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Reference documentation for deal.II version 9.6.0
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Reference documentation for deal.II version 9.6.0
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#include <deal.II/fe/fe_values_base.h>
Classes | |
| class | CellIteratorWrapper |
Public Member Functions | |
| FEValuesBase (const unsigned int n_q_points, const unsigned int dofs_per_cell, const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const FiniteElement< dim, spacedim > &fe) | |
| FEValuesBase & | operator= (const FEValuesBase &)=delete |
| FEValuesBase (const FEValuesBase &)=delete | |
| virtual | ~FEValuesBase () override |
| void | always_allow_check_for_cell_similarity (const bool allow) |
| 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 double & | shape_value (const unsigned int i, const unsigned int q_point) const |
| double | shape_value_component (const unsigned int i, const unsigned int q_point, const unsigned int component) const |
| const Tensor< 1, spacedim > & | shape_grad (const unsigned int i, const unsigned int q_point) const |
| Tensor< 1, spacedim > | shape_grad_component (const unsigned int i, const unsigned int q_point, const unsigned int component) const |
| const Tensor< 2, spacedim > & | shape_hessian (const unsigned int i, const unsigned int q_point) const |
| Tensor< 2, spacedim > | shape_hessian_component (const unsigned int i, const unsigned int q_point, const unsigned int component) const |
| const Tensor< 3, spacedim > & | shape_3rd_derivative (const unsigned int i, const unsigned int q_point) const |
| Tensor< 3, spacedim > | shape_3rd_derivative_component (const unsigned int i, const unsigned int q_point, const unsigned int component) const |
Access to values of global finite element fields | |
| template<typename Number > | |
| void | get_function_values (const ReadVector< Number > &fe_function, std::vector< Number > &values) const |
| template<typename Number > | |
| void | get_function_values (const ReadVector< Number > &fe_function, std::vector< Vector< Number > > &values) const |
| template<typename Number > | |
| void | get_function_values (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Number > &values) const |
| template<typename Number > | |
| void | get_function_values (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Vector< Number > > &values) const |
| template<typename Number > | |
| void | get_function_values (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Number > > values, const bool quadrature_points_fastest) const |
Access to derivatives of global finite element fields | |
| template<typename Number > | |
| void | get_function_gradients (const ReadVector< Number > &fe_function, std::vector< Tensor< 1, spacedim, Number > > &gradients) const |
| template<typename Number > | |
| void | get_function_gradients (const ReadVector< Number > &fe_function, std::vector< std::vector< Tensor< 1, spacedim, Number > > > &gradients) const |
| template<typename Number > | |
| void | get_function_gradients (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 1, spacedim, Number > > &gradients) const |
| template<typename Number > | |
| void | get_function_gradients (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 1, spacedim, Number > > > gradients, const bool quadrature_points_fastest=false) const |
Access to second derivatives | |
Hessian matrices and Laplacians of global finite element fields | |
| template<typename Number > | |
| void | get_function_hessians (const ReadVector< Number > &fe_function, std::vector< Tensor< 2, spacedim, Number > > &hessians) const |
| template<typename Number > | |
| void | get_function_hessians (const ReadVector< Number > &fe_function, std::vector< std::vector< Tensor< 2, spacedim, Number > > > &hessians, const bool quadrature_points_fastest=false) const |
| template<typename Number > | |
| void | get_function_hessians (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 2, spacedim, Number > > &hessians) const |
| template<typename Number > | |
| void | get_function_hessians (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 2, spacedim, Number > > > hessians, const bool quadrature_points_fastest=false) const |
| template<typename Number > | |
| void | get_function_laplacians (const ReadVector< Number > &fe_function, std::vector< Number > &laplacians) const |
| template<typename Number > | |
| void | get_function_laplacians (const ReadVector< Number > &fe_function, std::vector< Vector< Number > > &laplacians) const |
| template<typename Number > | |
| void | get_function_laplacians (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Number > &laplacians) const |
| template<typename Number > | |
| void | get_function_laplacians (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Vector< Number > > &laplacians) const |
| template<typename Number > | |
| void | get_function_laplacians (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< std::vector< Number > > &laplacians, const bool quadrature_points_fastest=false) const |
Access to third derivatives of global finite element fields | |
| template<typename Number > | |
