GridFunctions

Convenience classes in order to form Fem::Function objects for analytical functions. More...

Modules
	Building Blocks
	A couple of elementary grid functions which can be combined using GridFunctionExpressions.
	BoundaryFunctions
	Combine ordinary GridFunctions with BoundaryIndicators in order to support "complicated" boundary conditions.
	GridFunctionWrapper
	Augment global functions by a HasLocalFunction property.
	GridFunctionTests

Classes
class	Dune::ACFem::ConstantFunction< FunctionSpace >
	A class describing a constant function. More...
class	Dune::ACFem::ConstantGridFunction< FunctionSpace, GridPart >
	ConstantGridFunction implements a constant function. More...
class	Dune::ACFem::ZeroGridFunction< FunctionSpace, GridPart >
	A grid-function always returning 0. More...
struct	Dune::ACFem::ZeroGridFunctionTraits< FunctionSpace, GridPart >
	A grid-function tight to zero. More...
class	Dune::ACFem::FractionGridFunction< FunctionSpace, GridPart, numerator, denominator >
	A grid-function which is constant with a scalar fractional value. More...
struct	Dune::ACFem::FractionGridFunctionTraits< FunctionSpace, GridPart, numerator, denominator >
	A grid-function which is constant with a fractional value. More...
class	Dune::ACFem::IdentityFunction< Field, dim >
	A function which returns its argument. More...
class	Dune::ACFem::CoordinateFunction< Field, dim, N >
	Coordinate function returns a specific component of the world point, x_N, so to say. More...
class	Dune::ACFem::LocalMaxAdapter< GridFunction1, GridFunction2 >
	An adapter class to compute the (pointwise) maximum of two scalar GridFunctions. More...
class	Dune::ACFem::LocalNormAdapter< GridFunction, 2 >
	An adapter class to represent the pointwise euclidean norm of a (usually vector-valued) GridFunction. More...
class	Dune::ACFem::ParameterFunction< Parameter, FunctionSpace >
	A class describing a constant function. More...
class	Dune::ACFem::ParameterGridFunction< Parameter, FunctionSpace, GridPart >
	ParameterGridFunction implements a constant function where the value is defined by something which fulfills the ParameterInterface. More...

Typedefs
typedef F::EntityType	Dune::ACFem::BoundaryFunctionTraits< F, false >::EntityType
	Type of Entity.
typedef GridPartType::IntersectionType	Dune::ACFem::BoundaryFunctionTraits< F, false >::IntersectionType
	Type of Intersection.
typedef LocalFunction	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunctionType
	Type of local function to export.
typedef std::decay< decltype(*std::declval< Indicator >) &&*std::declval< InnerIndicatorType >))>::type	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::IndicatorType
	Resulting Boundary indicator type.
typedef GridFunction	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::GridFunctionType
	Type of wrapped grid-function.
typedef DiscreteFunctionSpaceType::GridType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::GridType
	type of grid
typedef DiscreteFunctionSpaceType::DomainFieldType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::DomainFieldType
	domain type (from function space)
typedef DiscreteFunctionSpaceType::RangeFieldType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::RangeFieldType
	range type (from function space)
typedef DiscreteFunctionSpaceType::DomainType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::DomainType
	domain type (from function space)
typedef DiscreteFunctionSpaceType::RangeType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::RangeType
	range type (from function space)
typedef DiscreteFunctionSpaceType::JacobianRangeType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::JacobianRangeType
	jacobian type (from function space)
typedef DiscreteFunctionSpaceType::HessianRangeType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::HessianRangeType
	hessian type (from function space)
typedef DiscreteFunctionSpaceType::DomainFieldType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::DomainFieldType
	domain type (from function space)
typedef DiscreteFunctionSpaceType::RangeFieldType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::RangeFieldType
	range type (from function space)
typedef DiscreteFunctionSpaceType::DomainType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::DomainType
	domain type (from function space)
typedef DiscreteFunctionSpaceType::RangeType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::RangeType
	range type (from function space)
typedef DiscreteFunctionSpaceType::JacobianRangeType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::JacobianRangeType
	jacobian type (from function space)
typedef DiscreteFunctionSpaceType::HessianRangeType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::HessianRangeType
	hessian type (from function space)

