Some utility function in order to conveniently define some standard models without having to go through the "typedef" trouble. More...

Functions
template<class Entity >
void	Dune::ACFem::PDEModel::BulkLoadFunctionModel< GridFunction >::bind (const Entity &entity)

void	Dune::ACFem::PDEModel::BulkLoadFunctionModel< GridFunction >::unbind ()

template<class Quadrature >
RangeType	Dune::ACFem::PDEModel::BulkLoadFunctionModel< GridFunction >::source (const QuadraturePoint< Quadrature > &x) const

template<class Fct , std::enable_if_t<(IsWrappableByConstLocalFunction< Fct >::value &&!GridFunction::HasRegularity< Fct, 1 >::value), int > = 0>
constexpr auto	Dune::ACFem::PDEModel::bulkLoadFunctionModel (Fct &&f, const std::string &name="")
	Generate a BulkLoadFunctionModel for the "right hand side". More...

JacobianRangeType	Dune::ACFem::PDEModel::DeformationTensorModel< FunctionSpace >::linearizedFlux (const JacobianRangeType &jacobian) const
	Evaluate the linearized flux in local coordinates. More...

template<class Point >
RangeType	Dune::ACFem::PDEModel::DeformationTensorModel< FunctionSpace >::fluxDivergence (const HessianRangeType &hessian) 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...

template<class Object >
auto	Dune::ACFem::PDEModel::deformationTensorModel (const Object &object, const std::string &name="")
	Generate a deformation tensor model fitting the specified object.

template<class Entity >
void	Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::bind (const Entity &entity)
	Bind to the given entity. More...

void	Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::unbind ()
	Unbind from the previously bound entity. More...

template<class Intersection >
auto	Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::classifyBoundary (const Intersection &intersection)
	Bind to the given intersection and classify the components w.r.t. More...

template<class Quadrature >
RangeType	Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::dirichlet (const QuadraturePoint< Quadrature > &x, const RangeType &value) const
	Dirichlet values. More...

auto	Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::linearizedDirichlet (const RangeType &value) const
	Linearized Dirichlet values. More...

template<class Intersection >
auto	Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<(!IndicatorTraits< Indicator >::emptySupport &&ExpressionTraits< GridFunction >::isZero)> >::classifyBoundary (const Intersection &intersection)
	Bind to the given intersection and classify the components w.r.t. More...

auto	Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<(!IndicatorTraits< Indicator >::emptySupport &&ExpressionTraits< GridFunction >::isZero)> >::linearizedDirichlet (const RangeType &value) const
	Linearized Dirichlet values. More...

template<class T , class Indicator , std::enable_if_t< ExpressionTraits< Indicator >::isZero, int > = 0>
constexpr auto	Dune::ACFem::PDEModel::dirichletBoundaryModel (T &&values, Indicator &&where, const std::string &name="")
	Generate the zero model for the empty indicator. More...

template<class Object , class Indicator = EntireBoundaryIndicator, std::enable_if_t<!IsWrappableByConstLocalFunction< Object >::value, int > = 0>
auto	Dune::ACFem::PDEModel::dirichletZeroModel (const Object &object, Indicator &&where=std::decay_t< Indicator >{}, const std::string &name="")
	Generate homogeneous Dirichlet boundary conditions fitting the specified object. More...

template<class Entity >
void	Dune::ACFem::PDEModel::DivergenceLoadModel< GridFunction >::bind (const Entity &entity)
	Bind to the given entity. More...

void	Dune::ACFem::PDEModel::DivergenceLoadModel< GridFunction >::unbind ()
	Unbind from the previously bound entity. More...

template<class Quadrature >
RangeType	Dune::ACFem::PDEModel::DivergenceLoadModel< GridFunction >::source (const QuadraturePoint< Quadrature > &x) const
	The zero-order term as function of local coordinates. More...

template<class GridFunction >
constexpr auto	Dune::ACFem::PDEModel::divergenceLoadModel (GridFunction &&f, const std::string &name="")
	Generate a divergence model which only contributes to the load-vector. More...

RangeRangeType	Dune::ACFem::PDEModel::DivergenceModel< FunctionSpace >::linearizedSource (const DomainJacobianRangeType &jacobian) const
	The linearized source term as function of local coordinates. More...

template<class Object , std::enable_if_t< Object::FunctionSpaceType::ScalarFunctionSpaceType::dimRange==1, int > = 0>
static auto	Dune::ACFem::PDEModel::divergenceModel (const Object &object, const std::string &name="")
	Generate a divergence model from some object which has a function-space. More...

template<class GridPartTraits >
static auto	Dune::ACFem::PDEModel::divergenceModel (const Fem::GridPartInterface< GridPartTraits > &gridPart, const std::string &name="")
	Generate a DivergenceModel from a GridPart, using ctype as field and dimensionWorld as dimension.

template<class Intersection >
auto	Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::classifyBoundary (const Intersection &intersection)
	Bind to the given intersection and classify the components w.r.t. More...

JacobianRangeType	Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::flux (const RangeType &value) const
	Evaluate $A(x, u)\nabla u(x)$ in local coordinates. More...

template<class Point >
JacobianRangeType	Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::linearizedFlux (const RangeType &uBar, const RangeType &value) const
	Evaluate the linearized flux in local coordinates. More...

RangeType	Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::fluxDivergence (const RangeType &value, const JacobianRangeType &jacobian) 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...

template<class Object >
static auto	Dune::ACFem::PDEModel::fluidSelfTransportModel (const Object &object, const std::string &name="")
	Generate a Navier-Stokes non-linearity fitting the given object. More...

template<class Entity >
void	Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::bind (const Entity &entity)
	Bind to the given entity. More...

void	Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::unbind ()
	Unbind from the previously bound entity. More...

template<class Quadrature >
auto	Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::flux (const QuadraturePoint< Quadrature > &x) const
	Evaluate $A(x, u)\nabla u(x)$ in local coordinates. More...

template<class Quadrature >
auto	Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::fluxDivergence (const QuadraturePoint< Quadrature > &x) 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...

template<class Intersection >
auto	Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::classifyBoundary (const Intersection &intersection) const
	Bind to the given intersection and classify the components w.r.t. More...

template<class GridFunction >
constexpr auto	Dune::ACFem::PDEModel::gradientLoadModel (GridFunction &&f, const std::string &name="")
	Generate a Gradient-model as contribution to the load vector from the given grid-function. More...

auto	Dune::ACFem::PDEModel::GradientModel< FunctionSpace >::linearizedFlux (const DomainRangeType &value) const
	The linearized source term as function of local coordinates. More...

template<class Intersection >
auto	Dune::ACFem::PDEModel::GradientModel< FunctionSpace >::classifyBoundary (const Intersection &intersection) const
	Bind to the given intersection and classify the components w.r.t. More...

template<class Object , std::enable_if_t< Object::FunctionSpaceType::ScalarFunctionSpaceType::dimRange==1, int > = 0>
static auto	Dune::ACFem::PDEModel::gradientModel (const Object &object, const std::string &name="")
	Generate a gradient model from some object which has a function-space. More...

template<class GridPartTraits >
static auto	Dune::ACFem::PDEModel::gradientModel (const Fem::GridPartInterface< GridPartTraits > &gridPart, const std::string &name="")
	Generate a GradientModel from a GridPart, using ctype as field and dimensionWorld as dimension.

auto	Dune::ACFem::PDEModel::IncompressibleSelfTransportModel< FunctionSpace >::source (const RangeType &value, const JacobianRangeType &jacobian) const
	The zero-order term as function of local coordinates. More...

auto	Dune::ACFem::PDEModel::IncompressibleSelfTransportModel< FunctionSpace >::linearizedSource (const RangeType &uBar, const JacobianRangeType &DuBar, const RangeType &value, const JacobianRangeType &jacobian) const
	The linearized source term as function of local coordinates. More...

template<class Object >
static auto	Dune::ACFem::PDEModel::incompressibleSelfTransportModel (const Object &object, const std::string &name="")
	Generate a Navier-Stokes non-linearity fitting the given object. More...

template<class Entity >
void	Dune::ACFem::PDEModel::IncompressibleTransportModel< FunctionSpace, GridFunction >::bind (const Entity &entity)
	Bind to the given entity. More...

void	Dune::ACFem::PDEModel::IncompressibleTransportModel< FunctionSpace, GridFunction >::unbind ()
	Unbind from the previously bound entity. More...

template<class Quadrature >
auto	Dune::ACFem::PDEModel::IncompressibleTransportModel< FunctionSpace, GridFunction >::linearizedSource (const QuadraturePoint< Quadrature > &x, const JacobianRangeType &jacobian) const
	The linearized source term as function of local coordinates. More...

template<class Object , class Velocity >
constexpr auto	Dune::ACFem::PDEModel::incompressibleTransportModel (Object &&object, Velocity &&velocity, const std::string &name="")
	Generate an advection-model object. More...

auto	Dune::ACFem::PDEModel::LaplacianModel< FunctionSpace >::linearizedFlux (const JacobianRangeType &jacobian) const
	Evaluate the linearized flux in local coordinates. More...

auto	Dune::ACFem::PDEModel::LaplacianModel< FunctionSpace >::fluxDivergence (const HessianRangeType &hessian) 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...

template<class Object >
static auto	Dune::ACFem::PDEModel::laplacianModel (const Object &object, const std::string &name="")
	Generate Model for a (weak, of course) Laplacian. More...

