Reference documentation for deal.II version Git cd8b20072f 2020-09-24 16:28:23 -0400
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Public Member Functions | Static Public Member Functions | Public Attributes | Static Public Attributes | Protected Member Functions | Protected Attributes | Private Member Functions | List of all members
FESubfaceValues< dim, spacedim > Class Template Reference

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

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

Public Member Functions

 FESubfaceValues (const Mapping< dim, spacedim > &mapping, const FiniteElement< dim, spacedim > &fe, const Quadrature< dim - 1 > &face_quadrature, const UpdateFlags update_flags)
 
 FESubfaceValues (const FiniteElement< dim, spacedim > &fe, const Quadrature< dim - 1 > &face_quadrature, const UpdateFlags update_flags)
 
template<bool level_dof_access>
void reinit (const TriaIterator< DoFCellAccessor< dim, spacedim, level_dof_access >> &cell, const unsigned int face_no, const unsigned int subface_no)
 
template<bool level_dof_access>
void reinit (const TriaIterator< DoFCellAccessor< dim, spacedim, level_dof_access >> &cell, const typename Triangulation< dim, spacedim >::face_iterator &face, const typename Triangulation< dim, spacedim >::face_iterator &subface)
 
void reinit (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no)
 
void reinit (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const typename Triangulation< dim, spacedim >::face_iterator &face, const typename Triangulation< dim, spacedim >::face_iterator &subface)
 
const FESubfaceValues< dim, spacedim > & get_present_fe_values () const
 
const Tensor< 1, spacedim > & boundary_form (const unsigned int i) const
 
const std::vector< Tensor< 1, spacedim > > & get_boundary_forms () const
 
unsigned int get_face_index () const
 
const Quadrature< dim - 1 > & get_quadrature () const
 
std::size_t memory_consumption () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
Access to shape function values

These fields are filled by the finite element.

const doubleshape_value (const unsigned int function_no, const unsigned int point_no) const
 
double shape_value_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const
 
const Tensor< 1, spacedim > & shape_grad (const unsigned int function_no, const unsigned int quadrature_point) const
 
Tensor< 1, spacedim > shape_grad_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const
 
const Tensor< 2, spacedim > & shape_hessian (const unsigned int function_no, const unsigned int point_no) const
 
Tensor< 2, spacedim > shape_hessian_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const
 
const Tensor< 3, spacedim > & shape_3rd_derivative (const unsigned int function_no, const unsigned int point_no) const
 
Tensor< 3, spacedim > shape_3rd_derivative_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const
 
Access to values of global finite element fields
template<class InputVector >
void get_function_values (const InputVector &fe_function, std::vector< typename InputVector::value_type > &values) const
 
template<class InputVector >
void get_function_values (const InputVector &fe_function, std::vector< Vector< typename InputVector::value_type >> &values) const
 
template<class InputVector >
void get_function_values (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< typename InputVector::value_type > &values) const
 
template<class InputVector >
void get_function_values (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Vector< typename InputVector::value_type >> &values) const
 
template<class InputVector >
void get_function_values (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< typename InputVector::value_type >> values, const bool quadrature_points_fastest) const
 
Access to derivatives of global finite element fields
template<class InputVector >
void get_function_gradients (const InputVector &fe_function, std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> &gradients) const
 
template<class InputVector >
void get_function_gradients (const InputVector &fe_function, std::vector< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>> &gradients) const
 
template<class InputVector >
void get_function_gradients (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> &gradients) const
 
template<class InputVector >
void get_function_gradients (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>> gradients, bool quadrature_points_fastest=false) const
 
Access to second derivatives

Hessian matrices and Laplacians of global finite element fields

template<class InputVector >
void get_function_hessians (const InputVector &fe_function, std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> &hessians) const
 
template<class InputVector >
void get_function_hessians (const InputVector &fe_function, std::vector< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>> &hessians, bool quadrature_points_fastest=false) const
 
template<class InputVector >
void get_function_hessians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> &hessians) const
 
template<class InputVector >
void get_function_hessians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>> hessians, bool quadrature_points_fastest=false) const
 
template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, std::vector< typename InputVector::value_type > &laplacians) const
 
template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, std::vector< Vector< typename InputVector::value_type >> &laplacians) const
 
template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< typename InputVector::value_type > &laplacians) const
 
template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Vector< typename InputVector::value_type >> &laplacians) const
 
template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< std::vector< typename InputVector::value_type >> &laplacians, bool quadrature_points_fastest=false) const
 
Access to third derivatives of global finite element fields
template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> &third_derivatives) const
 
template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, std::vector< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>> &third_derivatives, bool quadrature_points_fastest=false) const
 
template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> &third_derivatives) const
 
template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>> third_derivatives, bool quadrature_points_fastest=false) const
 
Cell degrees of freedom
std_cxx20::ranges::iota_view< unsigned int, unsigned intdof_indices () const
 
std_cxx20::ranges::iota_view< unsigned int, unsigned intdof_indices_starting_at (const unsigned int start_dof_index) const
 
std_cxx20::ranges::iota_view< unsigned int, unsigned intdof_indices_ending_at (const unsigned int end_dof_index) const
 
Geometry of the cell
std_cxx20::ranges::iota_view< unsigned int, unsigned intquadrature_point_indices () const
 
const Point< spacedim > & quadrature_point (const unsigned int q) const
 
const std::vector< Point< spacedim > > & get_quadrature_points () const
 
double JxW (const unsigned int quadrature_point) const
 
const std::vector< double > & get_JxW_values () const
 
const DerivativeForm< 1, dim, spacedim > & jacobian (const unsigned int quadrature_point) const
 
const std::vector< DerivativeForm< 1, dim, spacedim > > & get_jacobians () const
 
const DerivativeForm< 2, dim, spacedim > & jacobian_grad (const unsigned int quadrature_point) const
 
const std::vector< DerivativeForm< 2, dim, spacedim > > & get_jacobian_grads () const
 
const Tensor< 3, spacedim > & jacobian_pushed_forward_grad (const unsigned int quadrature_point) const
 
const std::vector< Tensor< 3, spacedim > > & get_jacobian_pushed_forward_grads () const
 
const DerivativeForm< 3, dim, spacedim > & jacobian_2nd_derivative (const unsigned int quadrature_point) const
 
const std::vector< DerivativeForm< 3, dim, spacedim > > & get_jacobian_2nd_derivatives () const
 
const Tensor< 4, spacedim > & jacobian_pushed_forward_2nd_derivative (const unsigned int quadrature_point) const
 
const std::vector< Tensor< 4, spacedim > > & get_jacobian_pushed_forward_2nd_derivatives () const
 
const DerivativeForm< 4, dim, spacedim > & jacobian_3rd_derivative (const unsigned int quadrature_point) const
 
const std::vector< DerivativeForm< 4, dim, spacedim > > & get_jacobian_3rd_derivatives () const
 
const Tensor< 5, spacedim > & jacobian_pushed_forward_3rd_derivative (const unsigned int quadrature_point) const
 