| void | get_function_third_derivatives (const ReadVector< Number > &fe_function, std::vector< Tensor< 3, spacedim, Number > > &third_derivatives) const |
| template<typename Number > | |
| void | get_function_third_derivatives (const ReadVector< Number > &fe_function, std::vector< std::vector< Tensor< 3, spacedim, Number > > > &third_derivatives, const bool quadrature_points_fastest=false) const |
| template<typename Number > | |
| void | get_function_third_derivatives (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 3, spacedim, Number > > &third_derivatives) const |
| template<typename Number > | |
| void | get_function_third_derivatives (const ReadVector< Number > &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 3, spacedim, Number > > > third_derivatives, const bool quadrature_points_fastest=false) const |
Cell degrees of freedom | |
| std_cxx20::ranges::iota_view< unsigned int, unsigned int > | dof_indices () const |
| std_cxx20::ranges::iota_view< unsigned int, unsigned int > | dof_indices_starting_at (const unsigned int start_dof_index) const |
| std_cxx20::ranges::iota_view< unsigned int, unsigned int > | dof_indices_ending_at (const unsigned int end_dof_index) const |
Geometry of the cell | |
| std_cxx20::ranges::iota_view< unsigned int, unsigned int > | quadrature_point_indices () const |
| const Point< spacedim > & | quadrature_point (const unsigned int q_point) const |
| const std::vector< Point< spacedim > > & | get_quadrature_points () const |
| double | JxW (const unsigned int q_point) const |
| const std::vector< double > & | get_JxW_values () const |
| const DerivativeForm< 1, dim, spacedim > & | jacobian (const unsigned int q_point) const |
| const std::vector< DerivativeForm< 1, dim, spacedim > > & | get_jacobians () const |
| const DerivativeForm< 2, dim, spacedim > & | jacobian_grad (const unsigned int q_point) const |
| const std::vector< DerivativeForm< 2, dim, spacedim > > & | get_jacobian_grads () const |
| const Tensor< 3, spacedim > & | jacobian_pushed_forward_grad (const unsigned int q_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 q_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 q_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 q_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 q_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 q_point) const |
| const std::vector< DerivativeForm< 1, spacedim, dim > > & | get_inverse_jacobians () const |
| const Tensor< 1, spacedim > & | normal_vector (const unsigned int q_point) 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 |
| Triangulation< dim, spacedim >::cell_iterator | get_cell () const |
| CellSimilarity::Similarity | get_cell_similarity () const |
| std::size_t | memory_consumption () 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 ::ExceptionBase & | ExcAccessToUninitializedField (std::string arg1) |
| static ::ExceptionBase & | ExcNotReinited () |
| static ::ExceptionBase & | ExcFEDontMatch () |
| static ::ExceptionBase & | ExcShapeFunctionNotPrimitive (int arg1) |
| static ::ExceptionBase & | ExcFENotPrimitive () |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Public Attributes | |
| const unsigned int | n_quadrature_points |
| const unsigned int | max_n_quadrature_points |
| const unsigned int | dofs_per_cell |
Static Public Attributes | |
| static constexpr unsigned int | dimension = dim |
| static constexpr unsigned int | space_dimension = spacedim |
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 | |
| CellIteratorWrapper | present_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 Types | |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
Private Member Functions | |
| void | check_no_subscribers () const noexcept |
Private Attributes | |
| ::internal::FEValuesViews::Cache< dim, spacedim > | fe_values_views_cache |
| bool | check_for_cell_similarity_allowed |
| std::atomic< unsigned int > | counter |
| std::map< std::string, unsigned int > | counter_map |
| std::vector< std::atomic< bool > * > | validity_pointers |
| const std::type_info * | object_info |
Static Private Attributes | |
| static std::mutex | mutex |
Friends | |
| template<int , int > | |
| class | FEValuesViews::Scalar |
| template<int , int > | |
| class | FEValuesViews::Vector |
| template<int , int , int > | |
| class | FEValuesViews::SymmetricTensor |
| template<int , int , int > | |
| class | FEValuesViews::Tensor |
FEValues, FEFaceValues and FESubfaceValues objects are interfaces to finite element and mapping classes on the one hand side, to cells and quadrature rules on the other side. They allow to evaluate values or derivatives of shape functions at the quadrature points of a quadrature formula when projected by a mapping from the unit cell onto a cell in real space. The reason for this abstraction is possible optimization: Depending on the type of finite element and mapping, some values can be computed once on the unit cell. Others must be computed on each cell, but maybe computation of several values at the same time offers ways for optimization. Since this interplay may be complex and depends on the actual finite element, it cannot be left to the applications programmer.