RangeType	Dune::ACFem::PDEModel::MassModel< FunctionSpace >::linearizedSource (const RangeType &value) const
	The linearized source term as function of local coordinates. More...

template<class Object >
auto	Dune::ACFem::PDEModel::massModel (const Object &object, const std::string &name="")
	Generate a mass model fitting the specified object. More...

JacobianRangeType	Dune::ACFem::PDEModel::MeanCurvatureModel< FunctionSpace, Regularization >::flux (const JacobianRangeType &jacobian) const
	Evaluate $A(x, u)\nabla u(x)$ in local coordinates. More...

JacobianRangeType	Dune::ACFem::PDEModel::MeanCurvatureModel< FunctionSpace, Regularization >::linearizedFlux (const JacobianRangeType &DuBar, const JacobianRangeType &jacobian) const
	Evaluate the linearized flux in local coordinates. More...

RangeType	Dune::ACFem::PDEModel::MeanCurvatureModel< FunctionSpace, Regularization >::fluxDivergence (const JacobianRangeType &jacobian, const HessianRangeType &hessian) 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...

template<class Object , class Regularization = Tensor::FieldVectorTensor<typename Object::FunctionSpaceType::RangeFieldType>>
auto	Dune::ACFem::PDEModel::meanCurvatureModel (Regularization &&regularization, const Object &object, const std::string &name="")
	Generate a MeanCurvature-model fitting the specified object. More...

std::string	Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::name () const

template<class Entity >
void	Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::bind (const Entity &entity)

void	Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::unbind ()

template<class Intersection >
auto	Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::classifyBoundary (const Intersection &intersection)

template<class Quadrature >
RangeType	Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::robinFlux (const QuadraturePoint< Quadrature > &x, const DomainType &unitOuterNormal) const
	The non-linearized Robin-type flux term. More...

template<class Fct , class Indicator = EntireBoundaryIndicator, std::enable_if_t<(IsWrappableByConstLocalFunction< Fct >::value &&!GridFunction::HasRegularity< Fct, 1UL >::value), int > = 0>
constexpr auto	Dune::ACFem::PDEModel::neumannBoundaryModel (Fct &&values, Indicator &&where=std::decay_t< Indicator >{}, const std::string &name="")
	Generate NeumannBoundaryModel from given grid-function and boundary indicator. More...

template<class Entity >
void	Dune::ACFem::PDEModel::NitscheDirichletBoundaryModel< Model, PenaltyFunction, Symmetrize >::bind (const Entity &entity)
	Unbind from the previously bound entity. More...

void	Dune::ACFem::PDEModel::NitscheDirichletBoundaryModel< Model, PenaltyFunction, Symmetrize >::unbind ()
	Unbind from the previously bound entity. More...

template<class Intersection >
auto	Dune::ACFem::PDEModel::NitscheDirichletBoundaryModel< Model, PenaltyFunction, Symmetrize >::classifyBoundary (const Intersection &intersection)
	Bind to the given intersection and classify the components w.r.t. More...

template<class Model , class PenaltyFunction , class Symmetrize = SkeletonSymmetrizeDefault<Model>, std::enable_if_t<(IsProperPDEModel< Model >::value &&IsWrappableByConstLocalFunction< PenaltyFunction >::value &&!Expressions::IsPromotedTopLevel< PenaltyFunction >::value &&ModelMethodExists< Model, ModelIntrospection::dirichlet >::value &&IsSign< Symmetrize >::value), int > = 0>
auto	Dune::ACFem::PDEModel::nitscheDirichletModel (const Model &m, const PenaltyFunction &p, Symmetrize=Symmetrize{})
	Wrap an existing model converting any Dirichlet boundary conditions into weak Dirichlet boundary conditions with a general penalty function.

template<class Model , class GridPart , class Param = decltype(ModelParameters::nitscheDirichletPenalty()), class Symmetrize = SkeletonSymmetrizeDefault<Model>, std::enable_if_t<(IsPDEModel< Model >::value &&ModelMethodExists< Model, ModelIntrospection::dirichlet >::value &&IsTensor< Param >::value &&IsSign< Symmetrize >::value), int > = 0>
auto	Dune::ACFem::PDEModel::nitscheDirichletModel (Model &&m, const GridPart &gridPart, Param &&p=ModelParameters::nitscheDirichletPenalty(), Symmetrize=Symmetrize{})
	Wrap existing model converting any Dirichlet boundary conditions into weak Dirichlet boundary conditions with a standard penalty function.

template<class Model , class... T, std::enable_if_t<(IsProperPDEModel< Model >::value &&!ModelMethodExists< Model, ModelIntrospection::dirichlet >::value), int > = 0>
constexpr auto	Dune::ACFem::PDEModel::nitscheDirichletModel (Model &&m, T &&...)
	Just return the original model if it does not have Dirichlet boundary conditions. More...

template<class GridFunction , class Param , class Indicator = EntireBoundaryIndicator, class Symmetrize = Sign<1>, std::enable_if_t<(IsWrappableByConstLocalFunction< GridFunction >::value &&IsBoundaryIndicator< Indicator >::value &&IsTensor< Param >::value &&IsSign< Symmetrize >::value), int > = 0>
auto	Dune::ACFem::PDEModel::nitscheDirichletModel (GridFunction &&values, Param &&p=ModelParameters::nitscheDirichletPenalty(), Indicator &&where=Indicator(), Symmetrize=Symmetrize{})
	Create a model supplying weak Dirichet conditions from a given grid-function.

auto	Dune::ACFem::PDEModel::P_LaplacianModel< FunctionSpace, PField >::flux (const JacobianRangeType &jacobian) const
	Evaluate $A(x, u)\nabla u(x)$ in local coordinates. More...

auto	Dune::ACFem::PDEModel::P_LaplacianModel< FunctionSpace, PField >::linearizedFlux (const JacobianRangeType &DuBar, const JacobianRangeType &jacobian) const
	Evaluate the linearized flux in local coordinates. More...

auto	Dune::ACFem::PDEModel::P_LaplacianModel< FunctionSpace, PField >::fluxDivergence (const JacobianRangeType &jacobian, const HessianRangeType &hessian) 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...

template<class Object , class PField >
constexpr auto	Dune::ACFem::PDEModel::p_LaplacianModel (PField &&p, const Object &object, const std::string &name="")
	Generate Model for a (weak, of course) p-Laplacian. More...

RangeType	Dune::ACFem::PDEModel::P_MassModel< FunctionSpace, PField >::source (const RangeType &value) const
	The zero-order term as function of local coordinates. More...

