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Reference documentation for deal.II version 9.0.0
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Reference documentation for deal.II version 9.0.0
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#include <deal.II/fe/fe_values.h>
Classes | |
| struct | OutputType |
| struct | ShapeFunctionData |
Public Types | |
| typedef ::Tensor< 1, spacedim > | value_type |
| typedef ::Tensor< 2, spacedim > | gradient_type |
| typedef ::SymmetricTensor< 2, spacedim > | symmetric_gradient_type |
| typedef double | divergence_type |
| typedef ::internal::CurlType< spacedim >::type | curl_type |
| typedef ::Tensor< 3, spacedim > | hessian_type |
| typedef ::Tensor< 4, spacedim > | third_derivative_type |
Public Member Functions | |
| Vector () | |
| Vector (const FEValuesBase< dim, spacedim > &fe_values_base, const unsigned int first_vector_component) | |
| Vector & | operator= (const Vector< dim, spacedim > &) |
| value_type | value (const unsigned int shape_function, const unsigned int q_point) const |
| gradient_type | gradient (const unsigned int shape_function, const unsigned int q_point) const |
| symmetric_gradient_type | symmetric_gradient (const unsigned int shape_function, const unsigned int q_point) const |
| divergence_type | divergence (const unsigned int shape_function, const unsigned int q_point) const |
| curl_type | curl (const unsigned int shape_function, const unsigned int q_point) const |
| hessian_type | hessian (const unsigned int shape_function, const unsigned int q_point) const |
| third_derivative_type | third_derivative (const unsigned int shape_function, const unsigned int q_point) const |
| template<class InputVector > | |
| void | get_function_values (const InputVector &fe_function, std::vector< typename ProductType< value_type, typename InputVector::value_type >::type > &values) const |
| template<class InputVector > | |
| void | get_function_values_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::value_type > &values) const |
| template<class InputVector > | |
| void | get_function_gradients (const InputVector &fe_function, std::vector< typename ProductType< gradient_type, typename InputVector::value_type >::type > &gradients) const |
| template<class InputVector > | |
| void | get_function_gradients_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::gradient_type > &gradients) const |
| template<class InputVector > | |
| void | get_function_symmetric_gradients (const InputVector &fe_function, std::vector< typename ProductType< symmetric_gradient_type, typename InputVector::value_type >::type > &symmetric_gradients) const |
| template<class InputVector > | |
| void | get_function_symmetric_gradients_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::symmetric_gradient_type > &symmetric_gradients) const |
| template<class InputVector > | |
| void | get_function_divergences (const InputVector &fe_function, std::vector< typename ProductType< divergence_type, typename InputVector::value_type >::type > &divergences) const |
| template<class InputVector > | |
| void | get_function_divergences_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::divergence_type > &divergences) const |
| template<class InputVector > | |
| void | get_function_curls (const InputVector &fe_function, std::vector< typename ProductType< curl_type, typename InputVector::value_type >::type > &curls) const |
| template<class InputVector > | |
| void | get_function_curls_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::curl_type > &curls) const |
| template<class InputVector > | |
| void | get_function_hessians (const InputVector &fe_function, std::vector< typename ProductType< hessian_type, typename InputVector::value_type >::type > &hessians) const |
| template<class InputVector > | |
| void | get_function_hessians_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::hessian_type > &hessians) const |
| template<class InputVector > | |
| void | get_function_laplacians (const InputVector &fe_function, std::vector< typename ProductType< value_type, typename InputVector::value_type >::type > &laplacians) const |
| template<class InputVector > | |
| void | get_function_laplacians_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::laplacian_type > &laplacians) const |
| template<class InputVector > | |
| void | get_function_third_derivatives (const InputVector &fe_function, std::vector< typename ProductType< third_derivative_type, typename InputVector::value_type >::type > &third_derivatives) const |
| template<class InputVector > | |
| void | get_function_third_derivatives_from_local_dof_values (const InputVector &dof_values, std::vector< typename OutputType< typename InputVector::value_type >::third_derivative_type > &third_derivatives) const |
Private Attributes | |
| const SmartPointer< const FEValuesBase< dim, spacedim > > | fe_values |
| const unsigned int | first_vector_component |
| std::vector< ShapeFunctionData > | shape_function_data |
A class representing a view to a set of spacedim components forming a vector part of a vector-valued finite element. Views are discussed in the Handling vector valued problems module.
