VectorPenaltyDirichletBC

Enforces a Dirichlet boundary condition for vector nonlinear variables in a weak sense by applying a penalty to the difference in the current solution and the Dirichlet data.

Description

VectorPenaltyDirichletBC implements a vector form of PenaltyDirichletBC, which enforces a weak sense of the Dirichlet boundary condition by setting the boundary as a penalty times the inner product of the test function and the difference between the current solution and Dirichlet data. This is given by $var element = document.getElementById("moose-equation-8e0eb352-4bce-4f5d-a0b6-6dd79f74f483");katex.render("p(\\vec{u}^\\ast, \\vec{u} - \\vec{u}_0)", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-9b77ce32-5acc-4d1c-8db2-e6404035b1e4");katex.render("p", element, {displayMode:false,throwOnError:false});$ is a scalar defining the penalty value, $var element = document.getElementById("moose-equation-2b26d572-26cc-47f0-b7e6-efe1ebc259ca");katex.render("\\vec{u}^\\ast", element, {displayMode:false,throwOnError:false});$ is the test function, and $var element = document.getElementById("moose-equation-60aed82a-50c1-460e-a344-8e3831c1e832");katex.render("\\vec{u} - \\vec{u}_0", element, {displayMode:false,throwOnError:false});$ is the vector difference between the current solution and Dirichlet data.

This boundary condition can be useful for problems where the mesh is not as refined and could potentially smooth out the problem data on a coarser mesh. It, however, has problems on refined meshes and leads to an ill-conditioned problem, which can be difficult to solve.

Example Input Syntax

[BCs]
  [./bnd_V]
    type = FunctionDirichletBC
    variable = V
    boundary = 'left right top bottom'
    function = 'V_exact_sln'
  [../]
  [./bnd_A]
    type = VectorPenaltyDirichletBC
    variable = A
    x_exact_sln = 'Ax_exact_sln'
    y_exact_sln = 'Ay_exact_sln'
    z_exact_sln = '0'
    penalty = 1e10
    boundary = 'left right top bottom'
  [../]
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
penaltyThe penalty coefficient
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The penalty coefficient
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
x_exact_sln0The exact solution for the x component
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The exact solution for the x component
y_exact_sln0The exact solution for the y component
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The exact solution for the y component
z_exact_sln0The exact solution for the z component
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The exact solution for the z component

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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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

(moose/test/tests/kernels/vector_fe/electromagnetic_coulomb_gauge.i)

# This is an MMS problem that demonstrates solution of Maxwell's equations in the
# Coulomb gauge potential form. The equations solved are:
# -\nabla^2 V = f_{V,mms}
# -\nabla^2 A - \omega^2 A + \nabla \frac{\partial V}{\partial t} = f_{A,mms}
# This tests the value and gradient of a VectorMooseVariable as well as the time
# derivative of the gradient of a standard MooseVariable
#
# This input file is subject to two tests:
# 1) An exodiff test of the physics
# 2) A Jacobian test to verify accuracy of hand-coded Jacobian routines

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 15
  ny = 15
  xmin = -1
  ymin = -1
[]

[Variables]
  [./V]
  [../]
  [./A]
    family = LAGRANGE_VEC
    order = FIRST
    scaling = 1e-10
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = V
    coef = 5
  [../]
  [./V_frc]
    type = BodyForce
    function = 'V_forcing_function'
    variable = V
  [../]
  [./A_diff]
    type = VectorCoefDiffusion
    variable = A
    coef = 5
  [../]
  [./A_coeff_reaction]
    type = VectorCoeffReaction
    variable = A
    coefficient = -.09
  [../]
  [./A_coupled_grad_td]
    type = VectorCoupledGradientTimeDerivative
    variable = A
    v = V
  [../]
  [./A_frc]
    type = VectorBodyForce
    variable = A
    function_x = 'Ax_forcing_function'
    function_y = 'Ay_forcing_function'
    function_z = '0'
  [../]
[]

[BCs]
  [./bnd_V]
    type = FunctionDirichletBC
    variable = V
    boundary = 'left right top bottom'
    function = 'V_exact_sln'
  [../]
  [./bnd_A]
    type = VectorPenaltyDirichletBC
    variable = A
    x_exact_sln = 'Ax_exact_sln'
    y_exact_sln = 'Ay_exact_sln'
    z_exact_sln = '0'
    penalty = 1e10
    boundary = 'left right top bottom'
  [../]
[]

[Functions]
  [./V_exact_sln]
    type = ParsedFunction
    expression = 'cos(0.3*t)*cos(1.1*x)*cos(1.2*y)'
  [../]
  [./Ax_exact_sln]
    type = ParsedFunction
    expression = 'cos(0.3*t)*cos(0.4*x)*cos(0.5*y)'
  [../]
  [./Ay_exact_sln]
    type = ParsedFunction
    expression = 'cos(0.3*t)*cos(0.6*x)*cos(0.7*y)'
  [../]
  [./V_forcing_function]
    type = ParsedFunction
    expression = '0.33*sin(0.3*t)*sin(1.1*x)*cos(1.2*y) + 13.25*cos(0.3*t)*cos(1.1*x)*cos(1.2*y)'
  [../]
  [./Ax_forcing_function]
    type = ParsedFunction
    expression = '0.33*sin(0.3*t)*sin(1.1*x)*cos(1.2*y) + 1.96*cos(0.3*t)*cos(0.4*x)*cos(0.5*y)'
  [../]
  [./Ay_forcing_function]
    type = ParsedFunction
    expression = '0.36*sin(0.3*t)*sin(1.2*y)*cos(1.1*x) + 4.16*cos(0.3*t)*cos(0.6*x)*cos(0.7*y)'
  [../]
[]

[Preconditioning]
  [./pre]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  end_time = 3
  l_max_its = 100
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'asm 100'
  petsc_options = '-ksp_converged_reason -ksp_monitor_true_residual -ksp_monitor_singular_value -snes_linesearch_monitor'
  line_search = 'bt'
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

[Debug]
  show_var_residual_norms = true
[]

Description
Example Input Syntax
Input Parameters