RangeType	Dune::ACFem::PDEModel::P_MassModel< FunctionSpace, PField >::linearizedSource (const RangeType &uBar, const RangeType &value) const
	The linearized source term as function of local coordinates. More...

template<class Object , class PField >
constexpr auto	Dune::ACFem::PDEModel::p_MassModel (PField &&p, const Object &object, const std::string &name="")
	Generate Model for a (weak, of course) Mass. More...

template<class Intersection >
auto	Dune::ACFem::PDEModel::RobinBoundaryModel< FunctionSpace, Indicator >::classifyBoundary (const Intersection &intersection)

auto	Dune::ACFem::PDEModel::RobinBoundaryModel< FunctionSpace, Indicator >::linearizedRobinFlux (const DomainType &unitOuterNormal, const RangeType &value) const

template<class Object , class Indicator = EntireBoundaryIndicator>
constexpr auto	Dune::ACFem::PDEModel::robinZeroModel (const Object &object, Indicator &&where=Indicator{}, const std::string &name="")
	Generate homogeneous Robin boundary conditions fitting the specified object. More...

template<class GridFunction , class Indicator = EntireBoundaryIndicator>
constexpr auto	Dune::ACFem::PDEModel::robinBoundaryModel (GridFunction &&values, Indicator &&where=Indicator(), const std::string &name="")
	Generate a RobinBoundaryModel from given grid-function and boundary indicator. More...

template<class Entity >
void	Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::bind (const Entity &entity)
	Bind to the given entity. More...

void	Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::unbind ()
	Unbind from the previously bound entity. More...

template<class Intersection >
auto	Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::classifyBoundary (const Intersection &intersection)
	Bind to the given intersection and classify the components w.r.t. More...

template<class Quadrature >
auto	Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::linearizedFlux (const QuadraturePoint< Quadrature > &x, const RangeType &value) const
	Evaluate the linearized flux in local coordinates. More...

template<class Quadrature >
auto	Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::fluxDivergence (const QuadraturePoint< Quadrature > &x, const RangeType &value, const JacobianRangeType &jacobian) const
	! More...

template<class Quadrature >
auto	Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::linearizedRobinFlux (const QuadraturePoint< Quadrature > &x, const DomainType &unitOuterNormal, const RangeType &value) const
	The linearized Robin-type flux term. More...

template<class Object , class GridFunction >
constexpr auto	Dune::ACFem::PDEModel::transportModel (const Object &object, GridFunction &&velocity, const std::string &name="")
	Generate an advection-model object. More...

template<class GridFunction , class Indicator = EntireBoundaryIndicator, std::enable_if_t< HasTag< GridFunction, Fem::HasLocalFunction >::value, int > = 0>
auto	Dune::ACFem::PDEModel::weakDirichletBoundaryModel (GridFunction &&values, Indicator &&where=Indicator{}, const double penalty=Dune::Fem::Parameter::getValue< double >("acfem.dgPenalty"))
	Generate homogeneous WeakDirichlet boundary conditions fitting the specified object. More...

template<class Entity >
void	Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::bind (const Entity &entity)
	Bind to the given entity. More...

void	Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::unbind ()
	Unbind from the previously bound entity. More...

template<class Quadrature >
JacobianRangeType	Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::flux (const QuadraturePoint< Quadrature > &x) const
	Evaluate $A(x, u)\nabla u(x)$ in local coordinates. More...

template<class Quadrature >
auto	Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::fluxDivergence (const QuadraturePoint< Quadrature > &x) 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...

template<class T , class F = Expressions::Closure, std::enable_if_t< IsPDEModel< T >::value, int > = 0>
auto	Dune::ACFem::PDEModel::zeroModel (const T &t, const std::string &name, F closure=F{})
	Generate a zero model fitting the specified object. More...

template<class T , class F = Expressions::Closure, std::enable_if_t< IsPDEModel< T >::value, int > = 0>
auto	Dune::ACFem::PDEModel::zeroModel (const T &, F closure=F{})
	Generate a zero model fitting the specified object. More...

template<class T , class F = Expressions::Closure, std::enable_if_t< IsPDEModel< T >::value, int > = 0>
auto	Dune::ACFem::PDEModel::zeroModel (F closure=F{})
	Generate a zero model fitting the specified object. More...

Detailed Description

Some utility function in order to conveniently define some standard models without having to go through the "typedef" trouble.

Function Documentation

◆ bind() [1/9]

template<class GridFunction >

template<class Entity >

void Dune::ACFem::PDEModel::BulkLoadFunctionModel< GridFunction >::bind ( const Entity & entity )

inline

◆ bind() [2/9]

template<class GridFunction , class Indicator >

template<class Entity >

void Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::bind ( const Entity & entity )

inline

Bind to the given entity.

Parameters

[in] entity The entity to bind to.

Warning: Calling any other method without first binding the model results in undefined behaviour.

◆ bind() [3/9]

template<class GridFunction >

template<class Entity >

void Dune::ACFem::PDEModel::DivergenceLoadModel< GridFunction >::bind ( const Entity & entity )

inline

Bind to the given entity.

Parameters

[in] entity The entity to bind to.

Warning: Calling any other method without first binding the model results in undefined behaviour.

◆ bind() [4/9]

template<class GridFunction >

template<class Entity >

void Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::bind ( const Entity & entity )

inline

Bind to the given entity.

Parameters

[in] entity The entity to bind to.

Warning: Calling any other method without first binding the model results in undefined behaviour.

◆ bind() [5/9]

template<class FunctionSpace , class GridFunction >

template<class Entity >

void Dune::ACFem::PDEModel::IncompressibleTransportModel< FunctionSpace, GridFunction >::bind ( const Entity & entity )

inline

Bind to the given entity.

Parameters

[in] entity The entity to bind to.

Warning: Calling any other method without first binding the model results in undefined behaviour.

◆ bind() [6/9]

template<class GridFunction , class Indicator = EntireBoundaryIndicator>

template<class Entity >

void Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::bind ( const Entity & entity )

inline

◆ bind() [7/9]

template<class Model , class PenaltyFunction , class Symmetrize = SkeletonSymmetrizeDefault<Model>>

template<class Entity >

void Dune::ACFem::PDEModel::NitscheDirichletBoundaryModel< Model, PenaltyFunction, Symmetrize >::bind ( const Entity & entity )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ bind() [8/9]

template<class FunctionSpace , class GridFunction >

template<class Entity >

void Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::bind ( const Entity & entity )

inline

Bind to the given entity.

Parameters

[in] entity The entity to bind to.

Warning: Calling any other method without first binding the model results in undefined behaviour.

◆ bind() [9/9]

template<class GridFunction >

template<class Entity >

void Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::bind ( const Entity & entity )

inline

Bind to the given entity.

Parameters

[in] entity The entity to bind to.

Warning: Calling any other method without first binding the model results in undefined behaviour.

◆ bulkLoadFunctionModel()

template<class Fct , std::enable_if_t<(IsWrappableByConstLocalFunction< Fct >::value &&!GridFunction::HasRegularity< Fct, 1 >::value), int > = 0>

constexpr auto Dune::ACFem::PDEModel::bulkLoadFunctionModel	(	Fct &&	f,
		const std::string &	name = `""`
	)

constexpr

Generate a BulkLoadFunctionModel for the "right hand side".

If the supplied grid-function is a BindableTensorFunction then first force the differentiability order to 0.

If Fct is a BindableTensorFunction then we first construct a non-differentiable variant and then feed it into the BulkLoadModel.

Parameters

[in]	f	The L2-function for the RHS.
[in]	name	Optional. If left empty some sensible name is built from f.name() for debugging purposes.

This spares stack-space and complexity.

References Dune::ACFem::Expressions::expressionClosure().

Referenced by main().

◆ classifyBoundary() [1/9]

template<class GridFunction , class Indicator >

template<class Intersection >

auto Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::classifyBoundary ( const Intersection & intersection )

inline

Bind to the given intersection and classify the components w.r.t.

to the kind of applicable boundary conditions.

Warning: Note that prior to calling this function the model has to be bound to the inside entity of the given intersection. Failing to do so generates undefined behaviour.; The result of calling the other boundary related methods without binding to an intersection is undefined.; If RESULT.first is false, then the result of calling any of the other boundary related functions is undefined. Philosophically, they should return 0 in this case, but in order to have decent performance they give a damn and just don't care.; If RESULT.first is true, then still you cannot rely on user-friendly behaviour:

only if the respective bit of RESULT.second is set to 1, then the Dirichlet value in this compoment is well-defined.
only if the respective bit of RESULT.second is set to 0, then the Robin value in this component is well defined.

Parameters

[in] intersection The intersection to bind to.