Note that in the current context, a vector is meant in the sense physics uses it: it has spacedim components that behave in specific ways under coordinate system transformations. Examples include velocity or displacement fields. This is opposed to how mathematics uses the word "vector" (and how we use this word in other contexts in the library, for example in the Vector class), where it really stands for a collection of numbers. An example of this latter use of the word could be the set of concentrations of chemical species in a flame; however, these are really just a collection of scalar variables, since they do not change if the coordinate system is rotated, unlike the components of a velocity vector, and consequently, this class should not be used for this context.
This class allows to query the value, gradient and divergence of (components of) shape functions and solutions representing vectors. The gradient of a vector \(d_{k}, 0\le k<\text{dim}\) is defined as \(S_{ij} = \frac{\partial d_{i}}{\partial x_j}, 0\le i,j<\text{dim}\).
You get an object of this type if you apply a FEValuesExtractors::Vector to an FEValues, FEFaceValues or FESubfaceValues object.
Definition at line 526 of file fe_values.h.
| typedef ::Tensor<1,spacedim> FEValuesViews::Vector< dim, spacedim >::value_type |
A typedef for the data type of values of the view this class represents. Since we deal with a set of dim components, the value type is a Tensor<1,spacedim>.
Definition at line 534 of file fe_values.h.
| typedef ::Tensor<2,spacedim> FEValuesViews::Vector< dim, spacedim >::gradient_type |
A typedef for the type of gradients of the view this class represents. Here, for a set of dim components of the finite element, the gradient is a Tensor<2,spacedim>.
See the general documentation of this class for how exactly the gradient of a vector is defined.
Definition at line 544 of file fe_values.h.
| typedef ::SymmetricTensor<2,spacedim> FEValuesViews::Vector< dim, spacedim >::symmetric_gradient_type |
A typedef for the type of symmetrized gradients of the view this class represents. Here, for a set of dim components of the finite element, the symmetrized gradient is a SymmetricTensor<2,spacedim>.
The symmetric gradient of a vector field \(\mathbf v\) is defined as \(\varepsilon(\mathbf v)=\frac 12 (\nabla \mathbf v + \nabla \mathbf v^T)\).
Definition at line 556 of file fe_values.h.
| typedef double FEValuesViews::Vector< dim, spacedim >::divergence_type |
A typedef for the type of the divergence of the view this class represents. Here, for a set of dim components of the finite element, the divergence of course is a scalar.
Definition at line 563 of file fe_values.h.
| typedef ::internal::CurlType<spacedim>::type FEValuesViews::Vector< dim, spacedim >::curl_type |
A typedef for the type of the curl of the view this class represents. Here, for a set of spacedim=2 components of the finite element, the curl is a Tensor<1, 1>. For spacedim=3 it is a Tensor<1, dim>.
Definition at line 571 of file fe_values.h.
| typedef ::Tensor<3,spacedim> FEValuesViews::Vector< dim, spacedim >::hessian_type |
A typedef for the type of second derivatives of the view this class represents. Here, for a set of dim components of the finite element, the Hessian is a Tensor<3,dim>.
Definition at line 578 of file fe_values.h.
| typedef ::Tensor<4,spacedim> FEValuesViews::Vector< dim, spacedim >::third_derivative_type |
A typedef for the type of third derivatives of the view this class represents. Here, for a set of dim components of the finite element, the third derivative is a Tensor<4,dim>.
Definition at line 585 of file fe_values.h.
Default constructor. Creates an invalid object.
Definition at line 274 of file fe_values.cc.
| Vector< dim, spacedim >::Vector | ( | const FEValuesBase< dim, spacedim > & | fe_values_base, |
| const unsigned int | first_vector_component | ||
| ) |
Constructor for an object that represents dim components of a FEValuesBase object (or of one of the classes derived from FEValuesBase), representing a vector-valued variable.
The second argument denotes the index of the first component of the selected vector.
Definition at line 198 of file fe_values.cc.
| Vector< dim, spacedim > & Vector< dim, spacedim >::operator= | ( | const Vector< dim, spacedim > & | ) |
Copy operator. This is not a lightweight object so we don't allow copying and generate an exception if this function is called.
