MFEMMixedVectorWeakDivergenceKernel

Overview

Adds the domain integrator for integrating the bilinear form

var element = document.getElementById("moose-equation-1b3306df-eeba-4cc5-a871-16fd79d182d7");katex.render("(-k \\vec u, \\vec\\nabla 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 $var element = document.getElementById("moose-equation-d128ee5f-8d5c-44f6-ae13-56f9b9dc4e1a");katex.render("u \\in H(\\mathrm{curl})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ or $var element = document.getElementById("moose-equation-516c0896-70fd-48d4-b8c0-23a8b3ca0055");katex.render("H(\\mathrm{div})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-97c61b2c-25d0-48dd-b727-4857239b8165");katex.render("v \\in H^1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and $var element = document.getElementById("moose-equation-a23dfdf2-794a-415a-8b43-0a33af1783ee");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a scalar coefficient.

This term arises from the weak form of the divergence operator

var element = document.getElementById("moose-equation-e288ff7e-7a0b-401a-95f0-a7b4f5898f32");katex.render("\\vec\\nabla \\cdot (k \\vec 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}"}});

Example Input File Syntax

[Kernels<<<{"href": "../../../syntax/Kernels/index.html"}>>>]
  [curlcurl_A]
    type = MFEMComplexKernel<<<{"description": "Holds MFEMKernel objects for the real and imaginary parts of a complex kernel.", "href": "MFEMComplexKernel.html"}>>>
    variable<<<{"description": "Variable labelling the weak form this kernel is added to"}>>> = A
    [RealComponent]
      type = MFEMCurlCurlKernel
      coefficient = 1.0
    []
  []
  [mixed_grad_V]
    type = MFEMMixedSesquilinearFormKernel<<<{"description": "Base class for mixed sesquilinear form kernels, allowing different trial and test variables. Transposition of each component is controlled individually via the `transpose` parameter on each `RealComponent`/`ImagComponent` sub-block.", "href": "MFEMMixedSesquilinearFormKernel.html"}>>>
    trial_variable<<<{"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."}>>> = V
    variable<<<{"description": "Variable labelling the weak form this kernel is added to"}>>> = A
    [RealComponent]
      type = MFEMMixedVectorGradientKernel
      coefficient = 1.0
    []
  []
  [mass_A]
    type = MFEMComplexKernel<<<{"description": "Holds MFEMKernel objects for the real and imaginary parts of a complex kernel.", "href": "MFEMComplexKernel.html"}>>>
    variable<<<{"description": "Variable labelling the weak form this kernel is added to"}>>> = A
    [ImagComponent]
      type = MFEMVectorFEMassKernel
      coefficient = ${omega}
    []
  []
  [diff_V]
    type = MFEMComplexKernel<<<{"description": "Holds MFEMKernel objects for the real and imaginary parts of a complex kernel.", "href": "MFEMComplexKernel.html"}>>>
    variable<<<{"description": "Variable labelling the weak form this kernel is added to"}>>> = V
    [RealComponent]
      type = MFEMDiffusionKernel
      coefficient = 1.0
    []
  []
  [mixed_mass_A]
    type = MFEMMixedSesquilinearFormKernel<<<{"description": "Base class for mixed sesquilinear form kernels, allowing different trial and test variables. Transposition of each component is controlled individually via the `transpose` parameter on each `RealComponent`/`ImagComponent` sub-block.", "href": "MFEMMixedSesquilinearFormKernel.html"}>>>
    trial_variable<<<{"description": "The trial variable this kernel is acting on and which will be solved for. If empty (default), it will be the same as the test variable."}>>> = A
    variable<<<{"description": "Variable labelling the weak form this kernel is added to"}>>> = V
    [ImagComponent]
      type = MFEMMixedVectorWeakDivergenceKernel
      coefficient = -${omega}
    []
  []
[]

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/complex/mixed_sesquilinear_ic.i)
(test/tests/mfem/complex/mixed_sesquilinear.i)

(test/tests/mfem/complex/mixed_sesquilinear.i)

a=1.0
b=2.0
c=3.0
omega=10.0

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

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

[Variables]
  [V]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
  [A]
    type = MFEMComplexVariable
    fespace = HCurlFESpace
  []
[]

[Functions]
  [V_exact_real]
    type = ParsedFunction
    expression = '${a}*x+${b}*y+${c}*z'
  []
  [A_exact_imag]
    type = ParsedVectorFunction
    expression_x = '${a}/${omega}'
    expression_y = '${b}/${omega}'
    expression_z = '${c}/${omega}'
  []
[]

[BCs]
  [dbc_V]
    type = MFEMComplexScalarDirichletBC
    variable = V
    coefficient_real = V_exact_real
    coefficient_imag = 0.0
  []
  [dbc_A_tan]
    type = MFEMComplexVectorTangentialDirichletBC
    variable = A
    vector_coefficient_real = '0 0 0'
    vector_coefficient_imag = A_exact_imag
  []
[]

[Kernels]
  [curlcurl_A]
    type = MFEMComplexKernel
    variable = A
    [RealComponent]
      type = MFEMCurlCurlKernel
      coefficient = 1.0
    []
  []
  [mixed_grad_V]
    type = MFEMMixedSesquilinearFormKernel
    trial_variable = V
    variable = A
    [RealComponent]
      type = MFEMMixedVectorGradientKernel
      coefficient = 1.0
    []
  []
  [mass_A]
    type = MFEMComplexKernel
    variable = A
    [ImagComponent]
      type = MFEMVectorFEMassKernel
      coefficient = ${omega}
    []
  []
  [diff_V]
    type = MFEMComplexKernel
    variable = V
    [RealComponent]
      type = MFEMDiffusionKernel
      coefficient = 1.0
    []
  []
  [mixed_mass_A]
    type = MFEMMixedSesquilinearFormKernel
    trial_variable = A
    variable = V
    [ImagComponent]
      type = MFEMMixedVectorWeakDivergenceKernel
      coefficient = -${omega}
    []
  []
[]