Returns: A tuple. First component is a bool which is true iff any of the boundary related data functions would result in non trivial results. Second component is a bitset of size dimRange which is true if the given component of the system is subject to Dirichlet boundary conditions and false if it is subject to Robin or Neumann boundary conditions. If first is false then the contents of the bitset is undefined.

◆ classifyBoundary() [2/9]

template<class GridFunction , class Indicator >

template<class Intersection >

auto Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<(!IndicatorTraits< Indicator >::emptySupport &&ExpressionTraits< GridFunction >::isZero)> >::classifyBoundary ( const Intersection & intersection )

inline

Bind to the given intersection and classify the components w.r.t.

to the kind of applicable boundary conditions.

Warning: Note that prior to calling this function the model has to be bound to the inside entity of the given intersection. Failing to do so generates undefined behaviour.; The result of calling the other boundary related methods without binding to an intersection is undefined.; If RESULT.first is false, then the result of calling any of the other boundary related functions is undefined. Philosophically, they should return 0 in this case, but in order to have decent performance they give a damn and just don't care.; If RESULT.first is true, then still you cannot rely on user-friendly behaviour:

only if the respective bit of RESULT.second is set to 1, then the Dirichlet value in this compoment is well-defined.
only if the respective bit of RESULT.second is set to 0, then the Robin value in this component is well defined.

Parameters

[in] intersection The intersection to bind to.

Returns: A tuple. First component is a bool which is true iff any of the boundary related data functions would result in non trivial results. Second component is a bitset of size dimRange which is true if the given component of the system is subject to Dirichlet boundary conditions and false if it is subject to Robin or Neumann boundary conditions. If first is false then the contents of the bitset is undefined.

◆ classifyBoundary() [3/9]

template<class FunctionSpace >

template<class Intersection >

auto Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::classifyBoundary ( const Intersection & intersection )

inline

Bind to the given intersection and classify the components w.r.t.

to the kind of applicable boundary conditions.

Warning: Note that prior to calling this function the model has to be bound to the inside entity of the given intersection. Failing to do so generates undefined behaviour.; The result of calling the other boundary related methods without binding to an intersection is undefined.; If RESULT.first is false, then the result of calling any of the other boundary related functions is undefined. Philosophically, they should return 0 in this case, but in order to have decent performance they give a damn and just don't care.; If RESULT.first is true, then still you cannot rely on user-friendly behaviour:

only if the respective bit of RESULT.second is set to 1, then the Dirichlet value in this compoment is well-defined.
only if the respective bit of RESULT.second is set to 0, then the Robin value in this component is well defined.

Parameters

[in] intersection The intersection to bind to.

Returns: A tuple. First component is a bool which is true iff any of the boundary related data functions would result in non trivial results. Second component is a bitset of size dimRange which is true if the given component of the system is subject to Dirichlet boundary conditions and false if it is subject to Robin or Neumann boundary conditions. If first is false then the contents of the bitset is undefined.

◆ classifyBoundary() [4/9]

template<class GridFunction , class Indicator = EntireBoundaryIndicator>

template<class Intersection >

auto Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::classifyBoundary ( const Intersection & intersection )

inline

◆ classifyBoundary() [5/9]

template<class Model , class PenaltyFunction , class Symmetrize = SkeletonSymmetrizeDefault<Model>>

template<class Intersection >

auto Dune::ACFem::PDEModel::NitscheDirichletBoundaryModel< Model, PenaltyFunction, Symmetrize >::classifyBoundary ( const Intersection & intersection )

inline

Bind to the given intersection and classify the components w.r.t.

to the kind of applicable boundary conditions.

Warning: Note that prior to calling this function the model has to be bound to the inside entity of the given intersection. Failing to do so generates undefined behaviour.; The result of calling the other boundary related methods without binding to an intersection is undefined.; If RESULT.first is false, then the result of calling any of the other boundary related functions is undefined. Philosophically, they should return 0 in this case, but in order to have decent performance they give a damn and just don't care.; If RESULT.first is true, then still you cannot rely on user-friendly behaviour:

only if the respective bit of RESULT.second is set to 1, then the Dirichlet value in this compoment is well-defined.
only if the respective bit of RESULT.second is set to 0, then the Robin value in this component is well defined.

Parameters

[in] intersection The intersection to bind to.

Returns: A tuple. First component is a bool which is true iff any of the boundary related data functions would result in non trivial results. Second component is a bitset of size dimRange which is true if the given component of the system is subject to Dirichlet boundary conditions and false if it is subject to Robin or Neumann boundary conditions. If first is false then the contents of the bitset is undefined.

◆ classifyBoundary() [6/9]

template<class FunctionSpace , class Indicator = EntireBoundaryIndicator>

template<class Intersection >

auto Dune::ACFem::PDEModel::RobinBoundaryModel< FunctionSpace, Indicator >::classifyBoundary ( const Intersection & intersection )

inline

◆ classifyBoundary() [7/9]

template<class FunctionSpace , class GridFunction >

template<class Intersection >

auto Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::classifyBoundary ( const Intersection & intersection )

inline

Bind to the given intersection and classify the components w.r.t.

to the kind of applicable boundary conditions.

Warning: Note that prior to calling this function the model has to be bound to the inside entity of the given intersection. Failing to do so generates undefined behaviour.; The result of calling the other boundary related methods without binding to an intersection is undefined.; If RESULT.first is false, then the result of calling any of the other boundary related functions is undefined. Philosophically, they should return 0 in this case, but in order to have decent performance they give a damn and just don't care.; If RESULT.first is true, then still you cannot rely on user-friendly behaviour:

only if the respective bit of RESULT.second is set to 1, then the Dirichlet value in this compoment is well-defined.
only if the respective bit of RESULT.second is set to 0, then the Robin value in this component is well defined.

Parameters

[in] intersection The intersection to bind to.

Returns: A tuple. First component is a bool which is true iff any of the boundary related data functions would result in non trivial results. Second component is a bitset of size dimRange which is true if the given component of the system is subject to Dirichlet boundary conditions and false if it is subject to Robin or Neumann boundary conditions. If first is false then the contents of the bitset is undefined.

◆ classifyBoundary() [8/9]

template<class GridFunction >

template<class Intersection >

auto Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::classifyBoundary ( const Intersection & intersection ) const

inline

Bind to the given intersection and classify the components w.r.t.

to the kind of applicable boundary conditions.

Warning: Note that prior to calling this function the model has to be bound to the inside entity of the given intersection. Failing to do so generates undefined behaviour.; The result of calling the other boundary related methods without binding to an intersection is undefined.; If RESULT.first is false, then the result of calling any of the other boundary related functions is undefined. Philosophically, they should return 0 in this case, but in order to have decent performance they give a damn and just don't care.; If RESULT.first is true, then still you cannot rely on user-friendly behaviour:

only if the respective bit of RESULT.second is set to 1, then the Dirichlet value in this compoment is well-defined.
only if the respective bit of RESULT.second is set to 0, then the Robin value in this component is well defined.

Parameters

[in] intersection The intersection to bind to.

Returns: A tuple. First component is a bool which is true iff any of the boundary related data functions would result in non trivial results. Second component is a bitset of size dimRange which is true if the given component of the system is subject to Dirichlet boundary conditions and false if it is subject to Robin or Neumann boundary conditions. If first is false then the contents of the bitset is undefined.

◆ classifyBoundary() [9/9]

template<class FunctionSpace >

template<class Intersection >

auto Dune::ACFem::PDEModel::GradientModel< FunctionSpace >::classifyBoundary ( const Intersection & intersection ) const

inline

Bind to the given intersection and classify the components w.r.t.

to the kind of applicable boundary conditions.

Warning: Note that prior to calling this function the model has to be bound to the inside entity of the given intersection. Failing to do so generates undefined behaviour.; The result of calling the other boundary related methods without binding to an intersection is undefined.; If RESULT.first is false, then the result of calling any of the other boundary related functions is undefined. Philosophically, they should return 0 in this case, but in order to have decent performance they give a damn and just don't care.; If RESULT.first is true, then still you cannot rely on user-friendly behaviour:

only if the respective bit of RESULT.second is set to 1, then the Dirichlet value in this compoment is well-defined.
only if the respective bit of RESULT.second is set to 0, then the Robin value in this component is well defined.

Parameters

[in] intersection The intersection to bind to.

