Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits > Class Template Reference

A wrapper representing the pullback of a grid function wrt a grid morphism. More...

#include <dune/fufem/functions/pullbackfunction.hh>

Public Types
using	GridView = typename GridMorphism::Inverse::GridView< RawGridView >
using	EntitySet = Dune::Functions::GridViewEntitySet< GridView, 0 >
using	Element = typename EntitySet::Element
using	Domain = typename EntitySet::GlobalCoordinate
using	LocalDomain = typename EntitySet::LocalCoordinate
using	Range = std::decay_t< decltype(std::declval< RawGridFunction >()(std::declval< RawDomain >()))>
using	LocalFunction = PullBackLocalFunction

Public Member Functions
	PullBackFunction (GridFunction function, GridMorphism morphism)
	Create PullBackFunction from GridFunction and GridMorphism.
Range	operator() (const Domain &x) const
	Evaluate function in global coordinates.
const EntitySet &	entitySet () const
	Return the EntitySet associated to this GridViewFunction.

Friends
auto	derivative (const PullBackFunction &f)
	Obtain global derivative of this function.
LocalFunction	localFunction (const PullBackFunction &f)
	Create a LocalFunction for evaluation in local coordinates.

Detailed Description

template<class GridFunction, class GridMorphism, template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>
class Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >

A wrapper representing the pullback of a grid function wrt a grid morphism.

Template Parameters

GridFunction	Type of the wrapped grid function
GridMorphism	The morphism from source grid to target grid

Let \( M : G_S \to G_T \) be a morphism between a source grid \(G_S\) and a target grid \(G_T\), i.e., \(M\) translates entities and gridviews of the source grid \(G_S\) to entities and gridviews of the target grid \(G_T\). Furthermore let \(f_T:G_T \to R\) be a grid function on the target grid \(G_T\) with some range \(R\). Then the morphism induces a grid function \(f_S = M^*f_T = f_T\circ M :G_S \to R\) which is denoted the pullback (in the sense of precomposition) of \(f_T\) with respect to \(M\). This class implements \(f_S\) for given \(f_T\) and \(M\).

A GridMorphism object morphism has to support the following operations to translate from source grid to target grid:

GridMorphism::Grid                     // Type of target grid
GridMorphism::GridView<SourceGridView> // Type of target gridview corresponding to source gridview
GridMorphism::Inverse                  // Type of inverse morphism
morphism.gridView(sourceGridView)      // Obtain target gridview from source gridview
morphism.entity(sourceEntity)          // Obtain target grid entity from source grid entity
morphism.inverse()                     // Obtain inverse morphism

Note

In case that the domains of \(G_S\) and \(G_T\) are smooth manifolds and that \(M\) corresponds to a diffeomorphism between these manifolds, the function \(f_S\) is denoted the pullback of \(f_T\) with respect to the diffeomorphism. Here we generalize this notation to the potentially nonsmooth case.

Note

While we consider abstract morphisms between grid objects, this should not be confused with the fiber product in category theory which is also denoted as pullback.

Member Typedef Documentation

Domain

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

using Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::Domain = typename EntitySet::GlobalCoordinate

Element

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

using Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::Element = typename EntitySet::Element

EntitySet

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

using Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::EntitySet = Dune::Functions::GridViewEntitySet<GridView, 0>

GridView

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

using Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::GridView = typename GridMorphism::Inverse::GridView<RawGridView>

LocalDomain

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

using Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::LocalDomain = typename EntitySet::LocalCoordinate

LocalFunction

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

using Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::LocalFunction = PullBackLocalFunction

Range

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

using Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::Range = std::decay_t<decltype(std::declval<RawGridFunction>()(std::declval<RawDomain>()))>

Constructor & Destructor Documentation

PullBackFunction()

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::PullBackFunction ( GridFunction  function, GridMorphism  morphism  )

inline

Create PullBackFunction from GridFunction and GridMorphism.

Parameters

function	The GridFunction that should be represented on gridView
morphism	The GridMorphism translating grid quantities

Notice that both arguments are stored by value.

Member Function Documentation

entitySet()

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

const EntitySet & Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::entitySet ( ) const

inline

Return the EntitySet associated to this GridViewFunction.

operator()()

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

Range Dune::Fufem::Experimental::PullBackFunction< GridFunction, GridMorphism, DerivativeTraits >::operator() ( const Domain &  x ) const

inline

Evaluate function in global coordinates.

Note

This is not implemented and will throw an exception.

Friends And Related Symbol Documentation

derivative

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

auto derivative ( const PullBackFunction< GridFunction, GridMorphism, DerivativeTraits > &  f )

friend

Obtain global derivative of this function.

localFunction

template<class GridFunction , class GridMorphism , template< class > class DerivativeTraits = Dune::Functions::DefaultDerivativeTraits>

LocalFunction localFunction ( const PullBackFunction< GridFunction, GridMorphism, DerivativeTraits > &  f )

friend

Create a LocalFunction for evaluation in local coordinates.

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

• pullbackfunction.hh