FunctionPenaltyDirichletBC

Enforces a (possibly) time and space-dependent MOOSE Function Dirichlet boundary condition in a weak sense by penalizing differences between the current solution and the Dirichlet data.

Description

FunctionPenaltyDirichletBC is a generalization of PenaltyDirichletBC which imposes a possibly temporally- and spatially-dependent value defined by a MOOSE Function object on a particular set of degrees of freedom (DOFs) defined by the boundary parameter. That is, for a PDE of the form

where is the domain, and is its boundary, a FunctionPenaltyDirichletBC object can be used to impose the condition (2) if the function is well-defined for . In this case, the function parameter corresponds to a MOOSE Function object which represents the mathematical function , and the user must define one or more sidesets corresponding to the boundary subset via the boundary parameter.

Instead of imposing the Dirichlet condition directly on the basis by replacing the equations associated with those degrees of freedom (DOFs) by the auxiliary equation , the FunctionPenaltyDirichletBC is based on the variational statement: find such that (1) holds for every . In Eq. (1), is a user-selected parameter which must be taken small enough to ensure that on . The user-selectable class parameter penalty corresponds to , and must be chosen large enough to ensure good agreement with the Dirichlet data, but not so large that the resulting Jacobian becomes ill-conditioned, resulting in failed solves and overall accuracy losses.

Benefits of the penalty-based approach include simplified Dirichlet boundary condition enforcement for non-Lagrange finite element bases, maintaining the symmetry (if any) of the original problem, and avoiding the need to zero out contributions from other rows in a special post-assembly step. Integrating by parts "in reverse" from Eq. (1), one obtains

(2)

We therefore recover a "perturbed" version of the original problem with the flux boundary condition

replacing the original Dirichlet boundary condition. It has been shown Juntunen and Stenberg (2009) that in order for the solution to this perturbed problem to converge to the solution of the original problem in the limit as , the penalty parameter must depend on the mesh size, and that as we refine the mesh, the problem becomes increasingly ill-conditioned. A related method for imposing Dirichlet boundary conditions, known as Nitsche's method Juntunen and Stenberg (2009), does not suffer from the same ill-conditioning issues, and is slated for inclusion in MOOSE some time in the future.

Example Input Syntax

[BCs]
  active = 'bc_all'
  [./bc_all]
    type = FunctionPenaltyDirichletBC
    variable = u
    function = solution
    boundary = 'top left right bottom'
    penalty = 1e6
  [../]
[]
(../moose/test/tests/bcs/penalty_dirichlet_bc/function_penalty_dirichlet_bc_test.i)

Input Parameters

  • boundaryThe list of boundary IDs from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Controllable:No

    Description:The list of boundary IDs from the mesh where this object applies

  • functionForcing function

    C++ Type:FunctionName

    Controllable:No

    Description:Forcing function

  • penaltyPenalty scalar

    C++ Type:double

    Controllable:No

    Description:Penalty scalar

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • displacementsThe displacements

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The displacements

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

Optional Parameters

  • absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution

    C++ Type:std::vector<TagName>

    Controllable:No

    Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution

  • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

    C++ Type:std::vector<TagName>

    Controllable:No

    Description:The extra tags for the matrices this Kernel should fill

  • extra_vector_tagsThe extra tags for the vectors this Kernel should fill

    C++ Type:std::vector<TagName>

    Controllable:No

    Description:The extra tags for the vectors this Kernel should fill

  • matrix_tagssystemThe tag for the matrices this Kernel should fill

    Default:system

    C++ Type:MultiMooseEnum

    Options:nontime, system

    Controllable:No

    Description:The tag for the matrices this Kernel should fill

  • vector_tagsnontimeThe tag for the vectors this Kernel should fill

    Default:nontime

    C++ Type:MultiMooseEnum

    Options:nontime, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Tagging Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Controllable:No

    Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Controllable:No

    Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Controllable:No

    Description:The seed for the master random number generator

  • use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

References

  1. M. Juntunen and R. Stenberg. Nitsche's method for general boundary conditions. Mathematics of Computation, 78(267):1353–1374, July 2009. URL: http://dx.doi.org/10.1090/S0025-5718-08-02183-2.[BibTeX]