Enumerations
enum	{ Dune::ACFem::BoundaryFunctionTraits< F, true >::hasBoundarySupport = true }
enum	{ Dune::ACFem::BoundaryFunctionTraits< F, false >::hasBoundarySupport = false }
enum	{ Dune::ACFem::BoundaryFunctionTraits< F, false >::emptySupport = false , Dune::ACFem::BoundaryFunctionTraits< F, false >::globalSupport = true }

Functions
static void	Dune::ACFem::BoundaryFunctionTraits< F, true >::init (LocalFunctionType &lf, const EntityType &entity, const IntersectionType &intersection)
	For BoundarySupportedFunction's we pass the intersection as well as the bulk entity on to the local function's init-method. More...
static bool	Dune::ACFem::BoundaryFunctionTraits< F, true >::supported (const LocalFunctionType &lf)
	Decide if we are supported on this IntersectionType. More...
static F::IndicatorType	Dune::ACFem::BoundaryFunctionTraits< F, true >::indicator (const F &f)
	Return the underlying BoundarySupportedFunction's indicator.
static void	Dune::ACFem::BoundaryFunctionTraits< F, false >::init (LocalFunctionType &lf, const EntityType &entity, const IntersectionType &intersection)
	Call the ordinary init-method for not BoundarySupportedFunction's.
static bool	Dune::ACFem::BoundaryFunctionTraits< F, false >::supported (const LocalFunctionType &lf)
	Not boundary-supported: implicity everywhere supported.
static IndicatorType	Dune::ACFem::BoundaryFunctionTraits< F, false >::indicator (const F &ignored)
	Not boundary-supported: implicity everywhere supported.
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::evaluate (const DomainType &global, RangeType &result) const
	evaluate function on local coordinate local
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::jacobian (const DomainType &global, JacobianRangeType &result) const
	evaluate function on local coordinate local
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::hessian (const DomainType &global, HessianRangeType &result) const
	evaluate function on local coordinate local
const LocalFunctionType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction (const EntityType &entity) const
	Generate an ordinary local-function object which is ignorant of the value of the boundary-indicator, but supplies an init() method which can be used to make it indicator aware. More...
LocalFunctionType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction (const EntityType &entity)
	Generate an ordinary local-function object which is ignorant of the value of the boundary-indicator, but supplies an init() method which can be used to make it indicator aware. More...
const LocalFunctionType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction (const EntityType &entity, const IntersectionType &intersection) const
	Initialize a wrapped local function object for the given intersection. More...
LocalFunctionType	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction (const EntityType &entity, const IntersectionType &intersection)
	Initialize a wrapped local function object for the given intersection. More...
	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::LocalFunction (const EntityType &entity, const DiscreteFunctionType &df)
	Bulk entity constructor.
	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::LocalFunction (const DiscreteFunctionType &df)
	Bulk entity constructor.
	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::LocalFunction (const EntityType &entity, const IntersectionType &intersection, const DiscreteFunctionType &df)
	Boundary intersection constructor.
template<class PointType >
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::evaluate (const PointType &x, RangeType &ret) const
	Evaluate local function. More...
template<class PointType >
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::jacobian (const PointType &x, JacobianRangeType &ret) const
	Evaluate Jacobian of local function. More...
template<class PointType >
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::hessian (const PointType &x, HessianRangeType &ret) const
	Evaluate Hessian of local function. More...
template<class QuadratureType , class VectorType >
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::evaluateQuadrature (const QuadratureType &quadrature, VectorType &values) const
	evaluate function or jacobian of function for given quadrature
int	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::order () const
	Return a bound on or suggestion for the piece-wise polynomial order.
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::init (const EntityType &entity)
	Bulk-entity initialization.
void	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::init (const EntityType &entity, const IntersectionType &isect)
	Intersection initialization.
bool	Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::supported () const
	Return true if potentially non-zero. More...
template<class GridFunction1 , class GridFunction2 >
LocalFunctionWrapper< LocalMaxAdapter< GridFunction1, GridFunction2 >, typename GridFunction1::GridPartType >	Dune::ACFem::max (const Fem::Function< typename GridFunction1::FunctionSpaceType, GridFunction1 > &f1, const Fem::Function< typename GridFunction2::FunctionSpaceType, GridFunction2 > &f2, const std::string &name="")
	Pointwise maximum of two given functions.
template<class GridFunction1 >
LocalFunctionWrapper< LocalMaxAdapter< GridFunction1, ConstantGridFunction< typename GridFunction1::FunctionSpaceType, typename GridFunction1::GridPartType > >, typename GridFunction1::GridPartType >	Dune::ACFem::max (const Fem::Function< typename GridFunction1::FunctionSpaceType, GridFunction1 > &f1, const typename GridFunction1::FunctionSpaceType::RangeType value2, const std::string &name="")
	Pointwise maximum of two given functions where one is given by a RangeType value.
template<class GridFunction >
LocalFunctionWrapper< LocalNormAdapter< GridFunction, 2 >, typename GridFunction::GridPartType >	Dune::ACFem::twoNorm (const Fem::Function< typename GridFunction::FunctionSpaceType, GridFunction > &f, const std::string &name="")
	Pointwise euclidean norm of a given function.