const std::vector< Tensor< 5, spacedim > > & get_jacobian_pushed_forward_3rd_derivatives () const
 
const DerivativeForm< 1, spacedim, dim > & inverse_jacobian (const unsigned int quadrature_point) const
 
const std::vector< DerivativeForm< 1, spacedim, dim > > & get_inverse_jacobians () const
 
const Tensor< 1, spacedim > & normal_vector (const unsigned int i) const
 
const std::vector< Tensor< 1, spacedim > > & get_normal_vectors () const
 
Extractors Methods to extract individual components
const FEValuesViews::Scalar< dim, spacedim > & operator[] (const FEValuesExtractors::Scalar &scalar) const
 
const FEValuesViews::Vector< dim, spacedim > & operator[] (const FEValuesExtractors::Vector &vector) const
 
const FEValuesViews::SymmetricTensor< 2, dim, spacedim > & operator[] (const FEValuesExtractors::SymmetricTensor< 2 > &tensor) const
 
const FEValuesViews::Tensor< 2, dim, spacedim > & operator[] (const FEValuesExtractors::Tensor< 2 > &tensor) const
 
Access to the raw data
const Mapping< dim, spacedim > & get_mapping () const
 
const FiniteElement< dim, spacedim > & get_fe () const
 
UpdateFlags get_update_flags () const
 
const Triangulation< dim, spacedim >::cell_iterator get_cell () const
 
CellSimilarity::Similarity get_cell_similarity () const
 
Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
unsigned int n_subscriptions () const
 
template<typename StreamType >
void list_subscribers (StreamType &stream) const
 
void list_subscribers () const
 

Static Public Member Functions

static ::ExceptionBaseExcReinitCalledWithBoundaryFace ()
 
static ::ExceptionBaseExcFaceHasNoSubfaces ()
 
static ::ExceptionBaseExcAccessToUninitializedField (std::string arg1)
 
static ::ExceptionBaseExcFEDontMatch ()
 
static ::ExceptionBaseExcShapeFunctionNotPrimitive (int arg1)
 
static ::ExceptionBaseExcFENotPrimitive ()
 
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

Public Attributes

const unsigned int n_quadrature_points
 
const unsigned int dofs_per_cell
 

Static Public Attributes

static const unsigned int dimension = dim
 
static const unsigned int space_dimension = spacedim
 
static const unsigned int integral_dimension = dim - 1
 

Protected Member Functions

void invalidate_present_cell ()
 
void maybe_invalidate_previous_present_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell)
 
UpdateFlags compute_update_flags (const UpdateFlags update_flags) const
 
void check_cell_similarity (const typename Triangulation< dim, spacedim >::cell_iterator &cell)
 

Protected Attributes

unsigned int present_face_index
 
const Quadrature< dim - 1 > quadrature
 
std::unique_ptr< const CellIteratorBasepresent_cell
 
boost::signals2::connection tria_listener_refinement
 
boost::signals2::connection tria_listener_mesh_transform
 
const SmartPointer< const Mapping< dim, spacedim >, FEValuesBase< dim, spacedim > > mapping
 
std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > mapping_data
 
::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > mapping_output
 
const SmartPointer< const FiniteElement< dim, spacedim >, FEValuesBase< dim, spacedim > > fe
 
std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > fe_data
 
::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > finite_element_output
 
UpdateFlags update_flags
 
CellSimilarity::Similarity cell_similarity
 

Private Member Functions

void initialize (const UpdateFlags update_flags)
 
void do_reinit (const unsigned int face_no, const unsigned int subface_no)
 

Detailed Description

template<int dim, int spacedim = dim>
class FESubfaceValues< dim, spacedim >

Finite element evaluated in quadrature points on a face.

This class adds the functionality of FEFaceValuesBase to FEValues; see there for more documentation.

This class is used for faces lying on a refinement edge. In this case, the neighboring cell is refined. To be able to compute differences between interior and exterior function values, the refinement of the neighboring cell must be simulated on this cell. This is achieved by applying a quadrature rule that simulates the refinement. The resulting data fields are split up to reflect the refinement structure of the neighbor: a subface number corresponds to the number of the child of the neighboring face.

Definition at line 42 of file fe.h.

Constructor & Destructor Documentation

◆ FESubfaceValues() [1/2]

template<int dim, int spacedim>
FESubfaceValues< dim, spacedim >::FESubfaceValues ( const Mapping< dim, spacedim > &  mapping,
const FiniteElement< dim, spacedim > &  fe,
const Quadrature< dim - 1 > &  face_quadrature,
const UpdateFlags  update_flags 
)

Constructor. Gets cell independent data from mapping and finite element objects, matching the quadrature rule and update flags.

Definition at line 4851 of file fe_values.cc.

◆ FESubfaceValues() [2/2]

template<int dim, int spacedim>
FESubfaceValues< dim, spacedim >::FESubfaceValues ( const FiniteElement< dim, spacedim > &  fe,
const Quadrature< dim - 1 > &  face_quadrature,
const UpdateFlags  update_flags 
)

Constructor. This constructor is equivalent to the other one except that it makes the object use a \(Q_1\) mapping (i.e., an object of type MappingQGeneric(1)) implicitly.

Definition at line 4869 of file fe_values.cc.

Member Function Documentation

◆ reinit() [1/4]

template<int dim, int spacedim>
template<bool lda>
void FESubfaceValues< dim, spacedim >::reinit ( const TriaIterator< DoFCellAccessor< dim, spacedim, lda >> &  cell,
const unsigned int  face_no,
const unsigned int  subface_no 
)

Reinitialize the gradients, Jacobi determinants, etc for the given cell of type "iterator into a DoFHandler object", and the finite element associated with this object. It is assumed that the finite element used by the given cell is also the one used by this FESubfaceValues object.

Definition at line 4936 of file fe_values.cc.

◆ reinit() [2/4]

template<int dim, int spacedim>
template<bool lda>
void FESubfaceValues< dim, spacedim >::reinit ( const TriaIterator< DoFCellAccessor< dim, spacedim, lda >> &  cell,
const typename Triangulation< dim, spacedim >::face_iterator &  face,
const typename Triangulation< dim, spacedim >::face_iterator &  subface 
)

Alternative reinitialization function that takes, as arguments, iterators to the face and subface instead of their numbers.

Definition at line 4984 of file fe_values.cc.

◆ reinit() [3/4]

template<int dim, int spacedim>
void FESubfaceValues< dim, spacedim >::reinit ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const unsigned int  face_no,
const unsigned int  subface_no 
)

Reinitialize the gradients, Jacobi determinants, etc for the given subface on a given cell of type "iterator into a Triangulation object", and the given finite element. Since iterators into a triangulation alone only convey information about the geometry of a cell, but not about degrees of freedom possibly associated with this cell, you will not be able to call some functions of this class if they need information about degrees of freedom. These functions are, above all, the get_function_value/gradients/hessians/third_derivatives functions. If you want to call these functions, you have to call the reinit variants that take iterators into DoFHandler or other DoF handler type objects.

Definition at line 4998 of file fe_values.cc.