FEValues, FEFaceValues and FESubfaceValues provide only data handling: computations are left to objects of type Mapping and FiniteElement. These provide functions get_*_data and fill_*_values which are called by the constructor and reinit functions of FEValues*, respectively.
Usually, an object of FEValues* is used in integration loops over all cells of a triangulation (or faces of cells). To take full advantage of the optimization features, it should be constructed before the loop so that information that does not depend on the location and shape of cells can be computed once and for all (this includes, for example, the values of shape functions at quadrature points for the most common elements: we can evaluate them on the unit cell and they will be the same when mapped to the real cell). Then, in the loop over all cells, it must be re-initialized for each grid cell to compute that part of the information that changes depending on the actual cell (for example, the gradient of shape functions equals the gradient on the unit cell – which can be computed once and for all – times the Jacobian matrix of the mapping between unit and real cell, which needs to be recomputed for each cell).
A typical piece of code, adding up local contributions to the Laplace matrix looks like this:
The individual functions used here are described below. Note that by design, the order of quadrature points used inside the FEValues object is the same as defined by the quadrature formula passed to the constructor of the FEValues object above.
The functions of this class fall into different categories:
shape_value(), shape_grad(), etc: return one of the values of this object at a time. These functions are inlined, so this is the suggested access to all finite element values. There should be no loss in performance with an optimizing compiler. If the finite element is vector valued, then these functions return the only non-zero component of the requested shape function. However, some finite elements have shape functions that have more than one non-zero component (we call them non-"primitive"), and in this case this set of functions will throw an exception since they cannot generate a useful result. Rather, use the next set of functions.
shape_value_component(), shape_grad_component(), etc: This is the same set of functions as above, except that for vector valued finite elements they return only one vector component. This is useful for elements of which shape functions have more than one non-zero component, since then the above functions cannot be used, and you have to walk over all (or only the non-zero) components of the shape function using this set of functions.
get_function_values(), get_function_gradients(), etc.: Compute a finite element function or its derivative in quadrature points.
The mechanisms by which this class work are discussed on the page on Update flags and about the How Mapping, FiniteElement, and FEValues work together.
Definition at line 154 of file fe_values_base.h.
|
privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
|
privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
| FEValuesBase< dim, spacedim >::FEValuesBase | ( | const unsigned int | n_q_points, |
| const unsigned int | dofs_per_cell, | ||
| const UpdateFlags | update_flags, | ||
| const Mapping< dim, spacedim > & | mapping, | ||
| const FiniteElement< dim, spacedim > & | fe ) |
Constructor. Set up the array sizes with n_q_points quadrature points, dofs_per_cell trial functions per cell and with the given pattern to update the fields when the reinit function of the derived classes is called. The fields themselves are not set up, this must happen in the constructor of the derived class.
Definition at line 212 of file fe_values_base.cc.
|
delete |
The copy constructor is deleted since objects of this class are not copyable.
|
overridevirtual |
Destructor.
Definition at line 237 of file fe_values_base.cc.
|
delete |
The copy assignment is deleted since objects of this class are not copyable.
| void FEValuesBase< dim, spacedim >::always_allow_check_for_cell_similarity | ( | const bool | allow | ) |
Explicitly allow to check for cell similarity. The detection of simple geometries with CellSimilarity is sensitive to the first cell detected. When using multiple threads, each thread might get a thread local copy of the FEValues object that is initialized to the first cell the thread sees. As this cell might be different between runs and number of threads used, this slight deviation leads to difference in roundoff errors that propagate through the program. Therefore, deal.II disables the CellSimilarity check by default in programs that use more than one thread. This function can be used to disable this behavior: When called, FEValues objects will always do the similarity check, even in cases where the program uses multiple threads. This substantially accelerates the operations of FEValues because many operations can be avoided if a cell is, for example, just a translation of the previous cell. On the other hand, you might get results that differ by an amount proportional to round-off between the case of using or not using cell similarity information, and because the order of cells assigned to individual threads may differ from run to run, when you call this function you may end up with results that differ by round-off between runs of the same program.
