Reference documentation for deal.II version GIT d1e6af55b6 2023-02-07 07:50:02+00:00
FEValuesViews::Scalar< dim, spacedim > Class Template Reference

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

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

Classes

struct  OutputType

struct  ShapeFunctionData

Public Types

using value_type = double

using gradient_type = ::Tensor< 1, spacedim >

using hessian_type = ::Tensor< 2, spacedim >

using third_derivative_type = ::Tensor< 3, spacedim >

template<typename Number >
using solution_value_type = typename ProductType< Number, value_type >::type

template<typename Number >

template<typename Number >
using solution_laplacian_type = typename ProductType< Number, value_type >::type

template<typename Number >
using solution_hessian_type = typename ProductType< Number, hessian_type >::type

template<typename Number >
using solution_third_derivative_type = typename ProductType< Number, third_derivative_type >::type

Public Member Functions

Scalar ()

Scalar (const FEValuesBase< dim, spacedim > &fe_values_base, const unsigned int component)

Scalar (const Scalar< dim, spacedim > &)=delete

Scalar (Scalar< dim, spacedim > &&)=default

~Scalar ()=default

Scalaroperator= (const Scalar< dim, spacedim > &)=delete

Scalaroperator= (Scalar< dim, spacedim > &&) noexcept=default

value_type value (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< solution_value_type< typename InputVector::value_type >> &values) const

template<class InputVector >
void get_function_values_from_local_dof_values (const InputVector &dof_values, std::vector< solution_value_type< typename InputVector::value_type >> &values) const

template<class InputVector >

template<class InputVector >

template<class InputVector >
void get_function_hessians (const InputVector &fe_function, std::vector< solution_hessian_type< typename InputVector::value_type >> &hessians) const

template<class InputVector >
void get_function_hessians_from_local_dof_values (const InputVector &dof_values, std::vector< solution_hessian_type< typename InputVector::value_type >> &hessians) const

template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, std::vector< solution_laplacian_type< typename InputVector::value_type >> &laplacians) const

template<class InputVector >
void get_function_laplacians_from_local_dof_values (const InputVector &dof_values, std::vector< solution_laplacian_type< typename InputVector::value_type >> &laplacians) const

template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, std::vector< solution_third_derivative_type< typename InputVector::value_type >> &third_derivatives) const

template<class InputVector >
void get_function_third_derivatives_from_local_dof_values (const InputVector &dof_values, std::vector< solution_third_derivative_type< typename InputVector::value_type >> &third_derivatives) const

Private Attributes

const SmartPointer< const FEValuesBase< dim, spacedim > > fe_values

const unsigned int component

std::vector< ShapeFunctionDatashape_function_data

Detailed Description

template<int dim, int spacedim = dim> class FEValuesViews::Scalar< dim, spacedim >

A class representing a view to a single scalar component of a possibly vector-valued finite element. Views are discussed in the Handling vector valued problems module.

You get an object of this type if you apply a FEValuesExtractors::Scalar to an FEValues, FEFaceValues or FESubfaceValues object.

Definition at line 147 of file fe_values.h.

◆ value_type

template<int dim, int spacedim = dim>
 using FEValuesViews::Scalar< dim, spacedim >::value_type = double

An alias for the data type of values of the view this class represents. Since we deal with a single components, the value type is a scalar double.

Definition at line 155 of file fe_values.h.

template<int dim, int spacedim = dim>
 using FEValuesViews::Scalar< dim, spacedim >::gradient_type = ::Tensor<1, spacedim>

An alias for the type of gradients of the view this class represents. Here, for a scalar component of the finite element, the gradient is a Tensor<1,dim>.

Definition at line 162 of file fe_values.h.

◆ hessian_type

template<int dim, int spacedim = dim>
 using FEValuesViews::Scalar< dim, spacedim >::hessian_type = ::Tensor<2, spacedim>

An alias for the type of second derivatives of the view this class represents. Here, for a scalar component of the finite element, the Hessian is a Tensor<2,dim>.

Definition at line 169 of file fe_values.h.

