Kaskade::FunctionViews::Gradient< Function, asVector > Class Template Reference

Derivative of a given finite element function. More...

#include <functionviews.hh>

Detailed Description

template<typename Function, bool asVector = Function::components==1>
class Kaskade::FunctionViews::Gradient< Function, asVector >

Derivative of a given finite element function.

For a finite element function \( \Omega \subset \mathbb{R}^n \to \mathbb{R}^m \), this provides a function view with values in

• \( \mathbb{R}^{m} \) if \( m == 1 \)
• \( \mathbb{R}^{n\times m} \) if \( m > 1 \) and asVector==false
• \( \mathbb{R}^{nm} \) if \( m > 1 \) and asVector==true, with columns of \( f_x \) concatenated.

For more information on the construction of such views cf. FunctionViews

Definition at line 114 of file functionviews.hh.

Public Types
typedef Function::Space	Space
typedef Function::Scalar	Scalar
using	ValueType = std::conditional_t< asVector, Dune::FieldVector< Scalar, dim *m >, Dune::FieldMatrix< Scalar, m, dim > >

Public Member Functions
	Gradient (Function const &f_)
Space const &	space () const
template<class SFS >
int	order (SFS const &sfs) const
ValueType	value (typename Function::Space::Evaluator const &evaluator) const
	evaluates the derivative More...
template<class Cell , class Position >
ValueType	value (Cell const &cell, Position const &xi) const
	evaluates the derivative More...

Static Public Attributes
static int const	dim = Space::dim

Related Functions
(Note that these are not member functions.)
template<class Function >
Gradient< Function, false >	gradient (Function const &f)
	creates a function view of the gradient More...
template<class Function >
Gradient< Function, true >	gradientAsVector (Function const &f)
	creates a function view of the gradient More...

Member Typedef Documentation

Scalar

template<typename Function , bool asVector = Function::components==1>

typedef Function::Scalar Kaskade::FunctionViews::Gradient< Function, asVector >::Scalar

Definition at line 122 of file functionviews.hh.

Space

template<typename Function , bool asVector = Function::components==1>

typedef Function::Space Kaskade::FunctionViews::Gradient< Function, asVector >::Space

Definition at line 119 of file functionviews.hh.

ValueType

template<typename Function , bool asVector = Function::components==1>

using Kaskade::FunctionViews::Gradient< Function, asVector >::ValueType = std::conditional_t<asVector, Dune::FieldVector<Scalar,dim*m>, Dune::FieldMatrix<Scalar,m,dim> >

Definition at line 125 of file functionviews.hh.

Constructor & Destructor Documentation

Gradient()

template<typename Function , bool asVector = Function::components==1>

Kaskade::FunctionViews::Gradient< Function, asVector >::Gradient ( Function const &  f_ )

inline

Definition at line 128 of file functionviews.hh.

Member Function Documentation

order()

template<typename Function , bool asVector = Function::components==1>

template<class SFS >

int Kaskade::FunctionViews::Gradient< Function, asVector >::order ( SFS const &  sfs ) const

inline

Definition at line 137 of file functionviews.hh.

space()

template<typename Function , bool asVector = Function::components==1>

Space const & Kaskade::FunctionViews::Gradient< Function, asVector >::space ( ) const

inline

Definition at line 131 of file functionviews.hh.

value() [1/2]

template<typename Function , bool asVector = Function::components==1>

template<class Cell , class Position >

ValueType Kaskade::FunctionViews::Gradient< Function, asVector >::value ( Cell const &  cell, Position const &  xi  ) const

inline

evaluates the derivative

Returns

for scalar functions, a derivative vector, for vectorial components, the Jacobian

Definition at line 156 of file functionviews.hh.

value() [2/2]

template<typename Function , bool asVector = Function::components==1>

ValueType Kaskade::FunctionViews::Gradient< Function, asVector >::value ( typename Function::Space::Evaluator const &  evaluator ) const

inline

evaluates the derivative

Returns

for scalar functions, a derivative vector, for vectorial components, the Jacobian

Definition at line 146 of file functionviews.hh.

Member Data Documentation

dim

template<typename Function , bool asVector = Function::components==1>

int const Kaskade::FunctionViews::Gradient< Function, asVector >::dim = Space::dim

static

Definition at line 120 of file functionviews.hh.

---

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

• functionviews.hh