◆ reinit() [4/4]

template<int dim, int spacedim>
void FESubfaceValues< dim, spacedim >::reinit ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell,
const typename Triangulation< dim, spacedim >::face_iterator &  face,
const typename Triangulation< dim, spacedim >::face_iterator &  subface 
)

Reinitialize the gradients, Jacobi determinants, etc for the given subface on a given cell of type "iterator into a Triangulation object", and the given finite element. Since iterators into a triangulation alone only convey information about the geometry of a cell, but not about degrees of freedom possibly associated with this cell, you will not be able to call some functions of this class if they need information about degrees of freedom. These functions are, above all, the get_function_value/gradients/hessians/third_derivatives functions. If you want to call these functions, you have to call the reinit variants that take iterators into DoFHandler or other DoF handler type objects.

This does the same thing as the previous function but takes iterators instead of numbers as arguments.

Note
face and subface must correspond to a face (and a subface of that face) of cell.

Definition at line 5030 of file fe_values.cc.

◆ get_present_fe_values()

template<int dim, int spacedim = dim>
const FESubfaceValues<dim, spacedim>& FESubfaceValues< dim, spacedim >::get_present_fe_values ( ) const

Return a reference to this very object.

Though it seems that it is not very useful, this function is there to provide capability to the hp::FEValues class, in which case it provides the FEValues object for the present cell (remember that for hp finite elements, the actual FE object used may change from cell to cell, so we also need different FEValues objects for different cells; once you reinitialize the hp::FEValues object for a specific cell, it retrieves the FEValues object for the FE on that cell and returns it through a function of the same name as this one; this function here therefore only provides the same interface so that one can templatize on FEValues and hp::FEValues).

◆ initialize()

template<int dim, int spacedim>
void FESubfaceValues< dim, spacedim >::initialize ( const UpdateFlags  update_flags)
private

Do work common to the two constructors.

Definition at line 4887 of file fe_values.cc.

◆ do_reinit()

template<int dim, int spacedim>
void FESubfaceValues< dim, spacedim >::do_reinit ( const unsigned int  face_no,
const unsigned int  subface_no 
)
private

The reinit() functions do only that part of the work that requires knowledge of the type of iterator. After setting present_cell(), they pass on to this function, which does the real work, and which is independent of the actual type of the cell iterator.

Definition at line 5044 of file fe_values.cc.

◆ boundary_form()

template<int dim, int spacedim = dim>
const Tensor<1, spacedim>& FEFaceValuesBase< dim, spacedim >::boundary_form ( const unsigned int  i) const
inherited

Boundary form of the transformation of the cell at the ith quadrature point. See GlossBoundaryForm.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_boundary_forms 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.

◆ get_boundary_forms()

template<int dim, int spacedim>
const std::vector< Tensor< 1, spacedim > > & FEFaceValuesBase< dim, spacedim >::get_boundary_forms ( ) const
inherited

Return the list of outward normal vectors times the Jacobian of the surface mapping.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_boundary_forms 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.

Definition at line 4620 of file fe_values.cc.

◆ get_face_index()

template<int dim, int spacedim = dim>
unsigned int FEFaceValuesBase< dim, spacedim >::get_face_index ( ) const
inherited

Return the index of the face selected the last time the reinit() function was called.

◆ get_quadrature()

template<int dim, int spacedim = dim>
const Quadrature<dim - 1>& FEFaceValuesBase< dim, spacedim >::get_quadrature ( ) const
inherited

Return a reference to the copy of the quadrature formula stored by this object.

◆ memory_consumption()

template<int dim, int spacedim>
std::size_t FEFaceValuesBase< dim, spacedim >::memory_consumption ( ) const
inherited

Determine an estimate for the memory consumption (in bytes) of this object.

Definition at line 4632 of file fe_values.cc.

◆ shape_value()

template<int dim, int spacedim>
const double& FEValuesBase< dim, spacedim >::shape_value ( const unsigned int  function_no,
const unsigned int  point_no 
) const
inherited

Value of a shape function at a quadrature point on the cell, face or subface selected the last time the reinit function of the derived class was called.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_value_component() function.

Parameters
function_noNumber of the shape function to be evaluated. Note that this number runs from zero to dofs_per_cell, even in the case of an FEFaceValues or FESubfaceValues object.
point_noNumber of the quadrature point at which function is to be evaluated
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ shape_value_component()

template<int dim, int spacedim>
double FEValuesBase< dim, spacedim >::shape_value_component ( const unsigned int  function_no,
const unsigned int  point_no,
const unsigned int  component 
) const
inherited

Compute one vector component of the value of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_value() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_value() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

Parameters
function_noNumber of the shape function to be evaluated.
point_noNumber of the quadrature point at which function is to be evaluated.
componentvector component to be evaluated.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ shape_grad()

template<int dim, int spacedim>
const Tensor<1, spacedim>& FEValuesBase< dim, spacedim >::shape_grad ( const unsigned int  function_no,
const unsigned int  quadrature_point 
) const
inherited

Compute the gradient of the function_noth shape function at the quadrature_pointth quadrature point with respect to real cell coordinates. If you want to get the derivative in one of the coordinate directions, use the appropriate function of the Tensor class to extract one component of the Tensor returned by this function. Since only a reference to the gradient's value is returned, there should be no major performance drawback.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then it will throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_grad_component() function.

The same holds for the arguments of this function as for the shape_value() function.

Parameters
function_noNumber of the shape function to be evaluated.
quadrature_pointNumber of the quadrature point at which function is to be evaluated.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ shape_grad_component()

template<int dim, int spacedim>
Tensor<1, spacedim> FEValuesBase< dim, spacedim >::shape_grad_component ( const unsigned int  function_no,
const unsigned int  point_no,
const unsigned int  component 
) const
inherited

Return one vector component of the gradient of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_grad() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_grad() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

The same holds for the arguments of this function as for the shape_value_component() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ shape_hessian()

template<int dim, int spacedim>
const Tensor<2, spacedim>& FEValuesBase< dim, spacedim >::shape_hessian ( const unsigned int  function_no,
const unsigned int  point_no 
) const
inherited

Second derivatives of the function_noth shape function at the point_noth quadrature point with respect to real cell coordinates. If you want to get the derivatives in one of the coordinate directions, use the appropriate function of the Tensor class to extract one component. Since only a reference to the hessian values is returned, there should be no major performance drawback.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_hessian_component() function.

The same holds for the arguments of this function as for the shape_value() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ shape_hessian_component()

template<int dim, int spacedim>
Tensor<2, spacedim> FEValuesBase< dim, spacedim >::shape_hessian_component ( const unsigned int  function_no,
const unsigned int  point_no,
const unsigned int  component 
) const
inherited

Return one vector component of the hessian of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_hessian() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_hessian() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

The same holds for the arguments of this function as for the shape_value_component() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ shape_3rd_derivative()

template<int dim, int spacedim>
const Tensor<3, spacedim>& FEValuesBase< dim, spacedim >::shape_3rd_derivative ( const unsigned int  function_no,
const unsigned int  point_no 
) const
inherited

Third derivatives of the function_noth shape function at the point_noth quadrature point with respect to real cell coordinates. If you want to get the 3rd derivatives in one of the coordinate directions, use the appropriate function of the Tensor class to extract one component. Since only a reference to the 3rd derivative values is returned, there should be no major performance drawback.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_3rdderivative_component() function.