Returns: A tuple. First component is a bool which is true iff any of the boundary related data functions would result in non trivial results. Second component is a bitset of size dimRange which is true if the given component of the system is subject to Dirichlet boundary conditions and false if it is subject to Robin or Neumann boundary conditions. If first is false then the contents of the bitset is undefined.

◆ dirichlet()

template<class GridFunction , class Indicator >

template<class Quadrature >

RangeType Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::dirichlet	(	const QuadraturePoint< Quadrature > &	x,
		const RangeType &	value
	)		const

inline

Dirichlet values.

Maybe slightly more complicated than necessary, but in order to have a consistent variational formulation we simply model Dirichlet values just the same way as all the other contributions. For ordinary Dirchlet constraints the method should just compute

\[ \text{result} = u(x) - g(x) \]

just the same way as all other non-linearized method also contain the "right hand side" contribution. Things become more interesting when doing arithmetic with models.

Parameters

[in]	x	The point of evaluation.
[in]	value	The value of the Ansatz-function at x.

Returns: The result of the computation.

◆ dirichletBoundaryModel()

template<class T , class Indicator , std::enable_if_t< ExpressionTraits< Indicator >::isZero, int > = 0>

constexpr auto Dune::ACFem::PDEModel::dirichletBoundaryModel	(	T &&	values,
		Indicator &&	where = `std::decay_t< Indicator >{}`,
		const std::string &	name = `""`
	)

constexpr

Generate the zero model for the empty indicator.

Generate DirichletBoundaryModel from given grid-function and boundary indicator.

Parameters

[in]	values	The Dirichlet boundary values.
[in]	where	Indicator which decides which part of the boundary is affected

References Dune::ACFem::PDEModel::zeroModel().

Referenced by main().

◆ dirichletZeroModel()

template<class Object , class Indicator = EntireBoundaryIndicator, std::enable_if_t<!IsWrappableByConstLocalFunction< Object >::value, int > = 0>

auto Dune::ACFem::PDEModel::dirichletZeroModel	(	const Object &	object,
		Indicator &&	where = `std::decay_t<Indicator>{}`,
		const std::string &	name = `""`
	)

Generate homogeneous Dirichlet boundary conditions fitting the specified object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType and a method object.gridPart().

Parameters

[in]	object	Super-object, the DirichletBoundaryModel generated will be compatible to this object.
[in]	where	Indicator which decides where the Dirichlet b.c. apply.

Examples of suitable objects are

another model
Fem::DiscreteFunctionSpace
Fem::BindableGridFunction

See also: CompatibleModel.

Referenced by main().

◆ divergenceLoadModel()

template<class GridFunction >

constexpr auto Dune::ACFem::PDEModel::divergenceLoadModel	(	GridFunction &&	f,
		const std::string &	name = `""`
	)

constexpr

Generate a divergence model which only contributes to the load-vector.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

◆ divergenceModel()

template<class Object , std::enable_if_t< Object::FunctionSpaceType::ScalarFunctionSpaceType::dimRange==1, int > = 0>

static auto Dune::ACFem::PDEModel::divergenceModel	(	const Object &	object,
		const std::string &	name = `""`
	)

inlinestatic

Generate a divergence model from some object which has a function-space.

The generated DivergenceModel uses the dimDomain as its dimension.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

References Dune::ACFem::Expressions::expressionClosure().

◆ fluidSelfTransportModel()

template<class Object >

static auto Dune::ACFem::PDEModel::fluidSelfTransportModel	(	const Object &	object,
		const std::string &	name = `""`
	)

inlinestatic

Generate a Navier-Stokes non-linearity fitting the given object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

References Dune::ACFem::Expressions::expressionClosure().

◆ flux() [1/5]

template<class FunctionSpace , class Regularization = Tensor::FieldVectorTensor<typename FunctionSpace::RangeFieldType>>

JacobianRangeType Dune::ACFem::PDEModel::MeanCurvatureModel< FunctionSpace, Regularization >::flux ( const JacobianRangeType & jacobian ) const

inline

Evaluate $A(x, u)\nabla u(x)$ in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\ps$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

◆ flux() [2/5]

template<class FunctionSpace , class PField >

auto Dune::ACFem::PDEModel::P_LaplacianModel< FunctionSpace, PField >::flux ( const JacobianRangeType & jacobian ) const

inline

Evaluate $A(x, u)\nabla u(x)$ in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\ps$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

References Dune::ACFem::Tensor::pow().

◆ flux() [3/5]

template<class GridFunction >

template<class Quadrature >

auto Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::flux ( const QuadraturePoint< Quadrature > & x ) const

inline

Evaluate $A(x, u)\nabla u(x)$ in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\ps$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

◆ flux() [4/5]

template<class GridFunction >

template<class Quadrature >

JacobianRangeType Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::flux ( const QuadraturePoint< Quadrature > & x ) const

inline

Evaluate $A(x, u)\nabla u(x)$ in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\ps$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

◆ flux() [5/5]

template<class FunctionSpace >

JacobianRangeType Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::flux ( const RangeType & value ) const

inline

Evaluate $A(x, u)\nabla u(x)$ in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\ps$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

Referenced by Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::linearizedFlux().

◆ fluxDivergence() [1/8]

template<class FunctionSpace >

template<class Point >

RangeType Dune::ACFem::PDEModel::DeformationTensorModel< FunctionSpace >::fluxDivergence ( const HessianRangeType & hessian ) const

inline

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.

Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

◆ fluxDivergence() [2/8]

template<class FunctionSpace >

auto Dune::ACFem::PDEModel::LaplacianModel< FunctionSpace >::fluxDivergence ( const HessianRangeType & hessian ) const

inline

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.

Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

References Dune::ACFem::ModelBase< FunctionSpace >::dimDomain, and Dune::ACFem::ModelBase< FunctionSpace >::dimRange.

◆ fluxDivergence() [3/8]

template<class FunctionSpace , class Regularization = Tensor::FieldVectorTensor<typename FunctionSpace::RangeFieldType>>

RangeType Dune::ACFem::PDEModel::MeanCurvatureModel< FunctionSpace, Regularization >::fluxDivergence	(	const JacobianRangeType &	jacobian,
		const HessianRangeType &	hessian
	)		const

inline

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.

Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

◆ fluxDivergence() [4/8]

template<class FunctionSpace , class PField >

auto Dune::ACFem::PDEModel::P_LaplacianModel< FunctionSpace, PField >::fluxDivergence	(	const JacobianRangeType &	jacobian,
		const HessianRangeType &	hessian
	)		const

inline

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.

Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

References Dune::ACFem::Tensor::pow().

◆ fluxDivergence() [5/8]

template<class GridFunction >

template<class Quadrature >

auto Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::fluxDivergence ( const QuadraturePoint< Quadrature > & x ) const

inline

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.

Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

◆ fluxDivergence() [6/8]

template<class GridFunction >

template<class Quadrature >

auto Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::fluxDivergence ( const QuadraturePoint< Quadrature > & x ) const

inline

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.

Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

This is the strong form, i.e. simply the divergence.

◆ fluxDivergence() [7/8]

template<class FunctionSpace , class GridFunction >

template<class Quadrature >

auto Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::fluxDivergence	(	const QuadraturePoint< Quadrature > &	x,
		const RangeType &	value,
		const JacobianRangeType &	jacobian
	)		const

inline

!

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. Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

The implementation also works for transport-velocities which are not divergence free.

References Dune::ACFem::ModelBase< FunctionSpace >::dimDomain.

◆ fluxDivergence() [8/8]

template<class FunctionSpace >

RangeType Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::fluxDivergence	(	const RangeType &	value,
		const JacobianRangeType &	jacobian
	)		const

inline

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.

Primarily useful for residual error estimators.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	In preparation for non-linear problems.
[in]	jacobian	The value of $\nabla u$.
[in]	hessian	The value of $D^2u$.

Returns: The result of the computation.

◆ gradientLoadModel()

template<class GridFunction >

constexpr auto Dune::ACFem::PDEModel::gradientLoadModel	(	GridFunction &&	f,
		const std::string &	name = `""`
	)

constexpr

Generate a Gradient-model as contribution to the load vector from the given grid-function.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

◆ gradientModel()

template<class Object , std::enable_if_t< Object::FunctionSpaceType::ScalarFunctionSpaceType::dimRange==1, int > = 0>

static auto Dune::ACFem::PDEModel::gradientModel	(	const Object &	object,
		const std::string &	name = `""`
	)

inlinestatic

Generate a gradient model from some object which has a function-space.