[Solvers]
  [main]
    type = MFEMMUMPS
  []
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Postprocessors]
  [error_V]
    type = MFEMComplexL2Error
    variable = V
    function_real = V_exact_real
    function_imag = 0.0
  []
  [error_A]
    type = MFEMComplexVectorL2Error
    variable = A
    function_real = '0 0 0'
    function_imag = A_exact_imag
  []
[]

[Outputs]
  csv = true
  file_base = OutputData/MixedSesquilinear
[]

(test/tests/mfem/complex/mixed_sesquilinear_ic.i)

a=1.0
b=2.0
c=3.0
d=4.0
e=5.0
f=6.0
omega=10.0

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = SECOND
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = SECOND
  []
[]

[Variables]
  [V]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
  [A]
    type = MFEMComplexVariable
    fespace = HCurlFESpace
  []
[]

[Functions]
  [V_exact_real]
    type = ParsedFunction
    expression = '${a}*x^2+${b}*y^2+${c}*z^2'
  []
  [V_exact_imag]
    type = ParsedFunction
    expression = '${d}*x^2+${e}*y^2+${f}*z^2'
  []
  [A_exact_real]
    type = ParsedVectorFunction
    expression_x = '-2*${d}*x/${omega}'
    expression_y = '-2*${e}*y/${omega}'
    expression_z = '-2*${f}*z/${omega}'
  []
  [A_exact_imag]
    type = ParsedVectorFunction
    expression_x = '2*${a}*x/${omega}'
    expression_y = '2*${b}*y/${omega}'
    expression_z = '2*${c}*z/${omega}'
  []
[]

[ICs]
  [A_vector_ic]
    type = MFEMComplexVectorIC
    variable = A
    vector_coefficient_real = A_exact_real
    vector_coefficient_imag = A_exact_imag
  []
[]

[BCs]
  [dbc_V]
    type = MFEMComplexScalarDirichletBC
    variable = V
    coefficient_real = V_exact_real
    coefficient_imag = V_exact_imag
  []
[]

[Kernels]
  [diff_V]
    type = MFEMComplexKernel
    variable = V
    [RealComponent]
      type = MFEMDiffusionKernel
      coefficient = 1.0
    []
  []
  [mass_A]
    type = MFEMMixedSesquilinearFormKernel
    trial_variable = A
    variable = V
    [ImagComponent]
      type = MFEMMixedVectorWeakDivergenceKernel
      coefficient = -${omega}
    []
  []
[]

[Solvers]
  [main]
    type = MFEMMUMPS
  []
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Postprocessors]
  [error]
    type = MFEMComplexL2Error
    variable = V
    function_real = V_exact_real
    function_imag = V_exact_imag
  []
[]

[Outputs]
  csv = true
  file_base = OutputData/MixedSesquilinearIC
[]

(test/tests/mfem/complex/mixed_sesquilinear.i)

a=1.0
b=2.0
c=3.0
omega=10.0

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

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

[Variables]
  [V]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
  [A]
    type = MFEMComplexVariable
    fespace = HCurlFESpace
  []
[]

[Functions]
  [V_exact_real]
    type = ParsedFunction
    expression = '${a}*x+${b}*y+${c}*z'
  []
  [A_exact_imag]
    type = ParsedVectorFunction
    expression_x = '${a}/${omega}'
    expression_y = '${b}/${omega}'
    expression_z = '${c}/${omega}'
  []
[]

[BCs]
  [dbc_V]
    type = MFEMComplexScalarDirichletBC
    variable = V
    coefficient_real = V_exact_real
    coefficient_imag = 0.0
  []
  [dbc_A_tan]
    type = MFEMComplexVectorTangentialDirichletBC
    variable = A
    vector_coefficient_real = '0 0 0'
    vector_coefficient_imag = A_exact_imag
  []
[]

[Kernels]
  [curlcurl_A]
    type = MFEMComplexKernel
    variable = A
    [RealComponent]
      type = MFEMCurlCurlKernel
      coefficient = 1.0
    []
  []
  [mixed_grad_V]
    type = MFEMMixedSesquilinearFormKernel
    trial_variable = V
    variable = A
    [RealComponent]
      type = MFEMMixedVectorGradientKernel
      coefficient = 1.0
    []
  []
  [mass_A]
    type = MFEMComplexKernel
    variable = A
    [ImagComponent]
      type = MFEMVectorFEMassKernel
      coefficient = ${omega}
    []
  []
  [diff_V]
    type = MFEMComplexKernel
    variable = V
    [RealComponent]
      type = MFEMDiffusionKernel
      coefficient = 1.0
    []
  []
  [mixed_mass_A]
    type = MFEMMixedSesquilinearFormKernel
    trial_variable = A
    variable = V
    [ImagComponent]
      type = MFEMMixedVectorWeakDivergenceKernel
      coefficient = -${omega}
    []
  []
[]

[Solvers]
  [main]
    type = MFEMMUMPS
  []
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Postprocessors]
  [error_V]
    type = MFEMComplexL2Error
    variable = V
    function_real = V_exact_real
    function_imag = 0.0
  []
  [error_A]
    type = MFEMComplexVectorL2Error
    variable = A
    function_real = '0 0 0'
    function_imag = A_exact_imag
  []
[]

[Outputs]
  csv = true
  file_base = OutputData/MixedSesquilinear
[]

Overview
Example Input File Syntax
Input Parameters
Input Files