The same holds for the arguments of this function as for the shape_value() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_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.

◆ shape_3rd_derivative_component()

template<int dim, int spacedim>
Tensor<3, spacedim> FEValuesBase< dim, spacedim >::shape_3rd_derivative_component ( const unsigned int  function_no,
const unsigned int  point_no,
const unsigned int  component 
) const
inherited

Return one vector component of the third derivative of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_3rdderivative() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_3rdderivative() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

The same holds for the arguments of this function as for the shape_value_component() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_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.

◆ get_function_values() [1/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector &  fe_function,
std::vector< typename InputVector::value_type > &  values 
) const
inherited

Return the values of a finite element function restricted to the current cell, face or subface selected the last time the reinit function of the derived class was called, at the quadrature points.

If the present cell is not active then values are interpolated to the current cell and point values are computed from that.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. To get values of multi- component elements, there is another get_function_values() below, returning a vector of vectors of results.

Parameters
[in]fe_functionA vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell.
[out]valuesThe values of the function specified by fe_function at the quadrature points of the current cell. The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the values of shape function times the type used to store the values of the unknowns \(U_j\) of your finite element vector \(U\) (represented by the fe_function argument). This happens to be equal to the type of the elements of the solution vector.
Postcondition
values[q] will contain the value of the field described by fe_function at the \(q\)th quadrature point.
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3568 of file fe_values.cc.

◆ get_function_values() [2/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector &  fe_function,
std::vector< Vector< typename InputVector::value_type >> &  values 
) const
inherited

This function does the same as the other get_function_values(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
values[q] is a vector of values of the field described by fe_function at the \(q\)th quadrature point. The size of the vector accessed by values[q] equals the number of components of the finite element, i.e. values[q](c) returns the value of the \(c\)th vector component at the \(q\)th quadrature point.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3617 of file fe_values.cc.

◆ get_function_values() [3/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< typename InputVector::value_type > &  values 
) const
inherited

Generate function values from an arbitrary vector.

This function offers the possibility to extract function values in quadrature points from vectors not corresponding to a whole discretization.

The vector indices corresponds to the degrees of freedom on a single cell. Its length may even be a multiple of the number of dofs per cell. Then, the vectors in value should allow for the same multiple of the components of the finite element.

You may want to use this function, if you want to access just a single block from a BlockVector, if you have a multi-level vector or if you already have a local representation of your finite element data.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3593 of file fe_values.cc.

◆ get_function_values() [4/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< Vector< typename InputVector::value_type >> &  values 
) const
inherited

Generate vector function values from an arbitrary vector.

This function offers the possibility to extract function values in quadrature points from vectors not corresponding to a whole discretization.

The vector indices corresponds to the degrees of freedom on a single cell. Its length may even be a multiple of the number of dofs per cell. Then, the vectors in value should allow for the same multiple of the components of the finite element.

You may want to use this function, if you want to access just a single block from a BlockVector, if you have a multi-level vector or if you already have a local representation of your finite element data.

Since this function allows for fairly general combinations of argument sizes, be aware that the checks on the arguments may not detect errors.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3645 of file fe_values.cc.

◆ get_function_values() [5/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
ArrayView< std::vector< typename InputVector::value_type >>  values,
const bool  quadrature_points_fastest 
) const
inherited

Generate vector function values from an arbitrary vector.

This function offers the possibility to extract function values in quadrature points from vectors not corresponding to a whole discretization.

The vector indices corresponds to the degrees of freedom on a single cell. Its length may even be a multiple of the number of dofs per cell. Then, the vectors in value should allow for the same multiple of the components of the finite element.

Depending on the value of the last argument, the outer vector of values has either the length of the quadrature rule (quadrature_points_fastest == false) or the length of components to be filled quadrature_points_fastest == true. If p is the current quadrature point number and i is the vector component of the solution desired, the access to values is values[p][i] if quadrature_points_fastest == false, and values[i][p] otherwise.

You may want to use this function, if you want to access just a single block from a BlockVector, if you have a multi-level vector or if you already have a local representation of your finite element data.

Since this function allows for fairly general combinations of argument sizes, be aware that the checks on the arguments may not detect errors.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3676 of file fe_values.cc.

◆ get_function_gradients() [1/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector &  fe_function,
std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> &  gradients 
) const
inherited

Compute the gradients of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's gradient instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
[in]fe_functionA vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell.
[out]gradientsThe gradients of the function specified by fe_function at the quadrature points of the current cell. The gradients are computed in real space (as opposed to on the unit cell). The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the gradients of shape function times the type used to store the values of the unknowns \(U_j\) of your finite element vector \(U\) (represented by the fe_function argument).
Postcondition
gradients[q] will contain the gradient of the field described by fe_function at the \(q\)th quadrature point. gradients[q][d] represents the derivative in coordinate direction \(d\) at quadrature point \(q\).
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3709 of file fe_values.cc.

◆ get_function_gradients() [2/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector &  fe_function,
std::vector< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>> &  gradients 
) const
inherited

This function does the same as the other get_function_gradients(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
gradients[q] is a vector of gradients of the field described by fe_function at the \(q\)th quadrature point. The size of the vector accessed by gradients[q] equals the number of components of the finite element, i.e. gradients[q][c] returns the gradient of the \(c\)th vector component at the \(q\)th quadrature point. Consequently, gradients[q][c][d] is the derivative in coordinate direction \(d\) of the \(c\)th vector component of the vector field at quadrature point \(q\) of the current cell.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3760 of file fe_values.cc.

◆ get_function_gradients() [3/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> &  gradients 
) const
inherited

Function gradient access with more flexibility. See get_function_values() with corresponding arguments.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3735 of file fe_values.cc.

◆ get_function_gradients() [4/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
ArrayView< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>>  gradients,
bool  quadrature_points_fastest = false 
) const
inherited

Function gradient access with more flexibility. See get_function_values() with corresponding arguments.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3789 of file fe_values.cc.

◆ get_function_hessians() [1/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector &  fe_function,
std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> &  hessians 
) const
inherited

Compute the tensor of second derivatives of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's second derivatives instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
[in]fe_functionA vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell.
[out]hessiansThe Hessians of the function specified by fe_function at the quadrature points of the current cell. The Hessians are computed in real space (as opposed to on the unit cell). The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the Hessians of shape function times the type used to store the values of the unknowns \(U_j\) of your finite element vector \(U\) (represented by the fe_function argument).
Postcondition
hessians[q] will contain the Hessian of the field described by fe_function at the \(q\)th quadrature point. hessians[q][i][j] represents the \((i,j)\)th component of the matrix of second derivatives at quadrature point \(q\).
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3822 of file fe_values.cc.

