Defines GridFunctions to be used in operators, boundary-conditions, interpolation and integration. More...

Classes
class	AnalyticGridFunction< Function, GridView >
	A Gridfunction that evaluates a function with global coordinates. More...

class	ConstantGridFunction< T, GridView >
	Gridfunction returning a constant value. More...

class	DerivativeGridFunction< GridFunction, Type >
	A Gridfunction that returns the derivative when calling localFunction. More...

class	DiscreteFunction< Coeff, GB, TreePath >
	A mutable view on the subspace of a DOFVector,. More...

class	FunctorGridFunction< Functor, GridFunctions >
	A Gridfunction that applies a functor to the evaluated Gridfunctions. More...

Functions
template<class Expr >
auto	gradientOf (Expr const &expr)

template<class PreGridFct , class GridView >
decltype(auto)	makeGridFunction (PreGridFct const &preGridFct, GridView const &gridView)
	Generator for Gridfunctions from Expressions (PreGridfunctions) More...

template<class T , REQUIRES(Concepts::AnyGridFunction< T >) >
auto	abs (T &&value)

template<class Functor , class... PreGridFcts>
auto	invokeAtQP (Functor const &f, PreGridFcts &&... gridFcts)
	Generator function for FunctorGridFunction. More...

template<class Lhs , REQUIRES(Concepts::AnyGridFunction< Lhs >) >
auto	operator- (Lhs &&lhs)
	Applies Operation::Negate to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	operator+ (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::Plus to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	operator- (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::Minus to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	operator* (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::Multiplies to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	operator/ (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::Divides to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	max (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::Max to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	min (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::Min to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	abs_max (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::AbsMax to GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	abs_min (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::AbsMin to GridFunctions. More...

template<class V , class T , REQUIRES(Concepts::AnyGridFunction< V >) >
auto	clamp (V &&v, T const &lo, T const &hi)
	Applies Operation::Clamp to GridFunction. More...

template<class T , REQUIRES(Concepts::AnyGridFunction< T >) >
auto	sqr (T &&value)
	Applies Operation::Sqr to GridFunction. More...

template<int p, class T , REQUIRES(Concepts::AnyGridFunction< T >) >
auto	pow (T &&value)
	Applies Operation::Pow. More...

template<class T , REQUIRES(Concepts::AnyGridFunction< T >) >
auto	pow (T &&value, int p)
	Applies Operation::Pow_ to GridFunction. More...

template<std::size_t I, class T , REQUIRES(Concepts::AnyGridFunction< T >) >
auto	get (T &&value)
	Applies Operation::Get<I> to GridFunction. More...

template<class T , REQUIRES(Concepts::AnyGridFunction< T >) >
auto	get (T &&value, std::size_t i)
	Applies Operation::Get_ to GridFunction. More...

template<class Vec , REQUIRES(Concepts::AnyGridFunction< Vec >) >
auto	sum (Vec &&vec)
	Applies a sum() functor to a vector-valued GridFunction. More...

template<class Vec , REQUIRES(Concepts::AnyGridFunction< Vec >) >
auto	unary_dot (Vec &&vec)
	Applies Operation::UnaryDot to a vector-valued GridFunction. More...

template<class Vec , REQUIRES(Concepts::AnyGridFunction< Vec >) >
auto	one_norm (Vec &&vec)
	Applies a one_norm() functor to a vector-valued GridFunction. More...

template<class Vec , REQUIRES(Concepts::AnyGridFunction< Vec >) >
auto	two_norm (Vec &&vec)
	Applies Operation::TwoNorm to a vector-valued GridFunction. More...

template<int p, class Vec , REQUIRES(Concepts::AnyGridFunction< Vec >) >
auto	p_norm (Vec &&vec)
	Applies a p_norm() functor to a vector-valued GridFunction. More...

template<class Vec , REQUIRES(Concepts::AnyGridFunction< Vec >) >
auto	infty_norm (Vec &&vec)
	Applies a infty_norm() functor to a vector-valued GridFunction. More...

template<class Mat , REQUIRES(Concepts::AnyGridFunction< Mat >) >
auto	trans (Mat &&mat)
	Applies Operation::Trans to a matrix-valued GridFunction. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	dot (Lhs &&lhs, Rhs &&rhs)
	Applies Operation::Dot to two vector-valued GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	distance (Lhs &&lhs, Rhs &&rhs)
	Applies a distance-functor to two vector-valued GridFunctions. More...

template<class Lhs , class Rhs , REQUIRES(Concepts::AnyGridFunction< Lhs, Rhs >) >
auto	outer (Lhs &&lhs, Rhs &&rhs)
	Applies an outer() functor to two vector-valued GridFunctions. More...

Detailed Description

Defines GridFunctions to be used in operators, boundary-conditions, interpolation and integration.

GridFunctions are expressions build up of some elementary terms and can be used to construct a GridFunctionOperator, can be interpolated to a DOFVector, and can be integrated over a GridView.

Thus, GridFunctions are an important incredient to formulate the bilinear and linear forms und to postprocess the solutions.

Examples:

Usage of GridFunctions to build Operators:
ProblemStat<Traits> prob("name");
prob.initialize(INIT_ALL);
auto opB = makeOperator(BiLinearForm, Expression);
prob.addMatrixOperator(opB, Row, Col);
auto opL = makeOperator(LinearForm, Expression);
prob.addVectorOperator(opL, Row);
Usage of GridFunctions in BoundaryConditions:
prob.addDirichletBC(Predicate, Row, Col, Expression);
Interpolate a GridFunction to a DOFVector:
prob.solution(_0).interpol(Expression);
Integrate a GridFunction on a GridView:
auto value = integrate(Expression, prob.gridView());

Remarks:

An Expression is anything, a GridFunction can be created from, sometimes also called PreGridFunction. It includes constants, functors callable with GlobalCoordinates, and any combination of GridFunctions.
Anything that needs a quadrature formula, e.g., makeOperator() and integrate(), needs to determine the (approximative) polynomial degree of the GridFunctions. If the Gridfunction builds a polynomial expression, it can be deduced automatically, i.e. if it includes constants, DOFVectors, and arithmetic operator operator+, operator-, or operator*.

