
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The FEFaceValues object for the neighboring cell.
Definition at line 2102 of file fe_interface_values.h.
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The FEFaceValues object for the neighboring cell if the cell is refined.
Definition at line 2108 of file fe_interface_values.h.
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An hp::FEValues object for the FEFaceValues on the present cell.
Definition at line 2121 of file fe_interface_values.h.
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An hp::FEValues object for the FESubfaceValues on the present cell.
Definition at line 2128 of file fe_interface_values.h.
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An hp::FEValues object for the FEFaceValues on the neighbor of the present cell.
Definition at line 2135 of file fe_interface_values.h.
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An hp::FEValues object for the FESubfaceValues on the neighboring cell.
Definition at line 2142 of file fe_interface_values.h.