Building Blocks

A couple of elementary grid functions which can be combined using GridFunctionExpressions. More...

Classes
struct	Dune::ACFem::X< N >
	Used as "tag" for coordinateGridFunction() and coordinateVectorFunction(). More...

Functions
template<class GridPart >
static auto	Dune::ACFem::identityGridFunction (const GridPart &gridPart)
	A grid-function which returns the world coordinates of its argument. More...
template<class GridPart , unsigned N>
static auto	Dune::ACFem::coordinateGridFunction (const GridPart &gridPart, const std::integral_constant< unsigned, N > &dummy)
	A grid-function which returns the N-th component of the world coordinates of its argument. More...
template<class GridPart , unsigned N>
static ConstantGridFunction< Fem::FunctionSpace< typename GridPart::ctype, typename GridPart::ctype, GridPart::dimensionworld, GridPart::dimensionworld >, GridPart >	Dune::ACFem::coordinateVectorFunction (const GridPart &gridPart, const std::integral_constant< unsigned, N > &dummy)
	Construct a unit coordinate vector.
template<class GridFunction >
LocalFunctionWrapper< LocalDivergenceAdapter< GridFunction >, typename GridFunction::GridPartType >	Dune::ACFem::divergence (const Fem::Function< typename GridFunction::FunctionSpaceType, GridFunction > &f_, const std::string &name="")
	Take the divergence of a given function.
template<class GridFunction >
LocalFunctionWrapper< LocalGradientAdapter< GridFunction >, typename GridFunction::GridPartType >	Dune::ACFem::gradient (const Fem::Function< typename GridFunction::FunctionSpaceType, GridFunction > &f_, const std::string &name="")
	Take the gradient of a given function.
template<class CharacteristicFunction , class GridFunction0 , class GridFunction1 >
LocalFunctionWrapper< LocalPiecewiseAdapter< CharacteristicFunction, GridFunction0, GridFunction1 >, typename GridFunction0::GridPartType >	Dune::ACFem::piecewise (const Fem::Function< typename CharacteristicFunction::FunctionSpaceType, CharacteristicFunction > &characteristic, const Fem::Function< typename GridFunction0::FunctionSpaceType, GridFunction0 > &function0, const Fem::Function< typename GridFunction1::FunctionSpaceType, GridFunction1 > &function1, const std::string &name="")
	Form a piecewise defined function where the domain decomposition is defined by the indicator function of one of the sub-domains. More...
template<class CharacteristicFunction , class GridFunction1 >
LocalFunctionWrapper< LocalPiecewiseAdapter< CharacteristicFunction, ConstantGridFunction< typename GridFunction1::FunctionSpaceType, typename GridFunction1::GridPartType >, GridFunction1 >, typename GridFunction1::GridPartType >	Dune::ACFem::piecewise (const Fem::Function< typename CharacteristicFunction::FunctionSpaceType, CharacteristicFunction > &characteristic, const typename GridFunction1::FunctionSpaceType::RangeType value0, const Fem::Function< typename GridFunction1::FunctionSpaceType, GridFunction1 > &function1, const std::string &name="")
	specialization for GridFunction0 of RangeType
template<class CharacteristicFunction , class GridFunction0 >
LocalFunctionWrapper< LocalPiecewiseAdapter< CharacteristicFunction, GridFunction0, ConstantGridFunction< typename GridFunction0::FunctionSpaceType, typename GridFunction0::GridPartType > >, typename GridFunction0::GridPartType >	Dune::ACFem::piecewise (const Fem::Function< typename CharacteristicFunction::FunctionSpaceType, CharacteristicFunction > &characteristic, const Fem::Function< typename GridFunction0::FunctionSpaceType, GridFunction0 > &function0, const typename GridFunction0::FunctionSpaceType::RangeType value1, const std::string &name="")
	specialization for GridFunction1 of RangeType
template<class CharacteristicFunction , class FunctionSpaceType >
LocalFunctionWrapper< LocalPiecewiseAdapter< CharacteristicFunction, ConstantGridFunction< FunctionSpaceType, typename CharacteristicFunction::GridPartType >, ConstantGridFunction< FunctionSpaceType, typename CharacteristicFunction::GridPartType > >, typename CharacteristicFunction::GridPartType >	Dune::ACFem::piecewise (const Fem::Function< typename CharacteristicFunction::FunctionSpaceType, CharacteristicFunction > &characteristic, const typename FunctionSpaceType::RangeType value0, const typename FunctionSpaceType::RangeType value1, const std::string &name="")
	specialization for GridFunction0 and GridFunction1 of RangeType
template<class GridFunction , class Indicator = EntireBoundaryIndicatorType>
BoundarySupportedFunction< GridFunction, Indicator >	Dune::ACFem::boundarySupportedFunction (const Fem::Function< typename GridFunction::FunctionSpaceType, GridFunction > &f, const BoundaryIndicatorInterface< Indicator > &c=EntireBoundaryIndicatorType())
	Generate a function with partial support on the boundary.
template<class GridFunction , class Indicator >
BoundarySupportedFunction< GridFunction, Indicator >	Dune::ACFem::boundarySupportedFunction (const BoundarySupportedFunction< GridFunction, Indicator > &f, const EntireBoundaryIndicatorType &=EntireBoundaryIndicatorType())
	Avoid re-wrapping.
template<class OperatorParts , class Solution >
LocalFunctionWrapper< LocalRightHandSideAdapter< OperatorParts, Solution >, typename Solution::GridPartType >	Dune::ACFem::rightHandSide (const OperatorPartsInterface< OperatorParts > &operatorParts, const Fem::Function< typename Solution::FunctionSpaceType, Solution > &solution_, const std::string &name="")
	Take any PDE operatorparts and an "exact solutio" and generate a right-hand-side force-density such that the PDE-operatorparts should reproduce the given "solution" – provided that the boundary conditions match also ...