Definition at line 247 of file fe_values_base.cc.
| const double & FEValuesBase< dim, spacedim >::shape_value | ( | const unsigned int | i, |
| const unsigned int | q_point ) const |
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.
| i | Number of the shape function \(\varphi_i\) to be evaluated. Note that this number runs from zero to dofs_per_cell, even in the case of an FEFaceValues or FESubfaceValues object. |
| q_point | Number of the quadrature point at which function is to be evaluated |
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. | double FEValuesBase< dim, spacedim >::shape_value_component | ( | const unsigned int | i, |
| const unsigned int | q_point, | ||
| const unsigned int | component ) const |
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.
| i | Number of the shape function \(\varphi_i\) to be evaluated. |
| q_point | Number of the quadrature point at which function is to be evaluated. |
| component | vector component to be evaluated. |
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. | const Tensor< 1, spacedim > & FEValuesBase< dim, spacedim >::shape_grad | ( | const unsigned int | i, |
| const unsigned int | q_point ) const |
Compute the gradient of the ith 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.
| i | Number of the shape function \(\varphi_i\) to be evaluated. |
| q_point | Number of the quadrature point at which function is to be evaluated. |
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. | Tensor< 1, spacedim > FEValuesBase< dim, spacedim >::shape_grad_component | ( | const unsigned int | i, |
| const unsigned int | q_point, | ||
| const unsigned int | component ) const |
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.
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. | const Tensor< 2, spacedim > & FEValuesBase< dim, spacedim >::shape_hessian | ( | const unsigned int | i, |
| const unsigned int | q_point ) const |
Second derivatives of the ith shape function at the q_pointth 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.
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. | Tensor< 2, spacedim > FEValuesBase< dim, spacedim >::shape_hessian_component | ( | const unsigned int | i, |
| const unsigned int | q_point, | ||
| const unsigned int | component ) const |
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.
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. | const Tensor< 3, spacedim > & FEValuesBase< dim, spacedim >::shape_3rd_derivative | ( | const unsigned int | i, |
| const unsigned int | q_point ) const |
Third derivatives of the ith shape function at the q_pointth 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.
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. | Tensor< 3, spacedim > FEValuesBase< dim, spacedim >::shape_3rd_derivative_component | ( | const unsigned int | i, |
| const unsigned int | q_point, | ||
| const unsigned int | component ) const |
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.
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. | void FEValuesBase< dim, spacedim >::get_function_values | ( | const ReadVector< Number > & | fe_function, |
| std::vector< Number > & | values ) const |
Return the values of a finite element function at the quadrature points of the current cell, face, or subface (selected the last time the reinit() function was called). That is, if the first argument fe_function is a vector of nodal values of a finite element function \(u_h(\mathbf x)\) defined on a DoFHandler object, then the output vector (the second argument, values) is the vector of values \(u_h(\mathbf x_q^K)\) where \(x_q^K\) are the quadrature points on the current cell \(K\). This function is first discussed in the Results section of step-4, and the related get_function_gradients() function is also used in step-15 along with numerous other tutorial programs.
If the current cell is not active (i.e., it has children), then the finite element function is, strictly speaking, defined by shape functions that live on these child cells. Rather than evaluating the shape functions on the child cells, with the quadrature points defined on the current cell, this function first interpolates the finite element function to shape functions defined on the current cell, and then evaluates this interpolated function.
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.
| [in] | fe_function | A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. |
| [out] | values | The 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. |
values[q] will contain the value of the field described by fe_function at the \(q\)th quadrature point.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 716 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_values | ( | const ReadVector< Number > & | fe_function, |
| std::vector< Vector< Number > > & | values ) const |
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.
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.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 763 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_values | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< Number > & | values ) const |
Generate function values from an arbitrary vector. This function does in essence the same as the first function of this name above, except that it does not make the assumption that the input vector corresponds to a DoFHandler that describes the unknowns of a finite element field (and for which we would then assume that fe_function.size() == dof_handler.n_dofs()). Rather, the nodal values corresponding to the current cell are elements of an otherwise arbitrary vector, and these elements are indexed by the second argument to this function. What the rest of the fe_function input argument corresponds to is of no consequence to this function.
Given this, the function above corresponds to passing fe_function as first argument to the current function, and using the local_dof_indices array that results from the following call as second argument to the current function:
(See DoFCellAccessor::get_dof_indices() for more information.)
Likewise, the function above is equivalent to calling
and then calling the current function with local_dof_values as first argument, and an array with indices {0,...,fe.dofs_per_cell-1} as second argument.