The generated GradientModel uses the dimDomain as its dimension.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

References Dune::ACFem::Expressions::expressionClosure().

◆ incompressibleSelfTransportModel()

template<class Object >

static auto Dune::ACFem::PDEModel::incompressibleSelfTransportModel	(	const Object &	object,
		const std::string &	name = `""`
	)

inlinestatic

Generate a Navier-Stokes non-linearity fitting the given object.

This variant moves the derivative to the test function at the cost of introducing a boundary integral.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

References Dune::ACFem::Expressions::expressionClosure().

◆ incompressibleTransportModel()

template<class Object , class Velocity >

constexpr auto Dune::ACFem::PDEModel::incompressibleTransportModel	(	Object &&	object,
		Velocity &&	velocity,
		const std::string &	name = `""`
	)

constexpr

Generate an advection-model object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Parameters

[in] velocity The advection-velocity. This must already be something with a localFunction() method. It is implicitly assumed that the divergence of this object vanishes.

◆ laplacianModel()

template<class Object >

static auto Dune::ACFem::PDEModel::laplacianModel	(	const Object &	object,
		const std::string &	name = `""`
	)

inlinestatic

Generate Model for a (weak, of course) Laplacian.

Parameters

[in]	object	Something with a public FunctionSpaceType typedef.
[in]	name	An optional name for debugging and pretty-printing.

References Dune::ACFem::Expressions::expressionClosure().

Referenced by main().

◆ linearizedDirichlet() [1/2]

template<class GridFunction , class Indicator >

auto Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::linearizedDirichlet ( const RangeType & value ) const

inline

Linearized Dirichlet values.

For ordinary Dirichlet constraints, this method should simply copy value to result.

Parameters

[in]	uBar	The point of linearization, evaluated at x.
[in]	x	The point (in space) of evaluation.
[in]	value	The value of the Ansatz function for the linearized problem at x.

Returns: The result of the computation.

◆ linearizedDirichlet() [2/2]

template<class GridFunction , class Indicator >

auto Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<(!IndicatorTraits< Indicator >::emptySupport &&ExpressionTraits< GridFunction >::isZero)> >::linearizedDirichlet ( const RangeType & value ) const

inline

Linearized Dirichlet values.

For ordinary Dirichlet constraints, this method should simply copy value to result.

Parameters

[in]	uBar	The point of linearization, evaluated at x.
[in]	x	The point (in space) of evaluation.
[in]	value	The value of the Ansatz function for the linearized problem at x.

Returns: The result of the computation.

◆ linearizedFlux() [1/7]

template<class FunctionSpace >

auto Dune::ACFem::PDEModel::GradientModel< FunctionSpace >::linearizedFlux ( const DomainRangeType & value ) const

inline

The linearized source term as function of local coordinates.

Note the "source" in this context includes all terms which are multiplied by the value (not the jacobian) of the test-functions und thus may also include first order terms.

Parameters

[in]	uBar	The point of linearization.
[in]	DuBar	The jacobian at the point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

References Dune::ACFem::PDEModel::GradientModel< FunctionSpace >::rangeDimRange.

◆ linearizedFlux() [2/7]

template<class FunctionSpace , class Regularization = Tensor::FieldVectorTensor<typename FunctionSpace::RangeFieldType>>

JacobianRangeType Dune::ACFem::PDEModel::MeanCurvatureModel< FunctionSpace, Regularization >::linearizedFlux	(	const JacobianRangeType &	DuBar,
		const JacobianRangeType &	jacobian
	)		const

inline

Evaluate the linearized flux in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	uBar	Point of linearization.
[in]	DuBar	Point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\psi$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

◆ linearizedFlux() [3/7]

template<class FunctionSpace , class PField >

auto Dune::ACFem::PDEModel::P_LaplacianModel< FunctionSpace, PField >::linearizedFlux	(	const JacobianRangeType &	DuBar,
		const JacobianRangeType &	jacobian
	)		const

inline

Evaluate the linearized flux in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	uBar	Point of linearization.
[in]	DuBar	Point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\psi$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

References Dune::ACFem::Tensor::pow().

◆ linearizedFlux() [4/7]

template<class FunctionSpace >

JacobianRangeType Dune::ACFem::PDEModel::DeformationTensorModel< FunctionSpace >::linearizedFlux ( const JacobianRangeType & jacobian ) const

inline

Evaluate the linearized flux in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	uBar	Point of linearization.
[in]	DuBar	Point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\psi$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

◆ linearizedFlux() [5/7]

template<class FunctionSpace >

auto Dune::ACFem::PDEModel::LaplacianModel< FunctionSpace >::linearizedFlux ( const JacobianRangeType & jacobian ) const

inline

Evaluate the linearized flux in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	uBar	Point of linearization.
[in]	DuBar	Point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\psi$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

◆ linearizedFlux() [6/7]

template<class FunctionSpace , class GridFunction >

template<class Quadrature >

auto Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::linearizedFlux	(	const QuadraturePoint< Quadrature > &	x,
		const RangeType &	value
	)		const

inline

Evaluate the linearized flux in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	uBar	Point of linearization.
[in]	DuBar	Point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\psi$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

References Dune::ACFem::ModelBase< FunctionSpace >::dimRange.

◆ linearizedFlux() [7/7]

template<class FunctionSpace >

template<class Point >

JacobianRangeType Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::linearizedFlux	(	const RangeType &	uBar,
		const RangeType &	value
	)		const

inline

Evaluate the linearized flux in local coordinates.

This can be interpreted as a diffusive "flux", at least when restricted to some surface. $\bar u$ denotes the point of linearization for non-linear problems.

Parameters

[in]	uBar	Point of linearization.
[in]	DuBar	Point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	To allow integration by parts for first order terms and in preparation for non-linear models.
[in]	jacobian	The value of $\nabla\bar\psi$.

Returns: The result of the computation.

Note: "flux" in this sense simply means something which is multiplied by the jacobians of the test-function and covers "diffusive fluxes" as well as advective fluxes.

References Dune::ACFem::PDEModel::FluidSelfTransportModel< FunctionSpace >::flux().

◆ linearizedRobinFlux() [1/2]

template<class FunctionSpace , class Indicator = EntireBoundaryIndicator>

auto Dune::ACFem::PDEModel::RobinBoundaryModel< FunctionSpace, Indicator >::linearizedRobinFlux	(	const DomainType &	unitOuterNormal,
		const RangeType &	value
	)		const

inline

References Dune::ACFem::zero().

◆ linearizedRobinFlux() [2/2]

template<class FunctionSpace , class GridFunction >

template<class Quadrature >

auto Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::linearizedRobinFlux	(	const QuadraturePoint< Quadrature > &	x,
		const DomainType &	unitOuterNormal,
		const RangeType &	value
	)		const

inline

The linearized Robin-type flux term.

Parameters

[in]	uBar	The point of linearization.
[in]	DuBar	The point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	unitOuterNormal	The outer normal (outer with respect to the current entity).
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

◆ linearizedSource() [1/5]

template<class FunctionSpace >

RangeRangeType Dune::ACFem::PDEModel::DivergenceModel< FunctionSpace >::linearizedSource ( const DomainJacobianRangeType & jacobian ) const

inline

The linearized source term as function of local coordinates.

Note the "source" in this context includes all terms which are multiplied by the value (not the jacobian) of the test-functions und thus may also include first order terms.

Parameters

[in]	uBar	The point of linearization.
[in]	DuBar	The jacobian at the point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

References Dune::ACFem::PDEModel::DivergenceModel< FunctionSpace >::domainDimRange.

◆ linearizedSource() [2/5]

template<class FunctionSpace , class GridFunction >

template<class Quadrature >

auto Dune::ACFem::PDEModel::IncompressibleTransportModel< FunctionSpace, GridFunction >::linearizedSource	(	const QuadraturePoint< Quadrature > &	x,
		const JacobianRangeType &	jacobian
	)		const

inline

The linearized source term as function of local coordinates.

Note the "source" in this context includes all terms which are multiplied by the value (not the jacobian) of the test-functions und thus may also include first order terms.