Definition at line 284 of file fe_values.cc.
| value_type FEValuesViews::Vector< dim, spacedim >::value | ( | const unsigned int | shape_function, |
| const unsigned int | q_point | ||
| ) | const |
Return the value of the vector components selected by this view, for the shape function and quadrature point selected by the arguments. Here, since the view represents a vector-valued part of the FEValues object with dim components, the return type is a tensor of rank 1 with dim components.
| shape_function | 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. |
| 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. | gradient_type FEValuesViews::Vector< dim, spacedim >::gradient | ( | const unsigned int | shape_function, |
| const unsigned int | q_point | ||
| ) | const |
Return the gradient (a tensor of rank 2) of the vector component selected by this view, for the shape function and quadrature point selected by the arguments.
See the general documentation of this class for how exactly the gradient of a vector is defined.
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. | symmetric_gradient_type FEValuesViews::Vector< dim, spacedim >::symmetric_gradient | ( | const unsigned int | shape_function, |
| const unsigned int | q_point | ||
| ) | const |
Return the symmetric gradient (a symmetric tensor of rank 2) of the vector component selected by this view, for the shape function and quadrature point selected by the arguments.
The symmetric gradient is defined as \(\frac 12 [(\nabla \phi_i(x_q)) + (\nabla \phi_i(x_q))^T]\), where \(\phi_i\) represents the dim components selected from the FEValuesBase object, and \(x_q\) is the location of the \(q\)-th quadrature point.
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. | divergence_type FEValuesViews::Vector< dim, spacedim >::divergence | ( | const unsigned int | shape_function, |
| const unsigned int | q_point | ||
| ) | const |
Return the scalar divergence of the vector components selected by this view, for the shape function and quadrature point selected by the arguments.
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. | curl_type FEValuesViews::Vector< dim, spacedim >::curl | ( | const unsigned int | shape_function, |
| const unsigned int | q_point | ||
| ) | const |
Return the vector curl of the vector components selected by this view, for the shape function and quadrature point selected by the arguments. For 1d this function does not make any sense. Thus it is not implemented for spacedim=1. In 2d the curl is defined as
\begin{equation*} \operatorname{curl}(u):=\frac{du_2}{dx} -\frac{du_1}{dy}, \end{equation*}
whereas in 3d it is given by
\begin{equation*} \operatorname{curl}(u):=\left( \begin{array}{c} \frac{du_3}{dy}-\frac{du_2}{dz}\\ \frac{du_1}{dz}-\frac{du_3}{dx}\\ \frac{du_2}{dx}-\frac{du_1}{dy} \end{array} \right). \end{equation*}
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. | hessian_type FEValuesViews::Vector< dim, spacedim >::hessian | ( | const unsigned int | shape_function, |
| const unsigned int | q_point | ||
| ) | const |
Return the Hessian (the tensor of rank 2 of all second derivatives) of the vector components selected by this view, for the shape function and quadrature point selected by the arguments.
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. | third_derivative_type FEValuesViews::Vector< dim, spacedim >::third_derivative | ( | const unsigned int | shape_function, |
| const unsigned int | q_point | ||
| ) | const |
Return the tensor of rank 3 of all third derivatives of the vector components selected by this view, for the shape function and quadrature point selected by the arguments.
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 Vector< dim, spacedim >::get_function_values | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< value_type, typename InputVector< dim, spacedim >::value_type >::type > & | values | ||
| ) | const |
Return the values of the selected vector components of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called.
This function is the equivalent of the FEValuesBase::get_function_values function but it only works on the selected vector components.
The data type stored by the output vector must be what you get when you multiply the values of shape functions (i.e., value_type) 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).
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 1638 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_values_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::value_type > & | values | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1662 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_gradients | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< gradient_type, typename InputVector< dim, spacedim >::value_type >::type > & | gradients | ||
| ) | const |
Return the gradients of the selected vector components of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called.
This function is the equivalent of the FEValuesBase::get_function_gradients function but it only works on the selected vector components.
The data type stored by the output vector must be what you get when you multiply the gradients of shape functions (i.e., gradient_type) 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).