The point of the current function is that one sometimes wants to evaluate finite element functions at quadrature points with nodal values that are not stored in a global vector – for example, one could modify these local values first, such as by applying a limiter or by ensuring that all nodal values are positive, before evaluating the finite element field that corresponds to these local values on the current cell. Another application is where one wants to postprocess the solution on a cell into a different finite element space on every cell, without actually creating a corresponding DoFHandler – in that case, all one would compute is a local representation of that postprocessed function, characterized by its nodal values; this function then allows the evaluation of that representation at quadrature points.
| [in] | fe_function | A vector of nodal values. This vector can have an arbitrary size, as long as all elements index by indices can actually be accessed. |
| [in] | indices | A vector of indices into fe_function. This vector must have length equal to the number of degrees of freedom on the current cell, and must identify elements in fe_function in the order in which degrees of freedom are indexed on the reference cell. |
| [out] | values | A vector of values of the given finite element field, at the quadrature points on the current object. |
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 740 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_values | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< Vector< Number > > & | values ) const |
Generate vector function values from an arbitrary vector.
This function corresponds to the previous one, just for the vector-valued case.
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 789 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_values | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| ArrayView< std::vector< Number > > | values, | ||
| const bool | quadrature_points_fastest ) const |
Generate vector function values from an arbitrary vector. This function is similar to the previous one, but the indices vector may also 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.
Since this function allows for fairly general combinations of argument sizes, be aware that the checks on the arguments may not detect errors.
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 819 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_gradients | ( | const ReadVector< Number > & | fe_function, |
| std::vector< Tensor< 1, spacedim, Number > > & | gradients ) const |
Return the gradients of a finite element function at the quadrature points of the current cell, face, or subface (selected the last time the reinit() function was called). That is, if the first argument fe_function is a vector of nodal values of a finite element function \(u_h(\mathbf x)\) defined on a DoFHandler object, then the output vector (the second argument, values) is the vector of values \(\nabla u_h(\mathbf x_q^K)\) where \(x_q^K\) are the quadrature points on the current cell \(K\). This function is first discussed in the Results section of step-4, and it is also used in step-15 along with numerous other tutorial programs.
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.
| [in] | fe_function | A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. |
| [out] | gradients | The 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). |
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 \(q\).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 851 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_gradients | ( | const ReadVector< Number > & | fe_function, |
| std::vector< std::vector< Tensor< 1, spacedim, Number > > > & | gradients ) const |
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.
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.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 898 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_gradients | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< Tensor< 1, spacedim, Number > > & | gradients ) const |
This function relates to the first of the get_function_gradients() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 875 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_gradients | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| ArrayView< std::vector< Tensor< 1, spacedim, Number > > > | gradients, | ||
| const bool | quadrature_points_fastest = false ) const |
This function relates to the first of the get_function_gradients() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 923 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_hessians | ( | const ReadVector< Number > & | fe_function, |
| std::vector< Tensor< 2, spacedim, Number > > & | hessians ) const |
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.
| [in] | fe_function | A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. |
| [out] | hessians | The 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). |
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 \(q\).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 954 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_hessians | ( | const ReadVector< Number > & | fe_function, |
| std::vector< std::vector< Tensor< 2, spacedim, Number > > > & | hessians, | ||
| const bool | quadrature_points_fastest = false ) const |
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.
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.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 1001 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_hessians | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< Tensor< 2, spacedim, Number > > & | hessians ) const |
This function relates to the first of the get_function_hessians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 978 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_hessians | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| ArrayView< std::vector< Tensor< 2, spacedim, Number > > > | hessians, | ||
| const bool | quadrature_points_fastest = false ) const |
This function relates to the first of the get_function_hessians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 1028 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_laplacians | ( | const ReadVector< Number > & | fe_function, |
| std::vector< Number > & | laplacians ) const |
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.
| [in] | fe_function | A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. |
| [out] | laplacians | The 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. |
laplacians[q] will contain the Laplacian of the field described by fe_function at the \(q\)th quadrature point.laplacians[q]=trace(hessians[q]), where hessians would be the output of the get_function_hessians() function.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 1057 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_laplacians | ( | const ReadVector< Number > & | fe_function, |
| std::vector< Vector< Number > > & | laplacians ) const |
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.
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.laplacians[q][c]=trace(hessians[q][c]), where hessians would be the output of the get_function_hessians() function.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 1104 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_laplacians | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< Number > & | laplacians ) const |
This function relates to the first of the get_function_laplacians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 1081 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_laplacians | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< Vector< Number > > & | laplacians ) const |
This function relates to the first of the get_function_laplacians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 1129 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_laplacians | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< std::vector< Number > > & | laplacians, | ||
| const bool | quadrature_points_fastest = false ) const |
This function relates to the first of the get_function_laplacians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 1159 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_third_derivatives | ( | const ReadVector< Number > & | fe_function, |
| std::vector< Tensor< 3, spacedim, Number > > & | third_derivatives ) const |
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.
| [in] | fe_function | A 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_derivatives | The 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). |
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 \(q\).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 1188 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_third_derivatives | ( | const ReadVector< Number > & | fe_function, |
| std::vector< std::vector< Tensor< 3, spacedim, Number > > > & | third_derivatives, | ||
| const bool | quadrature_points_fastest = false ) const |
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.