◆ get_function_hessians() [2/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector &  fe_function,
std::vector< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>> &  hessians,
bool  quadrature_points_fastest = false 
) const
inherited

This function does the same as the other get_function_hessians(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
hessians[q] is a vector of Hessians of the field described by fe_function at the \(q\)th quadrature point. The size of the vector accessed by hessians[q] equals the number of components of the finite element, i.e. hessians[q][c] returns the Hessian of the \(c\)th vector component at the \(q\)th quadrature point. Consequently, hessians[q][c][i][j] is the \((i,j)\)th component of the matrix of second derivatives of the \(c\)th vector component of the vector field at quadrature point \(q\) of the current cell.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3873 of file fe_values.cc.

◆ get_function_hessians() [3/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> &  hessians 
) const
inherited

Access to the second derivatives of a function with more flexibility. See get_function_values() with corresponding arguments.

Definition at line 3848 of file fe_values.cc.

◆ get_function_hessians() [4/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
ArrayView< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>>  hessians,
bool  quadrature_points_fastest = false 
) const
inherited

Access to the second derivatives of a function with more flexibility. See get_function_values() with corresponding arguments.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3904 of file fe_values.cc.

◆ get_function_laplacians() [1/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector &  fe_function,
std::vector< typename InputVector::value_type > &  laplacians 
) const
inherited

Compute the (scalar) Laplacian (i.e. the trace of the tensor of second derivatives) of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's second derivatives instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
[in]fe_functionA vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell.
[out]laplaciansThe Laplacians of the function specified by fe_function at the quadrature points of the current cell. The Laplacians are computed in real space (as opposed to on the unit cell). The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the Laplacians of shape function times the type used to store the values of the unknowns \(U_j\) of your finite element vector \(U\) (represented by the fe_function argument). This happens to be equal to the type of the elements of the input vector.
Postcondition
laplacians[q] will contain the Laplacian of the field described by fe_function at the \(q\)th quadrature point.
For each component of the output vector, there holds laplacians[q]=trace(hessians[q]), where hessians would be the output of the get_function_hessians() function.
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3935 of file fe_values.cc.

◆ get_function_laplacians() [2/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector &  fe_function,
std::vector< Vector< typename InputVector::value_type >> &  laplacians 
) const
inherited

This function does the same as the other get_function_laplacians(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
laplacians[q] is a vector of Laplacians of the field described by fe_function at the \(q\)th quadrature point. The size of the vector accessed by laplacians[q] equals the number of components of the finite element, i.e. laplacians[q][c] returns the Laplacian of the \(c\)th vector component at the \(q\)th quadrature point.
For each component of the output vector, there holds laplacians[q][c]=trace(hessians[q][c]), where hessians would be the output of the get_function_hessians() function.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3984 of file fe_values.cc.

◆ get_function_laplacians() [3/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< typename InputVector::value_type > &  laplacians 
) const
inherited

Access to the second derivatives of a function with more flexibility. See get_function_values() with corresponding arguments.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 3960 of file fe_values.cc.

◆ get_function_laplacians() [4/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< Vector< typename InputVector::value_type >> &  laplacians 
) const
inherited

Access to the second derivatives of a function with more flexibility. See get_function_values() with corresponding arguments.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 4011 of file fe_values.cc.

◆ get_function_laplacians() [5/5]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< std::vector< typename InputVector::value_type >> &  laplacians,
bool  quadrature_points_fastest = false 
) const
inherited

Access to the second derivatives of a function with more flexibility. See get_function_values() with corresponding arguments.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 4042 of file fe_values.cc.

◆ get_function_third_derivatives() [1/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector &  fe_function,
std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> &  third_derivatives 
) const
inherited

Compute the tensor of third derivatives of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's third derivatives instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
[in]fe_functionA vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell.
[out]third_derivativesThe third derivatives of the function specified by fe_function at the quadrature points of the current cell. The third derivatives are computed in real space (as opposed to on the unit cell). The object is assumed to already have the correct size. The data type stored by this output vector must be what you get when you multiply the third derivatives of shape function times the type used to store the values of the unknowns \(U_j\) of your finite element vector \(U\) (represented by the fe_function argument).
Postcondition
third_derivatives[q] will contain the third derivatives of the field described by fe_function at the \(q\)th quadrature point. third_derivatives[q][i][j][k] represents the \((i,j,k)\)th component of the 3rd order tensor of third derivatives at quadrature point \(q\).
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_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.

Definition at line 4072 of file fe_values.cc.

◆ get_function_third_derivatives() [2/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector &  fe_function,
std::vector< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>> &  third_derivatives,
bool  quadrature_points_fastest = false 
) const
inherited

This function does the same as the other get_function_third_derivatives(), but applied to multi-component (vector- valued) elements. The meaning of the arguments is as explained there.

Postcondition
third_derivatives[q] is a vector of third derivatives of the field described by fe_function at the \(q\)th quadrature point. The size of the vector accessed by third_derivatives[q] equals the number of components of the finite element, i.e. third_derivatives[q][c] returns the third derivative of the \(c\)th vector component at the \(q\)th quadrature point. Consequently, third_derivatives[q][c][i][j][k] is the \((i,j,k)\)th component of the tensor of third derivatives of the \(c\)th vector component of the vector field at quadrature point \(q\) of the current cell.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_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.

Definition at line 4125 of file fe_values.cc.

◆ get_function_third_derivatives() [3/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> &  third_derivatives 
) const
inherited

Access to the third derivatives of a function with more flexibility. See get_function_values() with corresponding arguments.

Definition at line 4099 of file fe_values.cc.

◆ get_function_third_derivatives() [4/4]

template<int dim, int spacedim>
template<class InputVector >
void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector &  fe_function,
const ArrayView< const types::global_dof_index > &  indices,
ArrayView< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>>  third_derivatives,
bool  quadrature_points_fastest = false 
) const
inherited

Access to the third derivatives of a function with more flexibility. See get_function_values() with corresponding arguments.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_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.

Definition at line 4156 of file fe_values.cc.

◆ dof_indices()

template<int dim, int spacedim>
std_cxx20::ranges::iota_view<unsigned int, unsigned int> FEValuesBase< dim, spacedim >::dof_indices ( ) const
inherited

Return an object that can be thought of as an array containing all indices from zero (inclusive) to dofs_per_cell (exclusive). This allows one to write code using range-based for loops of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q : fe_values.quadrature_point_indices())
for (const auto i : fe_values.dof_indices())
for (const auto j : fe_values.dof_indices())
cell_matrix(i,j) += ...; // Do something for DoF indices (i,j)
// at quadrature point q
}

Here, we are looping over all degrees of freedom on all cells, with i and j taking on all valid indices for cell degrees of freedom, as defined by the finite element passed to fe_values.