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 1682 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_gradients_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::gradient_type > & | gradients | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1706 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_symmetric_gradients | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< symmetric_gradient_type, typename InputVector< dim, spacedim >::value_type >::type > & | symmetric_gradients | ||
| ) | const |
Return the symmetrized gradients of the selected vector components of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called.
The symmetric gradient of a vector field \(\mathbf v\) is defined as \(\varepsilon(\mathbf v)=\frac 12 (\nabla \mathbf v + \nabla \mathbf v^T)\).
The data type stored by the output vector must be what you get when you multiply the symmetric gradients of shape functions (i.e., symmetric_gradient_type) 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).
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 1726 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_symmetric_gradients_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::symmetric_gradient_type > & | symmetric_gradients | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1751 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_divergences | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< divergence_type, typename InputVector< dim, spacedim >::value_type >::type > & | divergences | ||
| ) | const |
Return the divergence of the selected vector components of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called.
There is no equivalent function such as FEValuesBase::get_function_divergences in the FEValues classes but the information can be obtained from FEValuesBase::get_function_gradients, of course.
The data type stored by the output vector must be what you get when you multiply the divergences of shape functions (i.e., divergence_type) 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).
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 1772 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_divergences_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::divergence_type > & | divergences | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1797 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_curls | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< curl_type, typename InputVector< dim, spacedim >::value_type >::type > & | curls | ||
| ) | const |
Return the curl of the selected vector components of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called.
There is no equivalent function such as FEValuesBase::get_function_curls in the FEValues classes but the information can be obtained from FEValuesBase::get_function_gradients, of course.
The data type stored by the output vector must be what you get when you multiply the curls of shape functions (i.e., curl_type) 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).
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 1817 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_curls_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::curl_type > & | curls | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1841 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_hessians | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< hessian_type, typename InputVector< dim, spacedim >::value_type >::type > & | hessians | ||
| ) | const |
Return the Hessians of the selected vector components of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called.
This function is the equivalent of the FEValuesBase::get_function_hessians function but it only works on the selected vector components.
The data type stored by the output vector must be what you get when you multiply the Hessians of shape functions (i.e., hessian_type) 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).
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 1861 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_hessians_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::hessian_type > & | hessians | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1885 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_laplacians | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< value_type, typename InputVector< dim, spacedim >::value_type >::type > & | laplacians | ||
| ) | const |
Return the Laplacians of the selected vector components of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called. The Laplacians are the trace of the Hessians.
This function is the equivalent of the FEValuesBase::get_function_laplacians function but it only works on the selected vector components.
The data type stored by the output vector must be what you get when you multiply the Laplacians of shape functions (i.e., laplacian_type) 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).
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 1905 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_laplacians_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::laplacian_type > & | laplacians | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1932 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_third_derivatives | ( | const InputVector< dim, spacedim > & | fe_function, |
| std::vector< typename ProductType< third_derivative_type, typename InputVector< dim, spacedim >::value_type >::type > & | third_derivatives | ||
| ) | const |
Return the third derivatives of the selected scalar component of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called.
This function is the equivalent of the FEValuesBase::get_function_third_derivatives function but it only works on the selected scalar component.
The data type stored by the output vector must be what you get when you multiply the third derivatives of shape functions (i.e., third_derivative_type) 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).
update_third_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1954 of file fe_values.cc.
| void Vector< dim, spacedim >::get_function_third_derivatives_from_local_dof_values | ( | const InputVector< dim, spacedim > & | dof_values, |
| std::vector< typename OutputType< typename InputVector< dim, spacedim >::value_type >::third_derivative_type > & | third_derivatives | ||
| ) | const |
Same as above, but using a vector of local degree-of-freedom values.
The dof_values vector must have a length equal to number of DoFs on a cell, and each entry dof_values[i] is the value of the local DoF i. The fundamental prerequisite for the InputVector is that it must be possible to create an ArrayView from it; this is satisfied by the std::vector class.
The DoF values typically would be obtained in the following way:
or, for a generic Number type,
Definition at line 1978 of file fe_values.cc.
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A pointer to the FEValuesBase object we operate on.
Definition at line 1084 of file fe_values.h.
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The first component of the vector this view represents of the FEValuesBase object.
Definition at line 1090 of file fe_values.h.
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Store the data about shape functions.
Definition at line 1095 of file fe_values.h.
1.8.14