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.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 1234 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_third_derivatives | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| std::vector< Tensor< 3, spacedim, Number > > & | third_derivatives ) const |
This function relates to the first of the get_function_third_derivatives() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 1212 of file fe_values_base.cc.
| void FEValuesBase< dim, spacedim >::get_function_third_derivatives | ( | const ReadVector< Number > & | fe_function, |
| const ArrayView< const types::global_dof_index > & | indices, | ||
| ArrayView< std::vector< Tensor< 3, spacedim, Number > > > | third_derivatives, | ||
| const bool | quadrature_points_fastest = false ) const |
This function relates to the first of the get_function_third_derivatives() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.
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 1261 of file fe_values_base.cc.
| std_cxx20::ranges::iota_view< unsigned int, unsigned int > FEValuesBase< dim, spacedim >::dof_indices | ( | ) | const |
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:
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.
| std_cxx20::ranges::iota_view< unsigned int, unsigned int > FEValuesBase< dim, spacedim >::dof_indices_starting_at | ( | const unsigned int | start_dof_index | ) | const |
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:
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.
start_dof_index is equal to the number of DoFs in the cell, then the returned index range is empty. | std_cxx20::ranges::iota_view< unsigned int, unsigned int > FEValuesBase< dim, spacedim >::dof_indices_ending_at | ( | const unsigned int | end_dof_index | ) | const |
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:
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.
end_dof_index is equal to zero, then the returned index range is empty. | std_cxx20::ranges::iota_view< unsigned int, unsigned int > FEValuesBase< dim, spacedim >::quadrature_point_indices | ( | ) | const |
Return an object that can be thought of as an array containing all indices from zero to n_quadrature_points. This allows to write code using range-based for loops of the following kind:
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.
| const Point< spacedim > & FEValuesBase< dim, spacedim >::quadrature_point | ( | const unsigned int | q_point | ) | const |
Return the location of the q_pointth quadrature point in real space.
update_quadrature_points flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. | const std::vector< Point< spacedim > > & FEValuesBase< dim, spacedim >::get_quadrature_points | ( | ) | const |
Return a reference to the vector of quadrature points in real space.
update_quadrature_points flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. | double FEValuesBase< dim, spacedim >::JxW | ( | const unsigned int | q_point | ) | const |
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 q_pointth 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.
update_JxW_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. | const std::vector< double > & FEValuesBase< dim, spacedim >::get_JxW_values | ( | ) | const |
Return a reference to the array holding the values returned by JxW().
| const DerivativeForm< 1, dim, spacedim > & FEValuesBase< dim, spacedim >::jacobian | ( | const unsigned int | q_point | ) | const |
Return the Jacobian of the transformation at the specified quadrature point, i.e. \(J_{ij}=dx_i/d\hat x_j\)
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. | const std::vector< DerivativeForm< 1, dim, spacedim > > & FEValuesBase< dim, spacedim >::get_jacobians | ( | ) | const |
Return a reference to the array holding the values returned by jacobian().
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. | const DerivativeForm< 2, dim, spacedim > & FEValuesBase< dim, spacedim >::jacobian_grad | ( | const unsigned int | q_point | ) | const |
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. \(G_{ijk}=dJ_{jk}/d\hat x_i\).
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. | const std::vector< DerivativeForm< 2, dim, spacedim > > & FEValuesBase< dim, spacedim >::get_jacobian_grads | ( | ) | const |
Return a reference to the array holding the values returned by jacobian_grads().
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. | const Tensor< 3, spacedim > & FEValuesBase< dim, spacedim >::jacobian_pushed_forward_grad | ( | const unsigned int | q_point | ) | const |
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. \(G_{ijk}=dJ_{iJ}/d\hat x_K (J_{jJ})^{-1} (J_{kK})^{-1}\).
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. | const std::vector< Tensor< 3, spacedim > > & FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_grads | ( | ) | const |
Return a reference to the array holding the values returned by jacobian_pushed_forward_grads().