Parameters

[in]	uBar	The point of linearization.
[in]	DuBar	The jacobian at the point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

◆ linearizedSource() [3/5]

template<class FunctionSpace >

auto Dune::ACFem::PDEModel::IncompressibleSelfTransportModel< FunctionSpace >::linearizedSource	(	const RangeType &	uBar,
		const JacobianRangeType &	DuBar,
		const RangeType &	value,
		const JacobianRangeType &	jacobian
	)		const

inline

The linearized source term as function of local coordinates.

Note the "source" in this context includes all terms which are multiplied by the value (not the jacobian) of the test-functions und thus may also include first order terms.

Parameters

[in]	uBar	The point of linearization.
[in]	DuBar	The jacobian at the point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

◆ linearizedSource() [4/5]

template<class FunctionSpace , class PField >

RangeType Dune::ACFem::PDEModel::P_MassModel< FunctionSpace, PField >::linearizedSource	(	const RangeType &	uBar,
		const RangeType &	value
	)		const

inline

The linearized source term as function of local coordinates.

Note the "source" in this context includes all terms which are multiplied by the value (not the jacobian) of the test-functions und thus may also include first order terms.

Parameters

[in]	uBar	The point of linearization.
[in]	DuBar	The jacobian at the point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

References Dune::ACFem::Tensor::pow().

◆ linearizedSource() [5/5]

template<class FunctionSpace >

RangeType Dune::ACFem::PDEModel::MassModel< FunctionSpace >::linearizedSource ( const RangeType & value ) const

inline

The linearized source term as function of local coordinates.

Note the "source" in this context includes all terms which are multiplied by the value (not the jacobian) of the test-functions und thus may also include first order terms.

Parameters

[in]	uBar	The point of linearization.
[in]	DuBar	The jacobian at the point of linearization.
[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

◆ massModel()

template<class Object >

auto Dune::ACFem::PDEModel::massModel	(	const Object &	object,
		const std::string &	name = `""`
	)

inline

Generate a mass model fitting the specified object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

References Dune::ACFem::Expressions::expressionClosure().

Referenced by Dune::ACFem::l2Projection(), and main().

◆ meanCurvatureModel()

template<class Object , class Regularization = Tensor::FieldVectorTensor<typename Object::FunctionSpaceType::RangeFieldType>>

auto Dune::ACFem::PDEModel::meanCurvatureModel	(	Regularization &&	regularization,
		const Object &	object,
		const std::string &	name = `""`
	)

Generate a MeanCurvature-model fitting the specified object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Parameters

[in] regularization $\eta$, see MeanCurvatureModel. For the graph-case this should be 1.0, for the level-set approach this is a regularization parameter in order to be able to cope with fattening.

References Dune::ACFem::Expressions::expressionClosure().

◆ name()

template<class GridFunction , class Indicator = EntireBoundaryIndicator>

std::string Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::name ( ) const

inline

◆ neumannBoundaryModel()

template<class Fct , class Indicator = EntireBoundaryIndicator, std::enable_if_t<(IsWrappableByConstLocalFunction< Fct >::value &&!GridFunction::HasRegularity< Fct, 1UL >::value), int > = 0>

constexpr auto Dune::ACFem::PDEModel::neumannBoundaryModel	(	Fct &&	values,
		Indicator &&	where = `std::decay_t<Indicator>{}`,
		const std::string &	name = `""`
	)

constexpr

Generate NeumannBoundaryModel from given grid-function and boundary indicator.

Parameters

[in]	values	The Neumann boundary values.
[in]	where	Indicator which decides which part of ]the boundary is affected

◆ nitscheDirichletModel()

template<class Model , class... T, std::enable_if_t<(IsProperPDEModel< Model >::value &&!ModelMethodExists< Model, ModelIntrospection::dirichlet >::value), int > = 0>

constexpr auto Dune::ACFem::PDEModel::nitscheDirichletModel	(	Model &&	m,
		T &&	...
	)

constexpr

Just return the original model if it does not have Dirichlet boundary conditions.

This implies that Model is not an expression closure.

References Dune::ACFem::Expressions::expressionClosure().

◆ p_LaplacianModel()

template<class Object , class PField >

constexpr auto Dune::ACFem::PDEModel::p_LaplacianModel	(	PField &&	p,
		const Object &	object,
		const std::string &	name = `""`
	)

constexpr

Generate Model for a (weak, of course) p-Laplacian.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Parameters

[in]	p	The exponent, see P_LaplacianModel.
[in]	object	Something with a public FunctionSpaceType typedef.
[in]	name	An optional name for debugging and pretty-printing.

References Dune::ACFem::Expressions::expressionClosure().

◆ p_MassModel()

template<class Object , class PField >

constexpr auto Dune::ACFem::PDEModel::p_MassModel	(	PField &&	p,
		const Object &	object,
		const std::string &	name = `""`
	)

constexpr

Generate Model for a (weak, of course) Mass.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Parameters

[in]	p	The exponent, see P_MassModel.
[in]	object	Something with a public FunctionSpaceType typedef.
[in]	name	An optional name for debugging and pretty-printing.

References Dune::ACFem::Expressions::expressionClosure().

◆ robinBoundaryModel()

template<class GridFunction , class Indicator = EntireBoundaryIndicator>

constexpr auto Dune::ACFem::PDEModel::robinBoundaryModel	(	GridFunction &&	values,
		Indicator &&	where = `Indicator()`,
		const std::string &	name = `""`
	)

constexpr

Generate a RobinBoundaryModel from given grid-function and boundary indicator.

Parameters

[in]	values	The Robin boundary values.
[in]	where	Indicator which decides which part of the boundary is affected

◆ robinFlux()

template<class GridFunction , class Indicator = EntireBoundaryIndicator>

template<class Quadrature >

RangeType Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::robinFlux	(	const QuadraturePoint< Quadrature > &	x,
		const DomainType &	unitOuterNormal
	)		const

inline

The non-linearized Robin-type flux term.

This is "@f$\alpha@f$" from the Robin boundary condition.

Parameters

[in]	intersection	The current intersection.
[in]	x	The point of evaluation, local coordinates.
[in]	unitOuterNormal	The outer normal (outer with respect to the current entity).
[in]	value	The value of u.
[out]	result	The result of the computation.

◆ robinZeroModel()

template<class Object , class Indicator = EntireBoundaryIndicator>

constexpr auto Dune::ACFem::PDEModel::robinZeroModel	(	const Object &	object,
		Indicator &&	where = `Indicator{}`,
		const std::string &	name = `""`
	)

constexpr

Generate homogeneous Robin boundary conditions fitting the specified object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType and a method object.gridPart().

Parameters

[in]	object	Super-object, the RobinBoundaryModel generated will be compatible to this object.
[in]	where	Indicator which decides where the Robin b.c. apply.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

◆ source() [1/4]

template<class GridFunction >

template<class Quadrature >

RangeType Dune::ACFem::PDEModel::BulkLoadFunctionModel< GridFunction >::source ( const QuadraturePoint< Quadrature > & x ) const

inline

◆ source() [2/4]

template<class GridFunction >

template<class Quadrature >

RangeType Dune::ACFem::PDEModel::DivergenceLoadModel< GridFunction >::source ( const QuadraturePoint< Quadrature > & x ) const

inline

The zero-order term as function of local coordinates.

Has to evaluate $\nabla\cdot(b(x,u)\,u) + c(x, u)\,u$.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

References Dune::ACFem::Tensor::trace().

◆ source() [3/4]

template<class FunctionSpace , class PField >

RangeType Dune::ACFem::PDEModel::P_MassModel< FunctionSpace, PField >::source ( const RangeType & value ) const

inline

The zero-order term as function of local coordinates.

Has to evaluate $\nabla\cdot(b(x,u)\,u) + c(x, u)\,u$.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

References Dune::ACFem::Tensor::pow().

◆ source() [4/4]

template<class FunctionSpace >

auto Dune::ACFem::PDEModel::IncompressibleSelfTransportModel< FunctionSpace >::source	(	const RangeType &	value,
		const JacobianRangeType &	jacobian
	)		const

inline

The zero-order term as function of local coordinates.

