DUNE-ACFEM (2.5.1)
Interface class for second order elliptic models. More...
#include <dune/acfem/models/modelinterface.hh>
Classes | |
| struct | ForcesFunctionalTraits |
| Helper structure to define an optional functional as part of the "right hand side". More... | |
Public Types | |
Right-hand-side functional definitions | |
Bulk and boundary contributions to the "Right-Hand-Side". The ModelInterface allows for "Right-Hand-Side" functionals of the form \[ \langle\rho\chi\sigma, \phi\rangle = \int_\Omega f\,\phi + \int_{\partial\Omega} g\,\phi + \langle\Psi,\phi\rangle \] \(f\) is modelled by the ModelInterface::BulkForcesFunctionType, \(g\) is modelled by the ModelInterface::NeumannBoundaryFunctionType and the \(H^1\)-functional \(\Psi\) is modelled by ForcesFunctionalTraits::FunctionalType. The default is to keep everything at zero.
| |
| typedef TraitsType::BulkForcesFunctionType | BulkForcesFunctionType |
| A function modelling "force" terms in the bulk-phase. More... | |
| typedef TraitsType::NeumannBoundaryFunctionType | NeumannBoundaryFunctionType |
| A function modelling "force" terms in the bulk-phase. More... | |
| typedef TraitsType::NeumannIndicatorType | NeumannIndicatorType |
| A function modelling "force" terms in the bulk-phase. More... | |
Dirichlet boundary definitions | |
| typedef TraitsType::DirichletBoundaryFunctionType | DirichletBoundaryFunctionType |
| A BoundarySupportedFunction which must be sub-ordinate to the DirichletIndicatorType. More... | |
| typedef TraitsType::DirichletWeightFunctionType | DirichletWeightFunctionType |
| A BoundarySupportedFunction which must be sub-ordinate to the DirichletIndicatorType. More... | |
| typedef TraitsType::DirichletIndicatorType | DirichletIndicatorType |
| A BoundarySupportedFunction which must be sub-ordinate to the DirichletIndicatorType. More... | |
Public Member Functions | |
| std::string | name () const |
| Print a descriptive name for debugging and output. | |
| OperatorPartsType | operatorParts () const |
| Return the integral kernels for the bilinear form. | |
| BulkForcesFunctionType | bulkForcesFunction (const GridPartType &gridPart) const |
| Generate an instance of a class defining the bulk-forces the model is subject to. More... | |
| template<class DiscreteFunctionSpace > | |
| TraitsType::template ForcesFunctionalTraits< DiscreteFunctionSpace >::FunctionalType | forcesFunctional (const DiscreteFunctionSpace &space) const |
| Generate an instance of a class defining a functional which forms part of the force-terms for the model. | |
| DirichletBoundaryFunctionType | dirichletBoundaryFunction (const GridPartType &gridPart) const |
| Generate an instance of a class defining Dirichlet boundary values as a Fem grid-function. | |
| DirichletWeightFunctionType | dirichletWeightFunction (const GridPartType &gridPart) const |
| Generate an instance of a class defining a "left hand side" weight on the Dirichlet boundary conditions, DefaultModelTraits::DirichletWeightFunctionType. | |
| NeumannBoundaryFunctionType | neumannBoundaryFunction (const GridPartType &gridPart) const |
| Generate an instance of a class defining Neumann boundary values as a Fem grid-function. | |
| DirichletIndicatorType | dirichletIndicator () const |
| Generate an object to identify parts of the boundary subject to Dirichlet boundary conditions. More... | |
| NeumannIndicatorType | neumannIndicator () const |
| Generate an object to identify parts of the boundary subject to Neumann boundary conditions. More... | |
Detailed Description
template<class ModelType>
class Dune::ACFem::ModelInterface< ModelType >
Interface class for second order elliptic models.
The ModelInterface defines all the different parts needed to compute the weak form of a second order elliptic operator of the form
\[ \begin{split} -\nabla\cdot (A(x, u, \nabla u)\,\nabla u) + \nabla\cdot(b(x, u)\,u) + c(x, u)\,u &= f(x) + \Psi\quad \text{ in }\Omega,\\ u &= g_D \text{ on }\Gamma_D,\\ (A(x, u, \nabla u)\nabla u)\cdot\nu + \alpha(x, u)\,u &= g_N \text{ on }\Gamma_R,\\ (A(x, u, \nabla u)\nabla u)\cdot\nu &= g_N \text{ on }\Gamma_N,\\ \end{split} \]
In particular, \(\Psi\in H^{-1}\) models a functional, \(f\in L^2\) is the usual "right hand side".