Detailed Description

A couple of elementary grid functions which can be combined using GridFunctionExpressions.

Convenience funtions to aid in the construction of elementary function "atoms".

Function Documentation

coordinateGridFunction()

template<class GridPart , unsigned N>

static auto Dune::ACFem::coordinateGridFunction ( const GridPart &  gridPart, const std::integral_constant< unsigned, N > &  dummy  )

inlinestatic

A grid-function which returns the N-th component of the world coordinates of its argument.

See als IdentityGridFunction.

References Dune::ACFem::wrapToGridFunction().

Referenced by main().

identityGridFunction()

template<class GridPart >

static auto Dune::ACFem::identityGridFunction ( const GridPart &  gridPart )

inlinestatic

A grid-function which returns the world coordinates of its argument.

This can be used to conveniently define more complicated data-functions for bulk forces and the like, e.g.

IdentityGridFunction<GridPartType> X(gridPart);
CoordinateGridFunction<GridPartType, 0> X0(gridPart);
 
auto f = exp(10.0 * X * X) + sin(3.0 * X0 - 5.)

The resulting function object is in so far efficient as the GridFunctionExpression templates take care of the computation of the global coordinates; X will only be computed a single time.

References Dune::ACFem::wrapToGridFunction().

Referenced by main().

piecewise()

template<class CharacteristicFunction , class GridFunction0 , class GridFunction1 >

LocalFunctionWrapper< LocalPiecewiseAdapter< CharacteristicFunction, GridFunction0, GridFunction1 >, typename GridFunction0::GridPartType > Dune::ACFem::piecewise	(	const Fem::Function< typename CharacteristicFunction::FunctionSpaceType, CharacteristicFunction > &	characteristic,
		const Fem::Function< typename GridFunction0::FunctionSpaceType, GridFunction0 > &	function0,
		const Fem::Function< typename GridFunction1::FunctionSpaceType, GridFunction1 > &	function1,
		const std::string &	name = ""
	)

Form a piecewise defined function where the domain decomposition is defined by the indicator function of one of the sub-domains.

Parameters

[in]	characteristic	The indicitor function of the sub-domain where function1 defines the function values. characteristic may either be an analytic function or a grid-function.
[in]	function0	A grid-function defining the values of the compound-function where characteristic evaluates to less or equal than 0.5.
[in]	function1	A grid function defining the values of the compound-function where characteristic evaluates to greater than 0.5.

Returns

A LocalFunctionWrapper for the piecewise defined function.

References Dune::ACFem::max().

Referenced by main().