◆ dof_indices_starting_at()

template<int dim, int spacedim>
std_cxx20::ranges::iota_view<unsigned int, unsigned int> FEValuesBase< dim, spacedim >::dof_indices_starting_at ( const unsigned int  start_dof_index) const
inherited

Return an object that can be thought of as an array containing all indices from start_dof_index (inclusive) to dofs_per_cell (exclusive). This allows one to write code using range-based for loops of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q : fe_values.quadrature_point_indices())
for (const auto i : fe_values.dof_indices())
for (const auto j : fe_values.dof_indices_starting_at(i))
cell_matrix(i,j) += ...; // Do something for DoF indices (i,j)
// at quadrature point q
}

Here, we are looping over all local degrees of freedom on all cells, with i taking on all valid indices for cell degrees of freedom, as defined by the finite element passed to fe_values, and j taking on a specified subset of i's range, starting at i itself and ending at the number of cell degrees of freedom. In this way, we can construct the upper half and the diagonal of a stiffness matrix contribution (assuming it is symmetric, and that only one half of it needs to be computed), for example.

Note
If the start_dof_index is equal to the number of DoFs in the cell, then the returned index range is empty.

◆ dof_indices_ending_at()

template<int dim, int spacedim>
std_cxx20::ranges::iota_view<unsigned int, unsigned int> FEValuesBase< dim, spacedim >::dof_indices_ending_at ( const unsigned int  end_dof_index) const
inherited

Return an object that can be thought of as an array containing all indices from zero (inclusive) to end_dof_index (inclusive). This allows one to write code using range-based for loops of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q : fe_values.quadrature_point_indices())
for (const auto i : fe_values.dof_indices())
for (const auto j : fe_values.dof_indices_ending_at(i))
cell_matrix(i,j) += ...; // Do something for DoF indices (i,j)
// at quadrature point q
}

Here, we are looping over all local degrees of freedom on all cells, with i taking on all valid indices for cell degrees of freedom, as defined by the finite element passed to fe_values, and j taking on a specified subset of i's range, starting at zero and ending at i itself. In this way, we can construct the lower half and the diagonal of a stiffness matrix contribution (assuming it is symmetric, and that only one half of it needs to be computed), for example.

Note
If the end_dof_index is equal to zero, then the returned index range is empty.

◆ quadrature_point_indices()

template<int dim, int spacedim>
std_cxx20::ranges::iota_view<unsigned int, unsigned int> FEValuesBase< dim, spacedim >::quadrature_point_indices ( ) const
inherited

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 of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q_point : fe_values.quadrature_point_indices())
... do something at the quadrature point ...
}

Here, we are looping over all quadrature points on all cells, with q_point taking on all valid indices for quadrature points, as defined by the quadrature rule passed to fe_values.

See also
deal.II and the C++11 standard

◆ quadrature_point()

template<int dim, int spacedim>
const Point<spacedim>& FEValuesBase< dim, spacedim >::quadrature_point ( const unsigned int  q) const
inherited

Position of the qth quadrature point in real space.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ get_quadrature_points()

template<int dim, int spacedim>
const std::vector<Point<spacedim> >& FEValuesBase< dim, spacedim >::get_quadrature_points ( ) const
inherited

Return a reference to the vector of quadrature points in real space.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ JxW()

template<int dim, int spacedim>
double FEValuesBase< dim, spacedim >::JxW ( const unsigned int  quadrature_point) const
inherited

Mapped quadrature weight. If this object refers to a volume evaluation (i.e. the derived class is of type FEValues), then this is the Jacobi determinant times the weight of the *ith unit quadrature point.

For surface evaluations (i.e. classes FEFaceValues or FESubfaceValues), it is the mapped surface element times the weight of the quadrature point.

You can think of the quantity returned by this function as the volume or surface element \(dx, ds\) in the integral that we implement here by quadrature.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ get_JxW_values()

template<int dim, int spacedim>
const std::vector<double>& FEValuesBase< dim, spacedim >::get_JxW_values ( ) const
inherited

Return a reference to the array holding the values returned by JxW().

◆ jacobian()

template<int dim, int spacedim>
const DerivativeForm<1, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian ( const unsigned int  quadrature_point) const
inherited

Return the Jacobian of the transformation at the specified quadrature point, i.e. \(J_{ij}=dx_i/d\hat x_j\)

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobians 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.

◆ get_jacobians()

template<int dim, int spacedim>
const std::vector<DerivativeForm<1, dim, spacedim> >& FEValuesBase< dim, spacedim >::get_jacobians ( ) const
inherited

Return a reference to the array holding the values returned by jacobian().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobians 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.

◆ jacobian_grad()

template<int dim, int spacedim>
const DerivativeForm<2, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian_grad ( const unsigned int  quadrature_point) const
inherited

Return the second derivative of the transformation from unit to real cell, i.e. the first derivative of the Jacobian, at the specified quadrature point, i.e. \(G_{ijk}=dJ_{jk}/d\hat x_i\).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_grads 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.

◆ get_jacobian_grads()

template<int dim, int spacedim>
const std::vector<DerivativeForm<2, dim, spacedim> >& FEValuesBase< dim, spacedim >::get_jacobian_grads ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_grads().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_grads 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.

◆ jacobian_pushed_forward_grad()

template<int dim, int spacedim>
const Tensor<3, spacedim>& FEValuesBase< dim, spacedim >::jacobian_pushed_forward_grad ( const unsigned int  quadrature_point) const
inherited

Return the second derivative of the transformation from unit to real cell, i.e. the first derivative of the Jacobian, at the specified quadrature point, pushed forward to the real cell coordinates, i.e. \(G_{ijk}=dJ_{iJ}/d\hat x_K (J_{jJ})^{-1} (J_{kK})^{-1}\).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_grads 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.

◆ get_jacobian_pushed_forward_grads()

template<int dim, int spacedim>
const std::vector<Tensor<3, spacedim> >& FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_grads ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_pushed_forward_grads().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_grads 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.

◆ jacobian_2nd_derivative()

template<int dim, int spacedim>
const DerivativeForm<3, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian_2nd_derivative ( const unsigned int  quadrature_point) const
inherited

Return the third derivative of the transformation from unit to real cell, i.e. the second derivative of the Jacobian, at the specified quadrature point, i.e. \(G_{ijkl}=\frac{d^2J_{ij}}{d\hat x_k d\hat x_l}\).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_2nd_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.

◆ get_jacobian_2nd_derivatives()

template<int dim, int spacedim>
const std::vector<DerivativeForm<3, dim, spacedim> >& FEValuesBase< dim, spacedim >::get_jacobian_2nd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_2nd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_2nd_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.

◆ jacobian_pushed_forward_2nd_derivative()

template<int dim, int spacedim>
const Tensor<4, spacedim>& FEValuesBase< dim, spacedim >::jacobian_pushed_forward_2nd_derivative ( const unsigned int  quadrature_point) const
inherited

Return the third derivative of the transformation from unit to real cell, i.e. the second derivative of the Jacobian, at the specified quadrature point, pushed forward to the real cell coordinates, i.e. \(G_{ijkl}=\frac{d^2J_{iJ}}{d\hat x_K d\hat x_L} (J_{jJ})^{-1} (J_{kK})^{-1}(J_{lL})^{-1}\).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_2nd_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.

