Dune::ACFem::DeformationTensorOperatorParts< FunctionSpace > Class Template Reference

Define the a model where the flux-part is formed from the symmetric gradient. More...

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

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

Public Member Functions
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...
void	setEntity (const Entity &entity) const
bool	setIntersection (const Intersection &intersection) const
void	flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) 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 FunctionSpace>
class Dune::ACFem::DeformationTensorOperatorParts< FunctionSpace >

Define the a model where the flux-part is formed from the symmetric gradient.

The flux implement the second-order contribution

\[ \int_\Omega (\partial_i U_j + \partial_j U_i)\,\partial_i\phi_j = \frac12 \int_\Omega (\partial_i U_j + \partial_j U_i)\,(\partial_i\phi_j+\partial_j\phi_i) \]

Of course, the above formula uses sum-convention. This is indeed symmetric. Mind the factor 1/2. The DeformationTensorModel::fluxDivergence() takes the form

\[ -\partial_i(\partial_i U_\alpha + \partial_\alpha U_i) = -\Delta U_\alpha - \partial_\alpha\nabla\cdot U. \]

So for divergence free vector fields this would only be the component-wise Laplacian.

Note

Obviously, this model make only sense for when dimDomain = dimRange = GridPart::dimensionworld. For GridPart::dimensionworld != GridPart::dimension one would also have to discuss what the symmetric gradient means in terms of tangential derivatives. In some sense also the vectorfield U would have to be tangential.

Member Enumeration Documentation

ConstituentFlags

enum Dune::ACFem::DefaultOperatorParts::ConstituentFlags

inherited

StructureFlags

enum Dune::ACFem::DefaultOperatorParts::StructureFlags

inherited

Member Function Documentation

flux()

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

inlineinherited

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

setEntity()

void Dune::ACFem::DefaultOperatorParts< Expression >::setEntity ( const Entity &  entity ) 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/deformationtensormodel.hh