◆ third_derivative_type

template<int dim, int spacedim = dim>
 using FEValuesViews::Scalar< dim, spacedim >::third_derivative_type = ::Tensor<3, spacedim>

An alias for the type of third derivatives of the view this class represents. Here, for a scalar component of the finite element, the Third derivative is a Tensor<3,dim>.

Definition at line 176 of file fe_values.h.

◆ solution_value_type

template<int dim, int spacedim = dim>
template<typename Number >
 using FEValuesViews::Scalar< dim, spacedim >::solution_value_type = typename ProductType::type

An alias for the data type of the product of a Number and the values of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number.

Definition at line 185 of file fe_values.h.

template<int dim, int spacedim = dim>
template<typename Number >
 using FEValuesViews::Scalar< dim, spacedim >::solution_gradient_type = typename ProductType::type

An alias for the data type of the product of a Number and the gradients of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number.

Definition at line 194 of file fe_values.h.

◆ solution_laplacian_type

template<int dim, int spacedim = dim>
template<typename Number >
 using FEValuesViews::Scalar< dim, spacedim >::solution_laplacian_type = typename ProductType::type

An alias for the data type of the product of a Number and the laplacians of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number.

Definition at line 204 of file fe_values.h.

◆ solution_hessian_type

template<int dim, int spacedim = dim>
template<typename Number >
 using FEValuesViews::Scalar< dim, spacedim >::solution_hessian_type = typename ProductType::type

An alias for the data type of the product of a Number and the hessians of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number.

Definition at line 214 of file fe_values.h.

◆ solution_third_derivative_type

template<int dim, int spacedim = dim>
template<typename Number >
 using FEValuesViews::Scalar< dim, spacedim >::solution_third_derivative_type = typename ProductType::type

An alias for the data type of the product of a Number and the third derivatives of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number.

Definition at line 224 of file fe_values.h.

◆ Scalar() [1/4]

template<int dim, int spacedim>
 FEValuesViews::Scalar< dim, spacedim >::Scalar

Default constructor. Creates an invalid object.

Definition at line 182 of file fe_values.cc.

◆ Scalar() [2/4]

template<int dim, int spacedim>
 FEValuesViews::Scalar< dim, spacedim >::Scalar ( const FEValuesBase< dim, spacedim > & fe_values_base, const unsigned int component )

Constructor for an object that represents a single scalar component of a FEValuesBase object (or of one of the classes derived from FEValuesBase).

Definition at line 145 of file fe_values.cc.

◆ Scalar() [3/4]

template<int dim, int spacedim = dim>
 FEValuesViews::Scalar< dim, spacedim >::Scalar ( const Scalar< dim, spacedim > & )
delete

Copy constructor. This is not a lightweight object so we don't allow copying and generate a compile-time error if this function is called.

◆ Scalar() [4/4]

template<int dim, int spacedim = dim>
 FEValuesViews::Scalar< dim, spacedim >::Scalar ( Scalar< dim, spacedim > && )
default

Move constructor.

◆ ~Scalar()

template<int dim, int spacedim = dim>
 FEValuesViews::Scalar< dim, spacedim >::~Scalar ( )
default

Destructor.

◆ operator=() [1/2]

template<int dim, int spacedim = dim>
 Scalar& FEValuesViews::Scalar< dim, spacedim >::operator= ( const Scalar< dim, spacedim > & )
delete

Copy operator. This is not a lightweight object so we don't allow copying and generate a compile-time error if this function is called.

◆ operator=() [2/2]

template<int dim, int spacedim = dim>
 Scalar& FEValuesViews::Scalar< dim, spacedim >::operator= ( Scalar< dim, spacedim > && )
defaultnoexcept

Move assignment operator.

◆ value()

template<int dim, int spacedim = dim>
 value_type FEValuesViews::Scalar< dim, spacedim >::value ( const unsigned int shape_function, const unsigned int q_point ) const

Return the value of the vector component selected by this view, for the shape function and quadrature point selected by the arguments.

Parameters
 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.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim = dim>
 gradient_type FEValuesViews::Scalar< dim, spacedim >::gradient ( const unsigned int shape_function, const unsigned int q_point ) const

Return the gradient (a tensor of rank 1) of the vector component selected by this view, for the shape function and quadrature point selected by the arguments.