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. | const DerivativeForm< 3, dim, spacedim > & FEValuesBase< dim, spacedim >::jacobian_2nd_derivative | ( | const unsigned int | q_point | ) | const |
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. \(G_{ijkl}=\frac{d^2J_{ij}}{d\hat x_k d\hat x_l}\).
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. | const std::vector< DerivativeForm< 3, dim, spacedim > > & FEValuesBase< dim, spacedim >::get_jacobian_2nd_derivatives | ( | ) | const |
Return a reference to the array holding the values returned by jacobian_2nd_derivatives().
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. | const Tensor< 4, spacedim > & FEValuesBase< dim, spacedim >::jacobian_pushed_forward_2nd_derivative | ( | const unsigned int | q_point | ) | const |
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. \(G_{ijkl}=\frac{d^2J_{iJ}}{d\hat x_K d\hat x_L} (J_{jJ})^{-1} (J_{kK})^{-1}(J_{lL})^{-1}\).
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. | const std::vector< Tensor< 4, spacedim > > & FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_2nd_derivatives | ( | ) | const |
Return a reference to the array holding the values returned by jacobian_pushed_forward_2nd_derivatives().
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. | const DerivativeForm< 4, dim, spacedim > & FEValuesBase< dim, spacedim >::jacobian_3rd_derivative | ( | const unsigned int | q_point | ) | const |
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. \(G_{ijklm}=\frac{d^2J_{ij}}{d\hat x_k d\hat x_l d\hat x_m}\).
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. | const std::vector< DerivativeForm< 4, dim, spacedim > > & FEValuesBase< dim, spacedim >::get_jacobian_3rd_derivatives | ( | ) | const |
Return a reference to the array holding the values returned by jacobian_3rd_derivatives().
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. | const Tensor< 5, spacedim > & FEValuesBase< dim, spacedim >::jacobian_pushed_forward_3rd_derivative | ( | const unsigned int | q_point | ) | const |
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. \(G_{ijklm}=\frac{d^3J_{iJ}}{d\hat x_K d\hat x_L d\hat x_M} (J_{jJ})^{-1} (J_{kK})^{-1} (J_{lL})^{-1} (J_{mM})^{-1}\).
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. | const std::vector< Tensor< 5, spacedim > > & FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_3rd_derivatives | ( | ) | const |
Return a reference to the array holding the values returned by jacobian_pushed_forward_3rd_derivatives().
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. | const DerivativeForm< 1, spacedim, dim > & FEValuesBase< dim, spacedim >::inverse_jacobian | ( | const unsigned int | q_point | ) | const |
Return the inverse Jacobian of the transformation at the specified quadrature point, i.e. \(J_{ij}=d\hat x_i/dx_j\)
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. | const std::vector< DerivativeForm< 1, spacedim, dim > > & FEValuesBase< dim, spacedim >::get_inverse_jacobians | ( | ) | const |
Return a reference to the array holding the values returned by inverse_jacobian().
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. | const Tensor< 1, spacedim > & FEValuesBase< dim, spacedim >::normal_vector | ( | const unsigned int | q_point | ) | const |
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 q_pointth 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.
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. | const std::vector< Tensor< 1, spacedim > > & FEValuesBase< dim, spacedim >::get_normal_vectors | ( | ) | const |
Return the normal vectors at all quadrature points represented by this object. See the normal_vector() function for what the normal vectors represent.
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 1298 of file fe_values_base.cc.
| const FEValuesViews::Scalar< dim, spacedim > & FEValuesBase< dim, spacedim >::operator[] | ( | const FEValuesExtractors::Scalar & | scalar | ) | const |
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 topic.
| const FEValuesViews::Vector< dim, spacedim > & FEValuesBase< dim, spacedim >::operator[] | ( | const FEValuesExtractors::Vector & | vector | ) | const |
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 topic.
| const FEValuesViews::SymmetricTensor< 2, dim, spacedim > & FEValuesBase< dim, spacedim >::operator[] | ( | const FEValuesExtractors::SymmetricTensor< 2 > & | tensor | ) | const |
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 topic.
| const FEValuesViews::Tensor< 2, dim, spacedim > & FEValuesBase< dim, spacedim >::operator[] | ( | const FEValuesExtractors::Tensor< 2 > & | tensor | ) | const |
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 topic.
| const Mapping< dim, spacedim > & FEValuesBase< dim, spacedim >::get_mapping | ( | ) | const |
Constant reference to the selected mapping object.
| const FiniteElement< dim, spacedim > & FEValuesBase< dim, spacedim >::get_fe | ( | ) | const |
Constant reference to the selected finite element object.
| UpdateFlags FEValuesBase< dim, spacedim >::get_update_flags | ( | ) | const |
Return the update flags set for this object.
| Triangulation< dim, spacedim >::cell_iterator FEValuesBase< dim, spacedim >::get_cell | ( | ) | const |
Return a triangulation iterator to the current cell.