◆ get_jacobian_pushed_forward_2nd_derivatives()

template<int dim, int spacedim>
const std::vector<Tensor<4, spacedim> >& FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_2nd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_pushed_forward_2nd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_2nd_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.

◆ jacobian_3rd_derivative()

template<int dim, int spacedim>
const DerivativeForm<4, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian_3rd_derivative ( const unsigned int  quadrature_point) const
inherited

Return the fourth derivative of the transformation from unit to real cell, i.e. the third derivative of the Jacobian, at the specified quadrature point, i.e. \(G_{ijklm}=\frac{d^2J_{ij}}{d\hat x_k d\hat x_l d\hat x_m}\).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_3rd_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.

◆ get_jacobian_3rd_derivatives()

template<int dim, int spacedim>
const std::vector<DerivativeForm<4, dim, spacedim> >& FEValuesBase< dim, spacedim >::get_jacobian_3rd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_3rd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_3rd_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.

◆ jacobian_pushed_forward_3rd_derivative()

template<int dim, int spacedim>
const Tensor<5, spacedim>& FEValuesBase< dim, spacedim >::jacobian_pushed_forward_3rd_derivative ( const unsigned int  quadrature_point) const
inherited

Return the fourth derivative of the transformation from unit to real cell, i.e. the third derivative of the Jacobian, at the specified quadrature point, pushed forward to the real cell coordinates, i.e. \(G_{ijklm}=\frac{d^3J_{iJ}}{d\hat x_K d\hat x_L d\hat x_M} (J_{jJ})^{-1} (J_{kK})^{-1} (J_{lL})^{-1} (J_{mM})^{-1}\).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_3rd_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.

◆ get_jacobian_pushed_forward_3rd_derivatives()

template<int dim, int spacedim>
const std::vector<Tensor<5, spacedim> >& FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_3rd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_pushed_forward_3rd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_2nd_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.

◆ inverse_jacobian()

template<int dim, int spacedim>
const DerivativeForm<1, spacedim, dim>& FEValuesBase< dim, spacedim >::inverse_jacobian ( const unsigned int  quadrature_point) const
inherited

Return the inverse Jacobian of the transformation at the specified quadrature point, i.e. \(J_{ij}=d\hat x_i/dx_j\)

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_inverse_jacobians 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.

◆ get_inverse_jacobians()

template<int dim, int spacedim>
const std::vector<DerivativeForm<1, spacedim, dim> >& FEValuesBase< dim, spacedim >::get_inverse_jacobians ( ) const
inherited

Return a reference to the array holding the values returned by inverse_jacobian().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_inverse_jacobians 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.

◆ normal_vector()

template<int dim, int spacedim>
const Tensor<1, spacedim>& FEValuesBase< dim, spacedim >::normal_vector ( const unsigned int  i) const
inherited

Return the normal vector at a quadrature point. If you call this function for a face (i.e., when using a FEFaceValues or FESubfaceValues object), then this function returns the outward normal vector to the cell at the ith quadrature point of the face.

In contrast, if you call this function for a cell of codimension one (i.e., when using a FEValues<dim,spacedim> object with spacedim>dim), then this function returns the normal vector to the cell – in other words, an approximation to the normal vector to the manifold in which the triangulation is embedded. There are of course two normal directions to a manifold in that case, and this function returns the "up" direction as induced by the numbering of the vertices.

The length of the vector is normalized to one.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

◆ get_normal_vectors()

template<int dim, int spacedim>
const std::vector< Tensor< 1, spacedim > > & FEValuesBase< dim, spacedim >::get_normal_vectors ( ) const
inherited

Return the normal vectors at all quadrature points represented by this object. See the normal_vector() function for what the normal vectors represent.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the 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.

Definition at line 4195 of file fe_values.cc.

◆ operator[]() [1/4]

template<int dim, int spacedim>
const FEValuesViews::Scalar<dim, spacedim>& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::Scalar scalar) const
inherited

Create a view of the current FEValues 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 and in particular in the Handling vector valued problems module.

◆ operator[]() [2/4]

template<int dim, int spacedim>
const FEValuesViews::Vector<dim, spacedim>& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::Vector vector) const
inherited

Create a view of the current FEValues 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 and in particular in the Handling vector valued problems module.

◆ operator[]() [3/4]

template<int dim, int spacedim>
const FEValuesViews::SymmetricTensor<2, dim, spacedim>& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::SymmetricTensor< 2 > &  tensor) const
inherited

Create a view of the current FEValues object that represents a set of (dim*dim + dim)/2 scalar components (i.e. a symmetric 2nd order tensor) of the vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews and in particular in the Handling vector valued problems module.

◆ operator[]() [4/4]

template<int dim, int spacedim>
const FEValuesViews::Tensor<2, dim, spacedim>& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::Tensor< 2 > &  tensor) const
inherited

Create a view of the current FEValues object that represents a set of (dim*dim) scalar components (i.e. a 2nd order tensor) of the vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews and in particular in the Handling vector valued problems module.

◆ get_mapping()

template<int dim, int spacedim>
const Mapping<dim, spacedim>& FEValuesBase< dim, spacedim >::get_mapping ( ) const
inherited

Constant reference to the selected mapping object.

◆ get_fe()

template<int dim, int spacedim>
const FiniteElement<dim, spacedim>& FEValuesBase< dim, spacedim >::get_fe ( ) const
inherited

Constant reference to the selected finite element object.

◆ get_update_flags()

template<int dim, int spacedim>
UpdateFlags FEValuesBase< dim, spacedim >::get_update_flags ( ) const
inherited

Return the update flags set for this object.

◆ get_cell()

template<int dim, int spacedim>
const Triangulation< dim, spacedim >::cell_iterator FEValuesBase< dim, spacedim >::get_cell ( ) const
inherited

Return a triangulation iterator to the current cell.

Definition at line 4186 of file fe_values.cc.

◆ get_cell_similarity()

template<int dim, int spacedim>
CellSimilarity::Similarity FEValuesBase< dim, spacedim >::get_cell_similarity ( ) const
inherited

Return the relation of the current cell to the previous cell. This allows re-use of some cell data (like local matrices for equations with constant coefficients) if the result is CellSimilarity::translation.

Definition at line 4363 of file fe_values.cc.

◆ invalidate_present_cell()

template<int dim, int spacedim>
void FEValuesBase< dim, spacedim >::invalidate_present_cell ( )
protectedinherited

A function that is connected to the triangulation in order to reset the stored 'present_cell' iterator to an invalid one whenever the triangulation is changed and the iterator consequently becomes invalid.

Definition at line 4247 of file fe_values.cc.

◆ maybe_invalidate_previous_present_cell()

template<int dim, int spacedim>
void FEValuesBase< dim, spacedim >::maybe_invalidate_previous_present_cell ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell)
protectedinherited

This function is called by the various reinit() functions in derived classes. Given the cell indicated by the argument, test whether we have to throw away the previously stored present_cell argument because it would require us to compare cells from different triangulations. In checking all this, also make sure that we have tria_listener connected to the triangulation to which we will set present_cell right after calling this function.

Definition at line 4265 of file fe_values.cc.