The methods in this class provide all factors of the integrands not involving test functions. The multiplication by the test-functions is added in the class EllipticOperator. The weak formulation then reads:
\[ \int_\Omega (A(x,u,\nabla u)\,\nabla u)\cdot\nabla\phi\,dx + \int_\Omega (\nabla\cdot(b(x, u)\,u) + c(x, u)\,u)\,\phi\,dx + \int_{\Gamma_R} \alpha(x, u)\,u\,\phi\,do - \int_{\Gamma_N} g_N\,\phi\,do - \int_\Omega f(x)\,\phi\,dx - \langle\Psi,\,\phi\rangle = 0. \]
As the ModelInterface is potentially non-linear one has the option to leave the ModelInterface::BulkForcesFunctionType and ModelInterface::NeumannBoundaryFunctionType at zero and instead stuff the "right-hand-side" functions into the ModelInterface::robinFlux() and ModelInterface::source() methods. In principle even the functional \(\Psi\) could be expressed by a \(L^2\) scalar-product (don't shout at me: as the FEM-space is finite dimensional this is of course possible and one way to implement such a functional).
Nevertheless the different forces and other right-hand-side components are there and will be used by EllipticFemScheme and ParabolicFemScheme. Generally, the implementation checks for zero-objects (see ZeroExpression, ZeroGridFunction, ZeroFunctional, ZeroModel); the decision about which component has to be taken into account is taken at compile-time.
- Parameters
-
[in] ModelType The implementation.
- Bug:
- The setEntity() method is evil, because it in principle prevents models from being tagged as "const", or is the reason for the evil use of the "mutable" keyword in several places. Way out would be an "OperatorGerm"-class which is constructed from a given entity and/or intersection.
- Todo:
- In order to support systems there should be a DomainFunctionSpace (ansatz-functions) and a RangeFunctionSpace (test-functions). Example would be velocity-pressure for mixed discretizations of Stokes-like problems. Although it would be possible to stuff such a problem into the existing model-problem this does not feel like being desirable.
Member Typedef Documentation
◆ BulkForcesFunctionType
| typedef TraitsType::BulkForcesFunctionType Dune::ACFem::ModelInterface< ModelType >::BulkForcesFunctionType |
A function modelling "force" terms in the bulk-phase.
◆ DirichletBoundaryFunctionType
| typedef TraitsType::DirichletBoundaryFunctionType Dune::ACFem::ModelInterface< ModelType >::DirichletBoundaryFunctionType |
A BoundarySupportedFunction which must be sub-ordinate to the DirichletIndicatorType.
- See also
- BoundarySupportedFunction, in particular the "factory" function boundarySupportedFunction() and BoundaryFunctionExpressions for the set of supported algebraic operations for such functions.
◆ DirichletIndicatorType
| typedef TraitsType::DirichletIndicatorType Dune::ACFem::ModelInterface< ModelType >::DirichletIndicatorType |
A BoundarySupportedFunction which must be sub-ordinate to the DirichletIndicatorType.
- See also
- BoundarySupportedFunction, in particular the "factory" function boundarySupportedFunction() and BoundaryFunctionExpressions for the set of supported algebraic operations for such functions.
◆ DirichletWeightFunctionType
| typedef TraitsType::DirichletWeightFunctionType Dune::ACFem::ModelInterface< ModelType >::DirichletWeightFunctionType |
A BoundarySupportedFunction which must be sub-ordinate to the DirichletIndicatorType.
- See also
- BoundarySupportedFunction, in particular the "factory" function boundarySupportedFunction() and BoundaryFunctionExpressions for the set of supported algebraic operations for such functions.
◆ NeumannBoundaryFunctionType
| typedef TraitsType::NeumannBoundaryFunctionType Dune::ACFem::ModelInterface< ModelType >::NeumannBoundaryFunctionType |
A function modelling "force" terms in the bulk-phase.
◆ NeumannIndicatorType
| typedef TraitsType::NeumannIndicatorType Dune::ACFem::ModelInterface< ModelType >::NeumannIndicatorType |
A function modelling "force" terms in the bulk-phase.
Member Function Documentation
◆ bulkForcesFunction()
|
inline |
Generate an instance of a class defining the bulk-forces the model is subject to.
The return object is a Fem grid-function. This can be used for the case where the "right hand side" is an L2-function.
References Dune::ACFem::asImp().
Referenced by gridWalkTest().
◆ dirichletIndicator()
|
inline |
Generate an object to identify parts of the boundary subject to Dirichlet boundary conditions.
The return value has to obey the BoundaryIndicatorInterface.
References Dune::ACFem::asImp().
Referenced by gridWalkTest().
◆ neumannIndicator()
|
inline |
Generate an object to identify parts of the boundary subject to Neumann boundary conditions.
The return value has to obey the BoundaryIndicatorInterface.
References Dune::ACFem::asImp().
Referenced by gridWalkTest(), and Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::solve().
The documentation for this class was generated from the following file:
- dune/acfem/models/modelinterface.hh
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