Definition at line 1289 of file fe_values_base.cc.
| CellSimilarity::Similarity FEValuesBase< dim, spacedim >::get_cell_similarity | ( | ) | const |
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 1453 of file fe_values_base.cc.
| std::size_t FEValuesBase< dim, spacedim >::memory_consumption | ( | ) | const |
Determine an estimate for the memory consumption (in bytes) of this object.
Definition at line 1311 of file fe_values_base.cc.
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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 1351 of file fe_values_base.cc.
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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 1369 of file fe_values_base.cc.
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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 1332 of file fe_values_base.cc.
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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 1412 of file fe_values_base.cc.
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Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.
Definition at line 135 of file subscriptor.cc.
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inherited |
Unsubscribes a user from the object.
identifier and the validity pointer must be the same as the one supplied to subscribe(). Definition at line 155 of file subscriptor.cc.
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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.
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inlineinherited |
List the subscribers to the input stream.
Definition at line 317 of file subscriptor.h.
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List the subscribers to deallog.
Definition at line 203 of file subscriptor.cc.
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inlineinherited |
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
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.
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Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.
Definition at line 52 of file subscriptor.cc.
Definition at line 1790 of file fe_values_base.h.
Definition at line 1792 of file fe_values_base.h.
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Definition at line 1794 of file fe_values_base.h.
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friend |
Definition at line 1796 of file fe_values_base.h.
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Dimension in which this object operates.
Definition at line 160 of file fe_values_base.h.
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staticconstexpr |
Dimension of the space in which this object operates.
Definition at line 165 of file fe_values_base.h.
| const unsigned int FEValuesBase< dim, spacedim >::n_quadrature_points |
Number of quadrature points of the current object. Its value is initialized by the value of max_n_quadrature_points and is updated, e.g., if FEFaceValues::reinit() is called for a new cell/face.
Definition at line 174 of file fe_values_base.h.
| const unsigned int FEValuesBase< dim, spacedim >::max_n_quadrature_points |
Maximum number of quadrature points. This value might be different from n_quadrature_points, e.g., if a QCollection with different face quadrature rules has been passed to initialize FEFaceValues.
This is mostly useful to initialize arrays to allocate the maximum amount of memory that may be used when re-sizing later on to a the current number of quadrature points given by n_quadrature_points.
Definition at line 185 of file fe_values_base.h.
| const unsigned int FEValuesBase< dim, spacedim >::dofs_per_cell |
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 192 of file fe_values_base.h.
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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 1657 of file fe_values_base.h.
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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 1666 of file fe_values_base.h.
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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 1675 of file fe_values_base.h.
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A pointer to the mapping object associated with this FEValues object.
Definition at line 1702 of file fe_values_base.h.
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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 1710 of file fe_values_base.h.
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An object into which the Mapping::fill_fe_values() and similar functions place their output.
Definition at line 1717 of file fe_values_base.h.
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A pointer to the finite element object associated with this FEValues object.
Definition at line 1725 of file fe_values_base.h.
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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 1733 of file fe_values_base.h.
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An object into which the FiniteElement::fill_fe_values() and similar functions place their output.
Definition at line 1741 of file fe_values_base.h.
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Original update flags handed to the constructor of FEValues.
Definition at line 1747 of file fe_values_base.h.
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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 1765 of file fe_values_base.h.
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private |
A cache for all possible FEValuesViews objects.
Definition at line 1780 of file fe_values_base.h.
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private |
Whether checking for cell similarity is allowed.
Definition at line 1785 of file fe_values_base.h.
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mutableprivateinherited |
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
The creator (and owner) of an object is counted in the map below if HE manages to supply identification.
We use the mutable keyword in order to allow subscription to constant objects also.
This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.
Definition at line 218 of file subscriptor.h.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
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mutableprivateinherited |
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 240 of file subscriptor.h.
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mutableprivateinherited |
Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.
Definition at line 248 of file subscriptor.h.
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staticprivateinherited |
A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().
Definition at line 271 of file subscriptor.h.
1.11.0