Reference documentation for deal.II version GIT relicensing-43-g3fc2fae7c3 2024-03-03 21:10:02+00:00
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Classes | Public Types | Public Member Functions | Private Attributes | List of all members

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

Classes

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 >
using solution_gradient_type = typename ProductType< Number, gradient_type >::type
 
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
 
gradient_type gradient (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<typename Number >
void get_function_values (const ReadVector< Number > &fe_function, std::vector< solution_value_type< Number > > &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<typename Number >
void get_function_gradients (const ReadVector< Number > &fe_function, std::vector< solution_gradient_type< Number > > &gradients) const
 
template<class InputVector >
void get_function_gradients_from_local_dof_values (const InputVector &dof_values, std::vector< solution_gradient_type< typename InputVector::value_type > > &gradients) const
 
template<typename Number >
void get_function_hessians (const ReadVector< Number > &fe_function, std::vector< solution_hessian_type< Number > > &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<typename Number >
void get_function_laplacians (const ReadVector< Number > &fe_function, std::vector< solution_laplacian_type< Number > > &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<typename Number >
void get_function_third_derivatives (const ReadVector< Number > &fe_function, std::vector< solution_third_derivative_type< Number > > &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

SmartPointer< const FEValuesBase< dim, spacedim > > fe_values
 
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 125 of file fe_values_views.h.

Member Typedef Documentation

◆ 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 133 of file fe_values_views.h.

◆ gradient_type

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 140 of file fe_values_views.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 147 of file fe_values_views.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 154 of file fe_values_views.h.

◆ solution_value_type

template<int dim, int spacedim = dim>
template<typename Number >
using FEValuesViews::Scalar< dim, spacedim >::solution_value_type = typename ProductType<Number, value_type>::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 163 of file fe_values_views.h.

◆ solution_gradient_type

template<int dim, int spacedim = dim>
template<typename Number >
using FEValuesViews::Scalar< dim, spacedim >::solution_gradient_type = typename ProductType<Number, gradient_type>::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 172 of file fe_values_views.h.

◆ solution_laplacian_type

template<int dim, int spacedim = dim>
template<typename Number >
using FEValuesViews::Scalar< dim, spacedim >::solution_laplacian_type = typename ProductType<Number, value_type>::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 182 of file fe_values_views.h.

◆ solution_hessian_type

template<int dim, int spacedim = dim>
template<typename Number >
using FEValuesViews::Scalar< dim, spacedim >::solution_hessian_type = typename ProductType<Number, hessian_type>::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 192 of file fe_values_views.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<Number, third_derivative_type>::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 202 of file fe_values_views.h.

Constructor & Destructor Documentation

◆ Scalar() [1/4]

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

Default constructor. Creates an invalid object.

Definition at line 106 of file fe_values_views.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 69 of file fe_values_views.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.

Member Function Documentation

◆ 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_functionNumber 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_pointNumber of the quadrature point at which function is to be evaluated.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_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()

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<typename Number >
void FEValuesViews::Scalar< dim, spacedim >::get_function_values ( const ReadVector< Number > &  fe_function,
std::vector< solution_value_type< Number > > &  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 361 of file fe_values_views.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_valuesA 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]valuesA vector of values of the given finite element field, at the quadrature points on the current object.
Template Parameters
InputVectorThe InputVector type must allow creation of an ArrayView object from it; this is satisfied by the std::vector class, among others.

Definition at line 388 of file fe_values_views.cc.

◆ get_function_gradients()

template<int dim, int spacedim>
template<typename Number >
void FEValuesViews::Scalar< dim, spacedim >::get_function_gradients ( const ReadVector< Number > &  fe_function,
std::vector< solution_gradient_type< Number > > &  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 412 of file fe_values_views.cc.

◆ get_function_gradients_from_local_dof_values()

template<int dim, int spacedim>
template<typename 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 440 of file fe_values_views.cc.

◆ get_function_hessians()

template<int dim, int spacedim>
template<typename Number >
void FEValuesViews::Scalar< dim, spacedim >::get_function_hessians ( const ReadVector< Number > &  fe_function,
std::vector< solution_hessian_type< Number > > &  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 464 of file fe_values_views.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 492 of file fe_values_views.cc.

◆ get_function_laplacians()

template<int dim, int spacedim>
template<typename Number >
void FEValuesViews::Scalar< dim, spacedim >::get_function_laplacians ( const ReadVector< Number > &  fe_function,
std::vector< solution_laplacian_type< Number > > &  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 516 of file fe_values_views.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 544 of file fe_values_views.cc.

◆ get_function_third_derivatives()

template<int dim, int spacedim>
template<typename Number >
void FEValuesViews::Scalar< dim, spacedim >::get_function_third_derivatives ( const ReadVector< Number > &  fe_function,
std::vector< solution_third_derivative_type< Number > > &  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 568 of file fe_values_views.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 597 of file fe_values_views.cc.

Member Data Documentation

◆ fe_values

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

A pointer to the FEValuesBase object we operate on.

Definition at line 551 of file fe_values_views.h.

◆ component

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

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

Definition at line 557 of file fe_values_views.h.

◆ shape_function_data

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

Store the data about shape functions.

Definition at line 562 of file fe_values_views.h.


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