MFEMMixedVectorGradientKernel

Overview

Adds the domain integrator for integrating the mixed bilinear form

var element = document.getElementById("moose-equation-e77f1d27-a80e-4be2-8aac-e64ce607acfc");katex.render("(k \\vec \\nabla u, \\vec v)_\\Omega \\,\\,\\, \\forall \\vec v \\in V", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-e5c0f404-1d97-493f-a863-f11b66ef320e");katex.render("u \\in H^1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-f3bc3158-952a-49c3-9845-02faace03a9f");katex.render("\\vec v \\in H(\\mathrm{curl})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ or $var element = document.getElementById("moose-equation-ce89542d-fda5-467e-a09b-3c01d6b59990");katex.render("H(\\mathrm{div})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and $var element = document.getElementById("moose-equation-b4a000ee-a7f8-4438-b04a-4b5d09611794");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a scalar coefficient.

This term arises from the weak form of the gradient operator

var element = document.getElementById("moose-equation-51822253-0768-4946-87ce-df79adc1a91e");katex.render("k \\vec\\nabla u", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Input Parameters

blockThe list of subdomains (names or ids) that this object will be restricted to. Leave empty to apply to all subdomains.
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of subdomains (names or ids) that this object will be restricted to. Leave empty to apply to all subdomains.
coefficient1.Name of property k to use. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
Default:1.
C++ Type:MFEMScalarCoefficientName
Controllable:No
Description:Name of property k to use. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
transposeFalseIf true, adds the transpose of the integrator to the system instead.
Default:False
C++ Type:bool
Controllable:No
Description:If true, adds the transpose of the integrator to the system instead.
trial_variableThe trial variable this kernel is acting on and which will be solved for. If empty (default), it will be the same as the test variable.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:The trial variable this kernel is acting on and which will be solved for. If empty (default), it will be the same as the test variable.
variableVariable labelling the weak form this kernel is added to
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Variable labelling the weak form this kernel is added to

Optional 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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/mfem/submeshes/magnetostatic.i)

(test/tests/mfem/submeshes/magnetostatic.i)

# Definite Maxwell problem solved with Nedelec elements of the first kind
# based on MFEM Example 3.

[Mesh]
  type = MFEMMesh
  file = ../mesh/cylinder-hex-q2.gen
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
[]

[Variables]
  [a_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [electric_potential]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [b_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxKernels]
  [curl]
    type = MFEMCurlAux
    variable = b_field
    source = a_field
    execute_on = TIMESTEP_END
  []
[]

[BCs]
  [tangential_a_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = a_field
    boundary = '1 2 3'
  []
[]

[Kernels]
  inactive = coefficient_source
  [curlcurl]
    type = MFEMCurlCurlKernel
    variable = a_field
  []
  [auxvar_source]
    type = MFEMMixedVectorGradientKernel
    trial_variable = electric_potential
    variable = a_field
    block = 1
  []
  [coefficient_source]
    type = MFEMVectorFEDomainLFKernel
    vector_coefficient = electric_potential_grad
    variable = a_field
    block = 1
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
    singular = true
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = ams
  l_tol = 1e-12
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[MultiApps]
  [subapp]
    type = FullSolveMultiApp
    input_files = open_coil_source.i
    execute_on = INITIAL
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppMFEMCopyTransfer
    source_variables = electric_potential
    variables = electric_potential
    from_multi_app = subapp
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Magnetostatic
    vtk_format = ASCII
  []
[]

Overview
Input Parameters
Input Files