If the polynomial order can not be deduced, the compiler gives an error. Then, these functions accept an additional argument, to provide either the polynomial degree of the expression, or a quadrature rule explicitly.

Examples:
- auto op1 = makeOperator(B, 1.0 + pow<2>(prob.solution(_0)));
- auto op2 = makeOperator(B, sin(X(0)), 4);
- auto op3 = makeOperator(B, sin(X(0)), Dune::QuadratureRules(Dune::GeometryType::simplex, 4));
- auto value1 = integrate(sin(X(0)), 4);

Function Documentation

◆ abs_max()

auto abs_max	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ abs_min()

auto abs_min	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ clamp()

auto clamp	(	V &&	v,
		T const &	lo,
		T const &	hi
	)

◆ distance()

auto distance	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ dot()

auto dot	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ get() [1/2]

auto get ( T && value )

◆ get() [2/2]

auto get	(	T &&	value,
		std::size_t	i
	)

◆ gradientOf()

auto AMDiS::gradientOf ( Expr const & expr )

Generates a Gridfunction representing the gradient of a GridFunction. See DerivativeGridFunction.

Examples:

gradientOf(prob.solution(_0))
gradientOf(X(0) + X(1) + prob.solution(_0))

◆ infty_norm()

auto infty_norm ( Vec && vec )

◆ invokeAtQP()

auto invokeAtQP	(	Functor const &	f,
		PreGridFcts &&...	gridFcts
	)

Applies the functor f to the grid-functions gridFcts.... See FunctorGridFunction.

Examples:

invokeAtQP([](Dune::FieldVector<double, 2> const& x) { return two_norm(x); }, X());
invokeAtQP([](double u, auto const& x) { return u + x[0]; }, 1.0, X());
invokeAtQP(Operation::Plus{}, X(0), X(1));

References AMDiS::Concepts::Functor.

◆ makeGridFunction()

decltype(auto) AMDiS::makeGridFunction	(	PreGridFct const &	preGridFct,
		GridView const &	gridView
	)

Generator for Gridfunctions from Expressions (PreGridfunctions)

Create an evaluable GridFunction from an expression that itself can not be evaluated. Therefore, it binds the GridFunction to a GridView.

Example:

ProblemStat<Traits> prob("name");
prob.initialize(INIT_ALL);
auto gridFct = makeGridFunction(Expression, prob.leafGridView());
// eval GridFunction at GlobalCoordinates
auto value = gridFct(Dune::FieldVector<double,2>{1.0, 2.0});
auto localFct = localFunction(gridFct);
for (auto const& element : elements(prob.leafGridView())) {
  localFct.bind(element);
  // eval LocalFunction at local coordinates
  auto x = localFct(element.geometry().center());
  localFct.unbind();
}

In contrast to Expressions, GridFunctions can be evaluated and

have the free-function localFunction() to obtain a LocalFunction
its LocalFunctions have the free-function order() to obtain the polynomial order of the Expression (if available)
its LocalFunctions have the free-function derivativeOf() to differentiate the Expression with respect to global Coordinates. A derivative Expression can be created, using gradientOf() that can be converted to a GridFunction afterwards.

Referenced by ProblemStat< Traits >::addDirichletBC(), GridFunctionMarker< Grid, GridFct >::GridFunctionMarker(), AMDiS::integrate(), DiscreteFunction< Coeff, GB, TreePath >::interpolate_noalias(), AMDiS::makeLocalOperator(), and GridFunctionMarker< Grid, GridFct >::markElement().

◆ max()

auto max	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ min()

auto min	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ one_norm()

auto one_norm ( Vec && vec )

◆ operator*()

auto operator*	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

References AMDiS::Concepts::ConstantToGridFunction.

◆ operator+()

auto operator+	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ operator-() [1/2]

auto operator- ( Lhs && lhs )

◆ operator-() [2/2]

auto operator-	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ operator/()

auto operator/	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ outer()

auto outer	(	Lhs &&	lhs,
		Rhs &&	rhs
	)

◆ p_norm()

auto p_norm ( Vec && vec )

◆ pow() [1/2]

auto pow ( T && value )

to GridFunction.

◆ pow() [2/2]

auto pow	(	T &&	value,
		int	p
	)

◆ sqr()

auto sqr ( T && value )

◆ sum()

auto sum ( Vec && vec )

◆ trans()

auto trans ( Mat && mat )

◆ two_norm()

auto two_norm ( Vec && vec )

◆ unary_dot()

auto unary_dot ( Vec && vec )

Classes

Functions

Detailed Description

Function Documentation

◆ abs_max()

◆ abs_min()

◆ clamp()

◆ distance()

◆ dot()

◆ get() [1/2]

◆ get() [2/2]

◆ gradientOf()

◆ infty_norm()

◆ invokeAtQP()

◆ makeGridFunction()

◆ max()

◆ min()

◆ one_norm()

◆ operator*()

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator/()

◆ outer()

◆ p_norm()

◆ pow() [1/2]

◆ pow() [2/2]

◆ sqr()

◆ sum()

◆ trans()

◆ two_norm()

◆ unary_dot()