Has to evaluate $\nabla\cdot(b(x,u)\,u) + c(x, u)\,u$.

Parameters

[in]	x	The point of evaluation, local coordinates.
[in]	value	The value of u.
[in]	jacobian	The jacobian of u.

Returns: The result of the computation.

◆ transportModel()

template<class Object , class GridFunction >

constexpr auto Dune::ACFem::PDEModel::transportModel	(	const Object &	object,
		GridFunction &&	velocity,
		const std::string &	name = `""`
	)

constexpr

Generate an advection-model object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	object	Ignored. We use only the type to get hold of the FunctionSpaceType and the GridPartType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Parameters

[in] velocity The advection-velocity. This must already be something with a localFunction() method.

◆ unbind() [1/9]

template<class GridFunction >

void Dune::ACFem::PDEModel::BulkLoadFunctionModel< GridFunction >::unbind ( )

inline

◆ unbind() [2/9]

template<class GridFunction , class Indicator >

void Dune::ACFem::PDEModel::DirichletBoundaryModel< GridFunction, Indicator, std::enable_if_t<!IndicatorTraits< Indicator >::emptySupport &&!ExpressionTraits< GridFunction >::isZero > >::unbind ( )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ unbind() [3/9]

template<class GridFunction >

void Dune::ACFem::PDEModel::DivergenceLoadModel< GridFunction >::unbind ( )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ unbind() [4/9]

template<class GridFunction >

void Dune::ACFem::PDEModel::GradientLoadModel< GridFunction >::unbind ( )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ unbind() [5/9]

template<class FunctionSpace , class GridFunction >

void Dune::ACFem::PDEModel::IncompressibleTransportModel< FunctionSpace, GridFunction >::unbind ( )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ unbind() [6/9]

template<class GridFunction , class Indicator = EntireBoundaryIndicator>

void Dune::ACFem::PDEModel::NeumannBoundaryModel< GridFunction, Indicator >::unbind ( )

inline

◆ unbind() [7/9]

template<class Model , class PenaltyFunction , class Symmetrize = SkeletonSymmetrizeDefault<Model>>

void Dune::ACFem::PDEModel::NitscheDirichletBoundaryModel< Model, PenaltyFunction, Symmetrize >::unbind ( )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ unbind() [8/9]

template<class FunctionSpace , class GridFunction >

void Dune::ACFem::PDEModel::TransportModel< FunctionSpace, GridFunction >::unbind ( )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ unbind() [9/9]

template<class GridFunction >

void Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >::unbind ( )

inline

Unbind from the previously bound entity.

Warning: Calling this method on an unbound model may cause undefined behaviour.

◆ weakDirichletBoundaryModel()

template<class GridFunction , class Indicator = EntireBoundaryIndicator, std::enable_if_t< HasTag< GridFunction, Fem::HasLocalFunction >::value, int > = 0>

auto Dune::ACFem::PDEModel::weakDirichletBoundaryModel	(	GridFunction &&	values,
		Indicator &&	where = `Indicator{}`,
		const double	penalty = `Dune::Fem::Parameter::getValue<double>("acfem.dgPenalty")`
	)

Generate homogeneous WeakDirichlet boundary conditions fitting the specified object.

In order for this to work the data-type of the given object must have the two sub-types Object::FunctionSpaceType and Object::GridPartType and a method object.gridPart().

Parameters

[in]	object	Super-object, the WeakDirichletBoundaryModel generated will be compatible to this object.
[in]	where	Indicator which decides where the WeakDirichlet b.c. apply.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

◆ zeroModel() [1/3]

template<class T , class F = Expressions::Closure, std::enable_if_t< IsPDEModel< T >::value, int > = 0>

auto Dune::ACFem::PDEModel::zeroModel	(	const T &	,
		F	closure = `F{}`
	)

Generate a zero model fitting the specified object.

In order for this to work the data-type of the given object must have the sub-type Object::FunctionSpaceType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	t	Ignored. We use only the type to get hold of the FunctionSpaceType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Variant ommitting the name parameter.

◆ zeroModel() [2/3]

template<class T , class F = Expressions::Closure, std::enable_if_t< IsPDEModel< T >::value, int > = 0>

auto Dune::ACFem::PDEModel::zeroModel	(	const T &	t,
		const std::string &	name,
		F	closure = `F{}`
	)

Generate a zero model fitting the specified object.

In order for this to work the data-type of the given object must have the sub-type Object::FunctionSpaceType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	t	Ignored. We use only the type to get hold of the FunctionSpaceType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Referenced by Dune::ACFem::PDEModel::dirichletBoundaryModel(), and main().

◆ zeroModel() [3/3]

template<class T , class F = Expressions::Closure, std::enable_if_t< IsPDEModel< T >::value, int > = 0>

auto Dune::ACFem::PDEModel::zeroModel ( F closure = F{} )

Generate a zero model fitting the specified object.

In order for this to work the data-type of the given object must have the sub-type Object::FunctionSpaceType. The actual instance of the object is ignore and simply has to be passed in order that the compiler can deduce the correct types.

Parameters

[in]	t	Ignored. We use only the type to get hold of the FunctionSpaceType.
[in]	name	Optional. A descriptive name for the generated model. A suitable default will be chosen if omitted.

Examples of suitable objects are something that satisfies the

ModelInterface (another model)
Fem::DiscreteFunctionSpaceInterface
Fem::DiscreteFunctionInterface (including any wrapped or adapted non-discrete function)

See also: CompatibleModel.

Variant for use without an instance of T, and without a name.

Functions

Detailed Description

Function Documentation

◆ bind() [1/9]

◆ bind() [2/9]

◆ bind() [3/9]

◆ bind() [4/9]

◆ bind() [5/9]

◆ bind() [6/9]

◆ bind() [7/9]

◆ bind() [8/9]

◆ bind() [9/9]

◆ bulkLoadFunctionModel()

◆ classifyBoundary() [1/9]

◆ classifyBoundary() [2/9]

◆ classifyBoundary() [3/9]

◆ classifyBoundary() [4/9]

◆ classifyBoundary() [5/9]

◆ classifyBoundary() [6/9]

◆ classifyBoundary() [7/9]

◆ classifyBoundary() [8/9]

◆ classifyBoundary() [9/9]

◆ dirichlet()

◆ dirichletBoundaryModel()

◆ dirichletZeroModel()

◆ divergenceLoadModel()

◆ divergenceModel()

◆ fluidSelfTransportModel()

◆ flux() [1/5]

◆ flux() [2/5]

◆ flux() [3/5]

◆ flux() [4/5]

◆ flux() [5/5]

◆ fluxDivergence() [1/8]

◆ fluxDivergence() [2/8]

◆ fluxDivergence() [3/8]

◆ fluxDivergence() [4/8]

◆ fluxDivergence() [5/8]

◆ fluxDivergence() [6/8]

◆ fluxDivergence() [7/8]

◆ fluxDivergence() [8/8]

◆ gradientLoadModel()

◆ gradientModel()

◆ incompressibleSelfTransportModel()

◆ incompressibleTransportModel()

◆ laplacianModel()

◆ linearizedDirichlet() [1/2]

◆ linearizedDirichlet() [2/2]

◆ linearizedFlux() [1/7]

◆ linearizedFlux() [2/7]

◆ linearizedFlux() [3/7]

◆ linearizedFlux() [4/7]

◆ linearizedFlux() [5/7]

◆ linearizedFlux() [6/7]

◆ linearizedFlux() [7/7]

◆ linearizedRobinFlux() [1/2]

◆ linearizedRobinFlux() [2/2]

◆ linearizedSource() [1/5]

◆ linearizedSource() [2/5]

◆ linearizedSource() [3/5]

◆ linearizedSource() [4/5]

◆ linearizedSource() [5/5]

◆ massModel()

◆ meanCurvatureModel()

◆ name()

◆ neumannBoundaryModel()

◆ nitscheDirichletModel()

◆ p_LaplacianModel()

◆ p_MassModel()

◆ robinBoundaryModel()

◆ robinFlux()

◆ robinZeroModel()

◆ source() [1/4]

◆ source() [2/4]

◆ source() [3/4]

◆ source() [4/4]

◆ transportModel()

◆ unbind() [1/9]

◆ unbind() [2/9]

◆ unbind() [3/9]