Detailed Description

Convenience classes in order to form Fem::Function objects for analytical functions.

This extends the Fem::GridFunctionAdapter and forms also copyable function objects which then can conveniently be inserted into expression templates. See GridFunctionExpressions.

Enumeration Type Documentation

anonymous enum

template<class F >

anonymous enum

Enumerator
hasBoundarySupport	Yes, we have!

anonymous enum

template<class F >

anonymous enum

Enumerator
hasBoundarySupport	Not exclusively boundary-supported.

anonymous enum

template<class F >

anonymous enum

Enumerator
emptySupport	Support is everywhere.
globalSupport	Support is everywhere.

Function Documentation

evaluate()

template<class GridFunction , class Indicator >

template<class PointType >

void Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::evaluate ( const PointType &  x, RangeType &  ret  ) const

inline

Evaluate local function.

Evaluate to zero if the boundary indicator does not apply. If emptySupport == true then always evaluate to zero.

hessian()

template<class GridFunction , class Indicator >

template<class PointType >

void Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::hessian ( const PointType &  x, HessianRangeType &  ret  ) const

inline

Evaluate Hessian of local function.

Evaluate to zero if the boundary indicator does not apply. If emptySupport == true then always evaluate to zero.

init()

template<class F >

static void Dune::ACFem::BoundaryFunctionTraits< F, true >::init ( LocalFunctionType &  lf, const EntityType &  entity, const IntersectionType &  intersection  )

inlinestatic

For BoundarySupportedFunction's we pass the intersection as well as the bulk entity on to the local function's init-method.

Note that passing intersection.inside() is inherently dangerous as that is only a copy.

jacobian()

template<class GridFunction , class Indicator >

template<class PointType >

void Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::jacobian ( const PointType &  x, JacobianRangeType &  ret  ) const

inline

Evaluate Jacobian of local function.

Evaluate to zero if the boundary indicator does not apply. If emptySupport == true then always evaluate to zero.

localFunction() [1/4]

template<class GridFunction , class Indicator >

LocalFunctionType Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction ( const EntityType &  entity )

inline

Generate an ordinary local-function object which is ignorant of the value of the boundary-indicator, but supplies an init() method which can be used to make it indicator aware.

better call localFunction(const IntersectionTyp&) directly.

localFunction() [2/4]

template<class GridFunction , class Indicator >

const LocalFunctionType Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction ( const EntityType &  entity ) const

inline

Generate an ordinary local-function object which is ignorant of the value of the boundary-indicator, but supplies an init() method which can be used to make it indicator aware.

better call localFunction(const IntersectionTyp&) directly.

Referenced by gridWalkTest().

localFunction() [3/4]

template<class GridFunction , class Indicator >

LocalFunctionType Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction ( const EntityType &  entity, const IntersectionType &  intersection  )

inline

Initialize a wrapped local function object for the given intersection.

The resulting LocalFunction object will take the boundary indicator value into account.

localFunction() [4/4]

template<class GridFunction , class Indicator >

const LocalFunctionType Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::localFunction ( const EntityType &  entity, const IntersectionType &  intersection  ) const

inline

Initialize a wrapped local function object for the given intersection.

The resulting LocalFunction object will take the boundary indicator value into account.

supported() [1/2]

template<class GridFunction , class Indicator >

bool Dune::ACFem::BoundarySupportedFunction< GridFunction, Indicator >::LocalFunction::supported ( ) const

inline

Return true if potentially non-zero.

The state may be undefined unless init(const IntersectionType&) or the proper intersection initializer has been called. At any rate, if globalSupport == true then true is returned. If emptySupport == true then false is returned.

supported() [2/2]

template<class F >

static bool Dune::ACFem::BoundaryFunctionTraits< F, true >::supported ( const LocalFunctionType &  lf )

inlinestatic

Decide if we are supported on this IntersectionType.

Optimized for global/empty support.