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

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

Collaboration diagram for Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >:

Public Member Functions
template<class Entity >
void	bind (const Entity &entity)
	Bind to the given entity. More...

void	unbind ()
	Unbind from the previously bound entity. More...

template<class Quadrature >
JacobianRangeType	flux (const QuadraturePoint< Quadrature > &x) const
	Evaluate \(A(x, u)\nabla u(x)\) in local coordinates. More...

template<class Quadrature >
auto	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...

FunctionSpaceTypes
Forward some basic type from the supplied function-spaces to the model class. Note that FunctionSpace is defined as a shortcut for RangeFunctionSpace in order to simplify the common case DomainFunctionSpace == RangeFunctionSpace.
using	HessianRangeSelector = typename std::conditional< std::is_convertible< typename FunctionSpace::RangeType, typename FunctionSpace::HessianRangeType >::value, Fem::ExplicitFieldVector< typename FunctionSpace::HessianRangeType::value_type, FunctionSpace::dimRange >, typename FunctionSpace::HessianRangeType >::type
	The type returned by classifyBoundary().

using	RangeFunctionSpaceType = std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType
	The type returned by classifyBoundary().

using	DomainFunctionSpaceType = std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType
	The type returned by classifyBoundary().

using	FunctionSpaceType = RangeFunctionSpaceType
	The type returned by classifyBoundary().

using	HessianRangeType = HessianRangeSelector< FunctionSpaceType >
	The type returned by classifyBoundary().

using	DomainFieldType = typename FunctionSpaceType::DomainFieldType
	The type returned by classifyBoundary().

using	RangeFieldType = typename FunctionSpaceType::RangeFieldType
	The type returned by classifyBoundary().

using	DomainRangeType = typename DomainFunctionSpaceType::RangeType
	The type returned by classifyBoundary().

using	DomainDomainType = typename DomainFunctionSpaceType::DomainType
	The type returned by classifyBoundary().

using	DomainJacobianRangeType = typename DomainFunctionSpaceType::JacobianRangeType
	The type returned by classifyBoundary().

using	DomainHessianRangeType = HessianRangeSelector< DomainFunctionSpaceType >
	The type returned by classifyBoundary().

using	DomainDomainFieldType = typename DomainFunctionSpaceType::DomainFieldType
	The type returned by classifyBoundary().

using	DomainRangeFieldType = typename DomainFunctionSpaceType::RangeFieldType
	The type returned by classifyBoundary().

using	RangeRangeType = typename RangeFunctionSpaceType::RangeType
	The type returned by classifyBoundary().

using	RangeDomainType = typename RangeFunctionSpaceType::DomainType
	The type returned by classifyBoundary().

using	RangeJacobianRangeType = typename RangeFunctionSpaceType::JacobianRangeType
	The type returned by classifyBoundary().

using	RangeHessianRangeType = HessianRangeSelector< RangeFunctionSpaceType >
	The type returned by classifyBoundary().

using	RangeDomainFieldType = typename RangeFunctionSpaceType::DomainFieldType
	The type returned by classifyBoundary().

using	RangeRangeFieldType = typename RangeFunctionSpaceType::RangeFieldType
	The type returned by classifyBoundary().

using	BoundaryConditionsType = std::pair< bool, std::bitset< dimRange > >
	The type returned by classifyBoundary().

auto	classifyBoundary (const Intersection &intersection)
	Bind to the given intersection and classify the components w.r.t. More...

static constexpr int	domainDimDomain
	The type returned by classifyBoundary().

static constexpr int	domainDimRange

static constexpr int	rangeDimDomain
	The type returned by classifyBoundary().

static constexpr int	rangeDimRange

Detailed Description

template<class GridFunction>
class Dune::ACFem::PDEModel::WeakDivergenceLoadModel< GridFunction >

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

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

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

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

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

Parameters

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

Member Function Documentation

◆ classifyBoundary()

auto Dune::ACFem::ModelBase< std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType , std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType >::classifyBoundary ( const Intersection & intersection )

inlineinherited

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.

Member Data Documentation

◆ domainDimRange

constexpr int Dune::ACFem::ModelBase< std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType , std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType >::domainDimRange

staticconstexprinherited

◆ rangeDimRange

constexpr int Dune::ACFem::ModelBase< std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType , std::decay_t< GridFunction >::FunctionSpaceType::ScalarFunctionSpaceType >::rangeDimRange

staticconstexprinherited

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

dune/acfem/models/modules/weakdivergenceloadmodel.hh

DUNE Distributed and Unified Numerics Environment

DUNE-ACFEM (unstable)

Public Member Functions

FunctionSpaceTypes