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Reference documentation for deal.II version 9.3.3
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Reference documentation for deal.II version 9.3.3
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#include <deal.II/fe/fe_values.h>
Classes | |
| class | CellIterator |
| class | CellIteratorBase |
| class | TriaCellIterator |
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 |
Access to shape function values | |
These fields are filled by the finite element. | |
| const double & | shape_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, const 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, const 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, const 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, const 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, const 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, 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) 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 |
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 const unsigned int | dimension = dim |
| static const unsigned int | space_dimension = spacedim |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
| 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 |
| 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 |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
| static std::mutex | mutex |
| void | check_no_subscribers () const noexcept |
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 2412 of file fe_values.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 3030 of file fe_values.cc.
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delete |
The copy constructor is deleted since objects of this class are not copyable.
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overridevirtual |
Destructor.
Definition at line 3054 of file fe_values.cc.
|
delete |
The copy assignment is deleted since objects of this class are not copyable.
| const double & FEValuesBase< dim, spacedim >::shape_value | ( | const unsigned int | function_no, |
| const unsigned int | point_no | ||
| ) | 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.
| function_no | Number 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_no | 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 | function_no, |
| const unsigned int | point_no, | ||
| 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.
| function_no | Number of the shape function to be evaluated. |
| point_no | 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 | function_no, |
| const unsigned int | quadrature_point | ||
| ) | const |
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.
| function_no | Number of the shape function to be evaluated. |
| quadrature_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 | function_no, |
| const unsigned int | point_no, | ||
| 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 | function_no, |
| const unsigned int | point_no | ||
| ) | const |
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.
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 | function_no, |
| const unsigned int | point_no, | ||
| 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 | function_no, |
| const unsigned int | point_no | ||
| ) | const |
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.
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 | function_no, |
| const unsigned int | point_no, | ||
| 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 InputVector & | fe_function, |
| std::vector< typename InputVector::value_type > & | values | ||
| ) | const |
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.
| [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 3523 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_values | ( | const InputVector & | fe_function, |
| std::vector< Vector< typename InputVector::value_type > > & | 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 3572 of file fe_values.cc.
| 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 |
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 3548 of file fe_values.cc.
| 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 |
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 3600 of file fe_values.cc.
| 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 |
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 3631 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_gradients | ( | const InputVector & | fe_function, |
| std::vector< Tensor< 1, spacedim, typename InputVector::value_type > > & | gradients | ||
| ) | const |
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.
| [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 3664 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_gradients | ( | const InputVector & | fe_function, |
| std::vector< std::vector< Tensor< 1, spacedim, typename InputVector::value_type > > > & | 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 3715 of file fe_values.cc.
| 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 |
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 3690 of file fe_values.cc.
| 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, | ||
| 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 3744 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_hessians | ( | const InputVector & | fe_function, |
| std::vector< Tensor< 2, spacedim, typename InputVector::value_type > > & | 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 3777 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_hessians | ( | const InputVector & | fe_function, |
| std::vector< std::vector< Tensor< 2, spacedim, typename InputVector::value_type > > > & | 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 3828 of file fe_values.cc.
| 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 |
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 3803 of file fe_values.cc.
| 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, | ||
| 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 3859 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_laplacians | ( | const InputVector & | fe_function, |
| std::vector< typename InputVector::value_type > & | 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 3890 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_laplacians | ( | const InputVector & | fe_function, |
| std::vector< Vector< typename InputVector::value_type > > & | 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 3939 of file fe_values.cc.
| 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 |
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 3915 of file fe_values.cc.
| 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 |
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 3966 of file fe_values.cc.
| 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, | ||
| 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 3997 of file fe_values.cc.
| void FEValuesBase< dim, spacedim >::get_function_third_derivatives | ( | const InputVector & | fe_function, |
| std::vector< Tensor< 3, spacedim, typename InputVector::value_type > > & | 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 4027 of file fe_values.cc.
| 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, | ||
| 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 4080 of file fe_values.cc.
| 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 |
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 4054 of file fe_values.cc.
| 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, | ||
| 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 4111 of file fe_values.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 | ) | const |
Position of the qth 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 | quadrature_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 *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.
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 | quadrature_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 | quadrature_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 | quadrature_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 | quadrature_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 | quadrature_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 | quadrature_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 | quadrature_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 | quadrature_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 | i | ) | 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 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.
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 |
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 4150 of file fe_values.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 module.
| 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 module.
| 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 module.
| 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 module.
| 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.
| const Triangulation< dim, spacedim >::cell_iterator FEValuesBase< dim, spacedim >::get_cell |
Return a triangulation iterator to the current cell.
Definition at line 4141 of file fe_values.cc.
| CellSimilarity::Similarity FEValuesBase< dim, spacedim >::get_cell_similarity |
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 4319 of file fe_values.cc.
| std::size_t FEValuesBase< dim, spacedim >::memory_consumption |
Determine an estimate for the memory consumption (in bytes) of this object.
Definition at line 4163 of file fe_values.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 4203 of file fe_values.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 4221 of file fe_values.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 4184 of file fe_values.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 4264 of file fe_values.cc.
Definition at line 3972 of file fe_values.h.
Definition at line 3974 of file fe_values.h.
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Definition at line 3976 of file fe_values.h.
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Definition at line 3978 of file fe_values.h.
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Dimension in which this object operates.
Definition at line 2418 of file fe_values.h.
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Dimension of the space in which this object operates.
Definition at line 2423 of file fe_values.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 2432 of file fe_values.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 2443 of file fe_values.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 2450 of file fe_values.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 3843 of file fe_values.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 3852 of file fe_values.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 3861 of file fe_values.h.
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A pointer to the mapping object associated with this FEValues object.
Definition at line 3888 of file fe_values.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 3896 of file fe_values.h.
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An object into which the Mapping::fill_fe_values() and similar functions place their output.
Definition at line 3903 of file fe_values.h.
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A pointer to the finite element object associated with this FEValues object.
Definition at line 3912 of file fe_values.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 3920 of file fe_values.h.
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An object into which the FiniteElement::fill_fe_values() and similar functions place their output.
Definition at line 3928 of file fe_values.h.
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Original update flags handed to the constructor of FEValues.
Definition at line 3934 of file fe_values.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 3952 of file fe_values.h.
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A cache for all possible FEValuesViews objects.
Definition at line 3967 of file fe_values.h.
1.9.4