Note
The meaning of the arguments is as documented for the value() function.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

◆ hessian()

template<int dim, int spacedim = dim>
 hessian_type FEValuesViews::Scalar< 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 component selected by this view, for the shape function and quadrature point selected by the arguments.

Note
The meaning of the arguments is as documented for the value() function.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

◆ third_derivative()

template<int dim, int spacedim = dim>
 third_derivative_type FEValuesViews::Scalar< 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 component selected by this view, for the shape function and quadrature point selected by the arguments.

Note
The meaning of the arguments is as documented for the value() function.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_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.

◆ get_function_values()

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

Return the values 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_values 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 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).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 1547 of file fe_values.cc.

◆ get_function_values_from_local_dof_values()

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_values_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_value_type< typename InputVector::value_type >> & values ) const

Same as above, but using a vector of local degree-of-freedom values. In other words, instead of extracting the nodal values of the degrees of freedom located on the current cell from a global vector associated with a DoFHandler object (as the function above does), this function instead takes these local nodal values through its first argument. A typical way to obtain such a vector is by calling code such as

cell->get_dof_values (dof_values, local_dof_values);

(See DoFCellAccessor::get_dof_values() for more information on this function.) The point of the current function is then that one could modify these local values first, for example 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.

Parameters
 [in] dof_values A vector of local nodal values. This vector must have a length equal to number of DoFs on the current cell, and must be ordered in the same order as degrees of freedom are numbered on the reference cell. [out] values A vector of values of the given finite element field, at the quadrature points on the current object.
Template Parameters
 InputVector The InputVector type must allow creation of an ArrayView object from it; this is satisfied by the std::vector class, among others.

Definition at line 1578 of file fe_values.cc.

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_gradients ( const InputVector & fe_function, std::vector< solution_gradient_type< typename InputVector::value_type >> & gradients ) const

Return the gradients 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_gradients 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 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).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 1602 of file fe_values.cc.

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_gradients_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_gradient_type< typename InputVector::value_type >> & gradients ) const

This function relates to get_function_gradients() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information.

Definition at line 1632 of file fe_values.cc.

◆ get_function_hessians()

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_hessians ( const InputVector & fe_function, std::vector< solution_hessian_type< typename InputVector::value_type >> & hessians ) const

Return the Hessians 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_hessians 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 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).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 1656 of file fe_values.cc.

◆ get_function_hessians_from_local_dof_values()

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_hessians_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_hessian_type< typename InputVector::value_type >> & hessians ) const

This function relates to get_function_hessians() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information.

Definition at line 1686 of file fe_values.cc.

◆ get_function_laplacians()

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

Return the Laplacians 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. 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 scalar component.

The data type stored by the output vector must be what you get when you multiply the Laplacians 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).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 1710 of file fe_values.cc.

◆ get_function_laplacians_from_local_dof_values()

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_laplacians_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_laplacian_type< typename InputVector::value_type >> & laplacians ) const

This function relates to get_function_laplacians() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information.

Definition at line 1740 of file fe_values.cc.

◆ get_function_third_derivatives()

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_third_derivatives ( const InputVector & fe_function, std::vector< solution_third_derivative_type< typename InputVector::value_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).

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_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 1764 of file fe_values.cc.

◆ get_function_third_derivatives_from_local_dof_values()

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesViews::Scalar< dim, spacedim >::get_function_third_derivatives_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_third_derivative_type< typename InputVector::value_type >> & third_derivatives ) const

This function relates to get_function_third_derivatives() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information.

Definition at line 1795 of file fe_values.cc.

◆ fe_values

template<int dim, int spacedim = dim>
 const SmartPointer > FEValuesViews::Scalar< dim, spacedim >::fe_values
private

A pointer to the FEValuesBase object we operate on.

Definition at line 629 of file fe_values.h.

◆ component

template<int dim, int spacedim = dim>
 const unsigned int FEValuesViews::Scalar< dim, spacedim >::component
private

The single scalar component this view represents of the FEValuesBase object.

Definition at line 635 of file fe_values.h.

◆ shape_function_data

template<int dim, int spacedim = dim>
 std::vector FEValuesViews::Scalar< dim, spacedim >::shape_function_data
private

Store the data about shape functions.

Definition at line 640 of file fe_values.h.

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