◆ compute_update_flags()

template<int dim, int spacedim>
UpdateFlags FEValuesBase< dim, spacedim >::compute_update_flags ( const UpdateFlags  update_flags) const
protectedinherited

Initialize some update flags. Called from the initialize functions of derived classes, which are in turn called from their constructors.

Basically, this function finds out using the finite element and mapping object already stored which flags need to be set to compute everything the user wants, as expressed through the flags passed as argument.

Definition at line 4228 of file fe_values.cc.

◆ check_cell_similarity()

template<int dim, int spacedim>
void FEValuesBase< dim, spacedim >::check_cell_similarity ( const typename Triangulation< dim, spacedim >::cell_iterator &  cell)
inlineprotectedinherited

A function that checks whether the new cell is similar to the one previously used. Then, a significant amount of the data can be reused, e.g. the derivatives of the basis functions in real space, shape_grad.

Definition at line 4308 of file fe_values.cc.

◆ subscribe()

void Subscriptor::subscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

◆ unsubscribe()

void Subscriptor::unsubscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const
inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >
void Subscriptor::list_subscribers ( StreamType &  stream) const
inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

◆ serialize()

template<class Archive >
void Subscriptor::serialize ( Archive &  ar,
const unsigned int  version 
)
inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 309 of file subscriptor.h.

Member Data Documentation

◆ dimension

template<int dim, int spacedim = dim>
const unsigned int FESubfaceValues< dim, spacedim >::dimension = dim
static

Dimension in which this object operates.

Definition at line 3967 of file fe_values.h.

◆ space_dimension

template<int dim, int spacedim = dim>
const unsigned int FESubfaceValues< dim, spacedim >::space_dimension = spacedim
static

Dimension of the space in which this object operates.

Definition at line 3972 of file fe_values.h.

◆ integral_dimension

template<int dim, int spacedim = dim>
const unsigned int FESubfaceValues< dim, spacedim >::integral_dimension = dim - 1
static

Dimension of the object over which we integrate. For the present class, this is equal to dim-1.

Definition at line 3978 of file fe_values.h.

◆ present_face_index

template<int dim, int spacedim = dim>
unsigned int FEFaceValuesBase< dim, spacedim >::present_face_index
protectedinherited

Index of the face selected the last time the reinit() function was called.

Definition at line 3792 of file fe_values.h.

◆ quadrature

template<int dim, int spacedim = dim>
const Quadrature<dim - 1> FEFaceValuesBase< dim, spacedim >::quadrature
protectedinherited

Store a copy of the quadrature formula here.

Definition at line 3797 of file fe_values.h.

◆ n_quadrature_points

template<int dim, int spacedim>
const unsigned int FEValuesBase< dim, spacedim >::n_quadrature_points
inherited

Number of quadrature points.

Definition at line 2090 of file fe_values.h.

◆ dofs_per_cell

template<int dim, int spacedim>
const unsigned int FEValuesBase< dim, spacedim >::dofs_per_cell
inherited

Number of shape functions per cell. If we use this base class to evaluate a finite element on faces of cells, this is still the number of degrees of freedom per cell, not per face.

Definition at line 2097 of file fe_values.h.

◆ present_cell

template<int dim, int spacedim>
std::unique_ptr<const CellIteratorBase> FEValuesBase< dim, spacedim >::present_cell
protectedinherited

Store the cell selected last time the reinit() function was called. This is necessary for the get_function_* functions as well as the functions of same name in the extractor classes.

Definition at line 3445 of file fe_values.h.

◆ tria_listener_refinement

template<int dim, int spacedim>
boost::signals2::connection FEValuesBase< dim, spacedim >::tria_listener_refinement
protectedinherited

A signal connection we use to ensure we get informed whenever the triangulation changes by refinement. We need to know about that because it invalidates all cell iterators and, as part of that, the 'present_cell' iterator we keep around between subsequent calls to reinit() in order to compute the cell similarity.

Definition at line 3461 of file fe_values.h.

◆ tria_listener_mesh_transform

template<int dim, int spacedim>
boost::signals2::connection FEValuesBase< dim, spacedim >::tria_listener_mesh_transform
protectedinherited

A signal connection we use to ensure we get informed whenever the triangulation changes by mesh transformations. We need to know about that because it invalidates all cell iterators and, as part of that, the 'present_cell' iterator we keep around between subsequent calls to reinit() in order to compute the cell similarity.

Definition at line 3470 of file fe_values.h.

◆ mapping

template<int dim, int spacedim>
const SmartPointer<const Mapping<dim, spacedim>, FEValuesBase<dim, spacedim> > FEValuesBase< dim, spacedim >::mapping
protectedinherited

A pointer to the mapping object associated with this FEValues object.

Definition at line 3497 of file fe_values.h.

◆ mapping_data

template<int dim, int spacedim>
std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> FEValuesBase< dim, spacedim >::mapping_data
protectedinherited

A pointer to the internal data object of mapping, obtained from Mapping::get_data(), Mapping::get_face_data(), or Mapping::get_subface_data().

Definition at line 3505 of file fe_values.h.

◆ mapping_output

template<int dim, int spacedim>
::internal::FEValuesImplementation::MappingRelatedData<dim, spacedim> FEValuesBase< dim, spacedim >::mapping_output
protectedinherited

An object into which the Mapping::fill_fe_values() and similar functions place their output.

Definition at line 3512 of file fe_values.h.

◆ fe

template<int dim, int spacedim>
const SmartPointer<const FiniteElement<dim, spacedim>, FEValuesBase<dim, spacedim> > FEValuesBase< dim, spacedim >::fe
protectedinherited

A pointer to the finite element object associated with this FEValues object.

Definition at line 3521 of file fe_values.h.

◆ fe_data

template<int dim, int spacedim>
std::unique_ptr<typename FiniteElement<dim, spacedim>::InternalDataBase> FEValuesBase< dim, spacedim >::fe_data
protectedinherited

A pointer to the internal data object of finite element, obtained from FiniteElement::get_data(), Mapping::get_face_data(), or FiniteElement::get_subface_data().

Definition at line 3529 of file fe_values.h.

◆ finite_element_output

template<int dim, int spacedim>
::internal::FEValuesImplementation::FiniteElementRelatedData<dim, spacedim> FEValuesBase< dim, spacedim >::finite_element_output
protectedinherited

An object into which the FiniteElement::fill_fe_values() and similar functions place their output.

Definition at line 3537 of file fe_values.h.

◆ update_flags

template<int dim, int spacedim>
UpdateFlags FEValuesBase< dim, spacedim >::update_flags
protectedinherited

Original update flags handed to the constructor of FEValues.

Definition at line 3543 of file fe_values.h.

◆ cell_similarity

template<int dim, int spacedim>
CellSimilarity::Similarity FEValuesBase< dim, spacedim >::cell_similarity
protectedinherited

An enum variable that can store different states of the current cell in comparison to the previously visited cell. If wanted, additional states can be checked here and used in one of the methods used during reinit.

Definition at line 3561 of file fe_values.h.


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