MFEMMassKernel

Overview

Adds the domain integrator for integrating the bilinear form

var element = document.getElementById("moose-equation-8956f285-19dd-4d4a-a67c-1b3984ce241a");katex.render("(k u, v)_\\Omega \\,\\,\\, \\forall 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 $var element = document.getElementById("moose-equation-8aa3ebae-6c79-49ce-b839-ba6750e4cc2c");katex.render("u, v \\in H^1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-8dab848e-3a07-4c92-be9b-653fce28f9f6");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a scalar mass coefficient.

This term arises from the weak form of the mass operator

var element = document.getElementById("moose-equation-79d1401e-71bd-43c0-ad2f-e78af7e95991");katex.render("k 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 for the mass coefficient k. 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 for the mass coefficient k. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
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/periodic/periodic.i)
(test/tests/mfem/complex/complex.i)
(test/tests/mfem/functions/cylindrical_coefficients.i)
(test/tests/mfem/periodic/periodic_complex.i)
(test/tests/mfem/auxkernels/axisymmetric_magnetostatic.i)
(test/tests/mfem/submeshes/boundary_submesh.i)
(test/tests/mfem/periodic/periodic_eigenproblem.i)

Child Objects

(framework/include/mfem/kernels/MFEMTimeDerivativeMassKernel.h)

(test/tests/mfem/periodic/periodic.i)

# Screened Poisson problem -div(grad u) + u = f on a periodic square with no boundary elements,
# with exact solution u = sin(pi x) sin(pi y).

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/periodic-square.mesh
  serial_refine = 2
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = SECOND
  []
[]

[Variables]
  [u]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Functions]
  [source]
    type = ParsedFunction
    expression = '(1 + 2 * pi^2) * sin(pi * x) * sin(pi * y)'
  []
  [exact]
    type = ParsedFunction
    expression = 'sin(pi * x) * sin(pi * y)'
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = u
  []
  [mass]
    type = MFEMMassKernel
    variable = u
  []
  [source]
    type = MFEMDomainLFKernel
    variable = u
    coefficient = source
  []
[]

[Solvers]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    print_level = 0
  []
  [cg]
    type = MFEMHyprePCG
    preconditioner = boomeramg
    l_tol = 1e-12
    print_level = 0
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [l2_error]
    type = MFEML2Error
    variable = u
    function = exact
  []
[]

[Outputs]
  [CSV]
    type = CSV
    file_base = OutputData/Periodic
  []
[]

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

mu = 1.0
epsilon = 1.0
sigma = 20.0
omega = 10.0
kappa_i = '${fparse -sqrt(mu*omega*sqrt(epsilon^2*omega^2+sigma^2)-epsilon*mu*omega^2)/sqrt(2)}'
kappa_r = '${fparse -mu*omega*sigma/kappa_i/2}'

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/inline-quad.mesh
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

[Variables]
  [u]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
[]

[Functions]
  [u0_r]
    type = ParsedFunction
    expression = exp(y*${kappa_i})*cos(y*${kappa_r})
  []
  [u0_i]
    type = ParsedFunction
    expression = -exp(y*${kappa_i})*sin(y*${kappa_r})
  []
  [stiffnessCoef]
    type = ParsedFunction
    expression = 1.0/${mu}
  []
  [massCoef]
    type = ParsedFunction
    expression = -${omega}*${omega}*${epsilon}
  []
  [lossCoef]
    type = ParsedFunction
    expression = ${omega}*${sigma}
  []
[]

[BCs]
  [dbc]
    type = MFEMComplexScalarDirichletBC
    variable = u
    coefficient_real = u0_r
    coefficient_imag = u0_i
  []
[]

[Kernels]
  [diffusion_complex]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMDiffusionKernel
      coefficient = stiffnessCoef
    []
    [ImagComponent]
      type = MFEMDiffusionKernel
      coefficient = 0.0
    []
  []
  [mass_complex]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMMassKernel
      coefficient = massCoef
    []
    [ImagComponent]
      type = MFEMMassKernel
      coefficient = lossCoef
    []
  []
[]

