Dune::ACFem::WeakDivergenceOperatorParts< GridFunction > Class Template Reference

For a given grid-function define a model implementing the weak divergence. More...

#include <dune/acfem/models/modules/weakdivergencemodel.hh>

Collaboration diagram for Dune::ACFem::WeakDivergenceOperatorParts< GridFunction >:

Public Types
enum	StructureFlags
enum	ConstituentFlags
typedef Expression	ExpressionType
	The type of the underlying expression.

Public Member Functions
template<class Entity , class Point >
void	flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
	Evaluate \(A(x, u)\nabla u(x)\) in local coordinates. More...
template<class Entity , class Point >
void	linearizedFlux (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
	Evaluate the linearized flux in local coordinates. More...
template<class Entity , class Point >
void	fluxDivergence (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, const HessianRangeType &hessian, RangeType &result) const
	Compute the point-wise value of the flux-part of the operator, meaning the part of the differential operator which is multiplied by the derivative of the test function. More...
bool	setIntersection (const Intersection &intersection) const
void	source (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
void	linearizedSource (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
void	robinFlux (const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const
void	linearizedRobinFlux (const RangeType &uBar, const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const
const ExpressionType &	expression () const
	Return a const reference to the underlying expression.
ExpressionType &	expression ()
	Return a mutable reference to the underlying expression.
ExpressionType	operator* () const
	Return a copy from of the underlying expression.

Detailed Description

template<class GridFunction>
class Dune::ACFem::WeakDivergenceOperatorParts< GridFunction >

For a given grid-function define a model implementing the weak divergence.

In formulas: this fragment implements the bulk-part of the right-hand-side of the following equation, where \(\phi\) is a vector-valued test-function:

\[ \int_\Omega \partial_i p_i \, \cdot \phi = -\int_\Omega p_i \, \partial_i\phi + \int_{\partial\Omega} p_i \, \phi \nu_i \]

The boundary integral is not computed, intentionally it is substituted by suitable boundary conditions.

\(p\) acts as data, so this model just acts as a "constant", i.e. as a contribution to the right hand side.

Parameters

GridFunction

The type of the function the weak divergence has to be computed from. This must be a grid-function, i.e. it has to carry a local function and must have dimRange == dimWorld.

Member Enumeration Documentation

ConstituentFlags

enum Dune::ACFem::DefaultOperatorParts::ConstituentFlags

inherited

StructureFlags

enum Dune::ACFem::DefaultOperatorParts::StructureFlags

inherited

Member Function Documentation

linearizedRobinFlux()

void Dune::ACFem::DefaultOperatorParts< Expression >::linearizedRobinFlux ( const RangeType &  uBar, const Intersection &  intersection, const Point &  x, const DomainType &  unitOuterNormal, const RangeType &  value, RangeType &  result  ) const

inlineinherited

linearizedSource()

void Dune::ACFem::DefaultOperatorParts< Expression >::linearizedSource ( const RangeType &  uBar, const JacobianRangeType &  DuBar, const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, RangeType &  result  ) const

inlineinherited

robinFlux()

void Dune::ACFem::DefaultOperatorParts< Expression >::robinFlux ( const Intersection &  intersection, const Point &  x, const DomainType &  unitOuterNormal, const RangeType &  value, RangeType &  result  ) const

inlineinherited

setIntersection()

bool Dune::ACFem::DefaultOperatorParts< Expression >::setIntersection ( const Intersection &  intersection ) const

inlineinherited

source()

void Dune::ACFem::DefaultOperatorParts< Expression >::source ( const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, RangeType &  result  ) const

inlineinherited

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

• dune/acfem/models/modules/weakdivergencemodel.hh