MFEMVectorFEBoundaryFluxIntegratedBC

Overview

Adds the boundary integrator for integrating the linear form

var element = document.getElementById("moose-equation-b9ee201b-52ba-4e00-b638-e648a640eeed");katex.render("(f, \\vec v \\cdot \\hat n)_{\\partial\\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 $var element = document.getElementById("moose-equation-07f5fa3b-1901-4ef5-9d47-0175c351c529");katex.render("\\vec v \\in H(\\mathrm{div})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-66853136-f83f-4622-aa68-411e2a0072af");katex.render("f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a scalar coefficient, and $var element = document.getElementById("moose-equation-01d1b33f-98c8-4283-9cd3-59474c6db15f");katex.render("\\hat n", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the outward facing unit normal vector on the boundary.

Example Input File Syntax

[BCs<<<{"href": "../../../syntax/BCs/index.html"}>>>]
  [flux_boundaries]
    type = MFEMVectorFEBoundaryFluxIntegratedBC<<<{"description": "Adds the boundary integrator to an MFEM problem for the linear form $(f, \\vec v \\cdot \\hat n)_{\\partial\\Omega}$", "href": "MFEMVectorFEBoundaryFluxIntegratedBC.html"}>>>
    variable<<<{"description": "Variable on which to apply the boundary condition"}>>> = velocity
    coefficient<<<{"description": "The coefficient which will be used in the integrated BC. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = exact_pressure_rhs
  []
[]

Input Parameters

boundary-1 The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries.
Default:-1
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries.
coefficient1.The coefficient which will be used in the integrated BC. 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:The coefficient which will be used in the integrated BC. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
variableVariable on which to apply the boundary condition
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Variable on which to apply the boundary condition

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/kernels/darcy.i)
(test/tests/mfem/kernels/mixed_heattransfer.i)

(test/tests/mfem/kernels/darcy.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/star.mesh
  uniform_refine = 2
[]

[Problem]
  type = MFEMProblem
[]

[Functions]
  [exact_velocity]
    type = ParsedVectorFunction
    expression_x = '-exp(x) * sin(y)'
    expression_y = '-exp(x) * cos(y)'
  []
  [exact_pressure]
    type = ParsedFunction
    expression = 'exp(x) * sin(y)'
  []
  [exact_pressure_rhs]
    type = ParsedFunction
    expression = '-exp(x) * sin(y)'
  []
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = SECOND
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = SECOND
    basis = GaussLegendre
  []
[]

[Variables]
  [velocity]
    type = MFEMVariable
    fespace = HDivFESpace
  []
  [pressure]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[BCs]
  [flux_boundaries]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = velocity
    coefficient = exact_pressure_rhs
  []
[]

[Kernels]
  [VelocityMass]
    type = MFEMVectorFEMassKernel
    variable = velocity
  []
  [PressureGrad]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = pressure
    variable = velocity
    coefficient = -1
    transpose = true
  []
  [VelocityDiv]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = velocity
    variable = pressure
    coefficient = -1
  []
[]

[Solver]
  type = MFEMMUMPS
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
  []
  [pressure_error]
    type = MFEML2Error
    variable = pressure
    function = exact_pressure
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Darcy
    vtk_format = ASCII
  []
  [DarcyErrorCSV]
    type = CSV
    file_base = OutputData/Darcy
  []
[]

(test/tests/mfem/kernels/darcy.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/star.mesh
  uniform_refine = 2
[]

[Problem]
  type = MFEMProblem
[]

[Functions]
  [exact_velocity]
    type = ParsedVectorFunction
    expression_x = '-exp(x) * sin(y)'
    expression_y = '-exp(x) * cos(y)'
  []
  [exact_pressure]
    type = ParsedFunction
    expression = 'exp(x) * sin(y)'
  []
  [exact_pressure_rhs]
    type = ParsedFunction
    expression = '-exp(x) * sin(y)'
  []
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = SECOND
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = SECOND
    basis = GaussLegendre
  []
[]

[Variables]
  [velocity]
    type = MFEMVariable
    fespace = HDivFESpace
  []
  [pressure]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[BCs]
  [flux_boundaries]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = velocity
    coefficient = exact_pressure_rhs
  []
[]

[Kernels]
  [VelocityMass]
    type = MFEMVectorFEMassKernel
    variable = velocity
  []
  [PressureGrad]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = pressure
    variable = velocity
    coefficient = -1
    transpose = true
  []
  [VelocityDiv]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = velocity
    variable = pressure
    coefficient = -1
  []
[]

[Solver]
  type = MFEMMUMPS
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
  []
  [pressure_error]
    type = MFEML2Error
    variable = pressure
    function = exact_pressure
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Darcy
    vtk_format = ASCII
  []
  [DarcyErrorCSV]
    type = CSV
    file_base = OutputData/Darcy
  []
[]

(test/tests/mfem/kernels/mixed_heattransfer.i)

# Mixed heat transfer problem.
# Based on Firedrake Irksome demo_mixed_heat example:
# https://www.firedrakeproject.org/Irksome/demos/demo_mixed_heat.py.html

[Mesh]
  type = MFEMMesh
  file = ../mesh/square.e
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = FIRST
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = FIRST
  []
[]

[Variables]
  [time_integrated_heat_flux]
    type = MFEMVariable
    fespace = HDivFESpace
    time_derivative = heat_flux
  []
  [temperature]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Kernels]
  [dT_dt,T']
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
  [divh,T']
    type = MFEMVectorFEDivergenceKernel
    trial_variable = heat_flux
    variable = temperature
  []
  [h,h']
    type = MFEMTimeDerivativeVectorFEMassKernel
    variable = time_integrated_heat_flux
  []
  [-T,div.h']
    type = MFEMVectorFEDivergenceKernel
    trial_variable = temperature
    variable = time_integrated_heat_flux
    coefficient = -1.0
    transpose = true
  []
[]

[BCs]
  [gamma_T_right]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = time_integrated_heat_flux
    coefficient = 0.0
    boundary = 2
  []
  [gamma_T_left]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = time_integrated_heat_flux
    coefficient = -1.0
    boundary = 4
  []
  [gamma_h_topbottom]
    type = MFEMVectorNormalDirichletBC
    variable = time_integrated_heat_flux
    vector_coefficient = '0.0 0.0'
    boundary = '1 3'
  []
[]

[Solver]
  type = MFEMSuperLU
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 0.03
  start_time = 0.0
  end_time = 0.09
[]

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

Overview
Example Input File Syntax
Input Parameters
Input Files