[Solvers]
  [main]
    type = MFEMSuperLU
  []
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[VectorPostprocessors]
  [line_sample]
    type = MFEMComplexVariableLineValueSampler
    variables = 'u'
    start_point = '0 0 0'
    end_point = '1 1 0'
    num_points = 101
  []
[]

[Outputs]
  [CSV]
    type = CSV
    file_base = OutputData/complex_2d_quad
  []
[]

(test/tests/mfem/functions/cylindrical_coefficients.i)

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/star.mesh
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

[Variables]
  [u]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Functions]
  [cylindrical]
    type = MFEMCoordinateTransformations
    coord_type = RZ
    inv_r_eps = 0
  []
[]

[FunctorMaterials]
  [material]
    type = MFEMGenericFunctorMaterial
    prop_names = 'diffCoef massCoef'
    prop_values = 'cylindrical_r cylindrical_inv_r'
  []
[]

[BCs]
  [Dirichlet]
    type = MFEMScalarDirichletBC
    variable = u
    coefficient = 10
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = u
    coefficient = diffCoef
  []

  [mass]
    type = MFEMMassKernel
    variable = u
    coefficient = massCoef
  []
[]

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


[Executioner]
  type = MFEMSteady
  device = cpu
[]

[VectorPostprocessors]
  [LineSampler]
    type = MFEMVariableLineValueSampler
    variables = 'u'
    start_point = '-1 0 0'
    end_point = '1 0 0'
    num_points = 10
  []
[]

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

(test/tests/mfem/periodic/periodic_complex.i)

# Complex screened Poisson problem -div(grad u) + (1 + i) u = f on a periodic square with no
# boundary elements, with exact solution u = sin(pi x) sin(pi y).

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/periodic-square.mesh
  serial_refine = 2
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = SECOND
  []
[]

[Variables]
  [u]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
[]

[Functions]
  [source_real]
    type = ParsedFunction
    expression = '(1 + 2 * pi^2) * sin(pi * x) * sin(pi * y)'
  []
  [source_imag]
    type = ParsedFunction
    expression = 'sin(pi * x) * sin(pi * y)'
  []
  [exact]
    type = ParsedFunction
    expression = 'sin(pi * x) * sin(pi * y)'
  []
[]

[Kernels]
  [diffusion]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMDiffusionKernel
    []
  []
  [mass]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMMassKernel
    []
    [ImagComponent]
      type = MFEMMassKernel
    []
  []
  [source]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMDomainLFKernel
      coefficient = source_real
    []
    [ImagComponent]
      type = MFEMDomainLFKernel
      coefficient = source_imag
    []
  []
[]

[Solvers]
  [main]
    type = MFEMSuperLU
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [l2_error]
    type = MFEMComplexL2Error
    variable = u
    function_real = exact
    function_imag = 0
  []
[]

[Outputs]
  [CSV]
    type = CSV
    file_base = OutputData/PeriodicComplex
  []
[]

(test/tests/mfem/auxkernels/axisymmetric_magnetostatic.i)

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/hinomaru_offset.e
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [RTFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
  [Atheta]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Functions]
  # Meridional radius r = x
  [r]
    type = MFEMParsedFunction
    expression = 'x'
  []
  [inv_r]
    type = MFEMParsedFunction
    expression = '1.0/x'
  []
  # Weighted source coefficient r * J_theta = x * 8
  [Jtheta_r_wire]
    type = MFEMParsedFunction
    expression = '8.0*x'
  []
[]

[FunctorMaterials]
  [cyl_coeffs]
    type = MFEMGenericFunctorMaterial
    prop_names = 'diffCoef massCoef'
    prop_values = 'r inv_r'
  []
  [J_wire]
    type = MFEMGenericFunctorMaterial
    prop_names = 'Jtheta sourceCoef'
    prop_values = '8.0 Jtheta_r_wire'
    block = wire
  []
[]

[AuxVariables]
  [B]
    type = MFEMVariable
    fespace = RTFESpace
  []

  [J]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = Atheta
    coefficient = diffCoef
  []

