MFEMComplexL2Error

Overview

Postprocessor for calculating the L2 error of a complex scalar $var element = document.getElementById("moose-equation-88951bc5-de33-4b31-a871-e555e68d5463");katex.render("H^1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ or $var element = document.getElementById("moose-equation-503dd5c6-fa38-4eb5-8b16-1aec8c1815c8");katex.render("L^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ conforming source variable compared to a complex scalar function.

var element = document.getElementById("moose-equation-15518251-0636-4d2c-833b-623ee7ab4eb1");katex.render("\\left\\Vert u_{ex} - u_{h}\\right\\Vert_{\\mathrm{L2}}", 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 $var element = document.getElementById("moose-equation-d6447799-5f04-4c23-a7ac-cb6a5a4bfcdf");katex.render("u_{h} \\in H^1 \\lor L^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-48588c5a-4bd5-4020-8f08-f4dac3c050d5");katex.render("u_{ex}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a complex scalar function.

Example Input File Syntax

[Postprocessors<<<{"href": "../../../syntax/Postprocessors/index.html"}>>>]
  [error_V]
    type = MFEMComplexL2Error<<<{"description": "Computes L2 error $\\left\\Vert u_{ex} - u_{h}\\right\\Vert_{\\rm L2}$ for complex gridfunctions using H1 or L2 elements.", "href": "MFEMComplexL2Error.html"}>>>
    variable<<<{"description": "Name of the variable of which to find the norm of the error."}>>> = V
    function_real<<<{"description": "The real part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = V_exact_real
    function_imag<<<{"description": "The imaginary part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = 0.0
  []
  [error_A]
    type = MFEMComplexVectorL2Error<<<{"description": "Computes L2 error $\\left\\Vert \\vec u_{ex} - \\vec u_{h}\\right\\Vert_{\\rm L2}$ for complex vector gridfunctions.", "href": "MFEMComplexVectorL2Error.html"}>>>
    variable<<<{"description": "Name of the vector variable of which to find the norm of the error."}>>> = A
    function_real<<<{"description": "The real part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a numeric vector value (enclosed in curly braces)."}>>> = '0 0 0'
    function_imag<<<{"description": "The imaginary part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a numeric vector value (enclosed in curly braces)."}>>> = A_exact_imag
  []
[]

Input Parameters

variableName of the variable of which to find the norm of the error.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Name of the variable of which to find the norm of the error.

Required Parameters

execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, MULTISYSTEM_FIXED_POINT_ITERATION_END, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
function_imagThe imaginary part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
C++ Type:MFEMScalarCoefficientName
Controllable:No
Description:The imaginary part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
function_realThe real part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
C++ Type:MFEMScalarCoefficientName
Controllable:No
Description:The real part of the analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.

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.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Advanced Parameters

Input Files

(test/tests/mfem/complex/mixed_sesquilinear_real_imag.i)
(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_real_imag.i)

a=1.0
b=2.0
c=3.0
d=4.0
e=5.0
f=6.0
omega=10.0
alpha=1.0
beta=0.5

[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 = FIRST
  []
[]

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

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

[BCs]
  [dbc_V]
    type = MFEMComplexScalarDirichletBC
    variable = V
    coefficient_real = V_exact_real
    coefficient_imag = V_exact_imag
  []
  [dbc_A_tan]
    type = MFEMComplexVectorTangentialDirichletBC
    variable = A
    vector_coefficient_real = A_exact_real
    vector_coefficient_imag = A_exact_imag
  []
[]

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

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

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Postprocessors]
  [error_V]
    type = MFEMComplexL2Error
    variable = V
    function_real = V_exact_real
    function_imag = V_exact_imag
  []
  [error_A]
    type = MFEMComplexVectorL2Error
    variable = A
    function_real = A_exact_real
    function_imag = A_exact_imag
  []
[]

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

(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