  [mass]
    type = MFEMMassKernel
    variable = Atheta
    coefficient = massCoef
  []

  [source_wire]
    type = MFEMDomainLFKernel
    variable = Atheta
    coefficient = sourceCoef
  []
[]

[AuxKernels]
  [B_from_Atheta]
    type = MFEMMeridionalCurlAux
    variable = B
    source = Atheta
  []
  [J]
    type = MFEMScalarProjectionAux
    variable = J
    coefficient = Jtheta
  []
[]

[BCs]
  [essential]
    type = MFEMScalarDirichletBC
    variable = Atheta
    boundary = skin
  []
[]

[Solvers]
  [BoomerAMG]
    type = MFEMHypreBoomerAMG
  []
  [PCG]
    type = MFEMHyprePCG
    l_tol = 1e-8
    preconditioner = BoomerAMG
  []
[]

[Postprocessors]
  [norm] # should be sqrt(8*pi)
    type = MFEMVectorL2Error
    variable = B
    function = '0. 0.'
  []
[]

[Executioner]
  type = MFEMSteady
[]

[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = AxisymmetricMagnetostatic
  []
[]

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

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/cylinder-hex-q2.gen
  uniform_refine = 1
[]

[Problem]
  type = MFEMProblem
[]

[SubMeshes]
  [exterior]
    type = MFEMBoundarySubMesh
    boundary = curved_surface
  []
[]

[FESpaces]
  [SubMeshH1FESpace]
    type = MFEMGenericFESpace
    fec_name = H1_2D_P1
    submesh = exterior
  []
[]

[Variables]
  [submesh_potential]
    type = MFEMVariable
    fespace = SubMeshH1FESpace
  []
[]

[Kernels]
  [mass]
    type = MFEMMassKernel
    variable = submesh_potential
  []
  [source]
    type = MFEMDomainLFKernel
    variable = submesh_potential
    coefficient = 3.0
  []
[]


[Solvers]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
  [main]
    type = MFEMHypreGMRES
    preconditioner = boomeramg
    l_tol = 1e-8
    l_max_its = 1000
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/BoundaryPotential
    vtk_format = ASCII
    submesh = exterior
  []
[]

(test/tests/mfem/periodic/periodic_eigenproblem.i)

# Eigenproblem -div(grad u) + u = lambda u on a periodic square with no boundary elements, whose
# exact eigenvalues are 1 + pi^2 (k^2 + l^2) for integers k and l.

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/periodic-square.mesh
  serial_refine = 2
  parallel_refine = 1
[]

[Problem]
  type = MFEMEigenproblem
  num_modes = 5
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

[Variables]
  [u]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = u
  []
  [mass]
    type = MFEMMassKernel
    variable = u
  []
[]

[Solvers]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    print_level = 0
  []
  [LOBPCG]
    type = MFEMHypreLOBPCG
    preconditioner = boomeramg
    print_level = 0
    l_tol = 1e-8
    l_max_its = 200
    random_seed = 75
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[VectorPostprocessors]
  [eigenvalues]
    type = MFEMEigenvaluesPostprocessor
  []
[]

[Outputs]
  [CSV]
    type = CSV
    file_base = OutputData/PeriodicEigenproblem
  []
[]

(framework/include/mfem/kernels/MFEMTimeDerivativeMassKernel.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#ifdef MOOSE_MFEM_ENABLED

#pragma once

#include "MFEMMassKernel.h"

/**
 * \f[
 * (k du/dt, v)
 * \f]
 */
class MFEMTimeDerivativeMassKernel : public MFEMMassKernel
{
public:
  static InputParameters validParams();

  MFEMTimeDerivativeMassKernel(const InputParameters & parameters);

  /// Get name of the trial variable (gridfunction) the kernel acts on.
  /// Defaults to the name of the test variable labelling the weak form.
  virtual const VariableName & getTrialVariableName() const override { return _var_dot_name; }

protected:
  /// Name of variable (gridfunction) representing time derivative of variable.
  const VariableName _var_dot_name;
};

#endif

Overview
Input Parameters
Input Files
Child Objects