MFEMHypreADS

Overview

Defines and builds an mfem::HypreADS solver to use as a preconditioner or solver to solve the MFEM equation system. Most effective for preconditioning and solving a grad-divergence problem when using Raviart-Thomas elements, in which case the $var element = document.getElementById("moose-equation-0c745736-b404-44b6-96dc-95c84b440aea");katex.render("H(\\mathrm{div})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ FE space should be passed to the mfem::HypreADS solver during construction.

A Low-Order-Refined (LOR) version of this solver may be used instead by setting the parameter "low_order_refined" to true. Using an LOR solver improves performance for high polynomial order systems.

Example Input File Syntax

[FESpaces<<<{"href": "../../../syntax/FESpaces/index.html"}>>>]
  [HDivFESpace]
    type = MFEMVectorFESpace<<<{"description": "Convenience class to construct vector finite element spaces, abstracting away some of the mathematical complexity of specifying the dimensions.", "href": "../fespaces/MFEMVectorFESpace.html"}>>>
    fec_type<<<{"description": "Specifies the family of FE shape functions."}>>> = RT
    fec_order<<<{"description": "Order of the FE shape function to use."}>>> = CONSTANT
    ordering<<<{"description": "Ordering style to use for vector DoFs."}>>> = "vdim"
  []
[]

[Preconditioner<<<{"href": "../../../syntax/Preconditioner/index.html"}>>>]
  [ADS]
    type = MFEMHypreADS<<<{"description": "Hypre auxiliary-space divergence solver and preconditioner for the iterative solution of MFEM equation systems.", "href": "MFEMHypreADS.html"}>>>
    fespace<<<{"description": "H(div) FESpace to use in HypreADS setup."}>>> = HDivFESpace
  []
[]

[Solvers<<<{"href": "../../../syntax/Solvers/index.html"}>>>]
  [main]
    type = MFEMCGSolver<<<{"description": "MFEM native solver for the iterative solution of MFEM equation systems using the conjugate gradient method.", "href": "MFEMCGSolver.html"}>>>
    preconditioner<<<{"description": "Optional choice of preconditioner to use."}>>> = ADS
    l_tol<<<{"description": "Set the relative tolerance."}>>> = 1e-16
    l_max_its<<<{"description": "Set the maximum number of iterations."}>>> = 1000
    print_level<<<{"description": "Set the solver verbosity."}>>> = 2
  []
[]

Input Parameters

fespaceH(div) FESpace to use in HypreADS setup.
C++ Type:MFEMFESpaceName
Controllable:No
Description:H(div) FESpace to use in HypreADS setup.
low_order_refinedFalseSet usage of Low-Order Refined solver.
Default:False
C++ Type:bool
Controllable:No
Description:Set usage of Low-Order Refined solver.
print_level2Set the solver verbosity.
Default:2
C++ Type:int
Controllable:No
Description:Set the solver verbosity.
use_initial_guessFalseWhether to preserve the current MFEM solution vector as the initial guess for an iterative solver.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to preserve the current MFEM solution vector as the initial guess for an iterative solver.

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/graddiv.i)

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

# Grad-div problem using method of manufactured solutions,
# based on MFEM Example 4.

[Mesh]
  type = MFEMMesh
  file = ../mesh/beam-tet.mesh
  uniform_refine = 1
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
    ordering = "vdim"
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
  [F]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxVariables]
  [divF]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[AuxKernels]
  [div]
    type = MFEMDivAux
    variable = divF
    source = F
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [f]
    type = ParsedVectorFunction
    expression_x = '(1. + 2*kappa * kappa) * cos(kappa * x) * sin(kappa * y)'
    expression_y = '(1. + 2*kappa * kappa) * cos(kappa * y) * sin(kappa * x)'
    expression_z = '0'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
  [F_exact]
    type = ParsedVectorFunction
    expression_x = 'cos(kappa * x) * sin(kappa * y)'
    expression_y = 'cos(kappa * y) * sin(kappa * x)'
    expression_z = '0'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
[]

[BCs]
  [dirichlet]
    type = MFEMVectorNormalDirichletBC
    variable = F
    boundary = '1 2 3'
    vector_coefficient = F_exact
  []
[]

[Kernels]
  [divdiv]
    type = MFEMDivDivKernel
    variable = F
  []
  [mass]
    type = MFEMVectorFEMassKernel
    variable = F
  []
  [source]
    type = MFEMVectorFEDomainLFKernel
    variable = F
    vector_coefficient = f
  []
[]

[Preconditioner]
  [ADS]
    type = MFEMHypreADS
    fespace = HDivFESpace
  []
[]

[Solvers]
  [main]
    type = MFEMCGSolver
    preconditioner = ADS
    l_tol = 1e-16
    l_max_its = 1000
    print_level = 2
  []
[]

[Executioner]
  type = MFEMSteady
  device = "cpu"
[]

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

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

# Grad-div problem using method of manufactured solutions,
# based on MFEM Example 4.

[Mesh]
  type = MFEMMesh
  file = ../mesh/beam-tet.mesh
  uniform_refine = 1
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
    ordering = "vdim"
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
  [F]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxVariables]
  [divF]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[AuxKernels]
  [div]
    type = MFEMDivAux
    variable = divF
    source = F
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [f]
    type = ParsedVectorFunction
    expression_x = '(1. + 2*kappa * kappa) * cos(kappa * x) * sin(kappa * y)'
    expression_y = '(1. + 2*kappa * kappa) * cos(kappa * y) * sin(kappa * x)'
    expression_z = '0'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
  [F_exact]
    type = ParsedVectorFunction
    expression_x = 'cos(kappa * x) * sin(kappa * y)'
    expression_y = 'cos(kappa * y) * sin(kappa * x)'
    expression_z = '0'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
[]

[BCs]
  [dirichlet]
    type = MFEMVectorNormalDirichletBC
    variable = F
    boundary = '1 2 3'
    vector_coefficient = F_exact
  []
[]

[Kernels]
  [divdiv]
    type = MFEMDivDivKernel
    variable = F
  []
  [mass]
    type = MFEMVectorFEMassKernel
    variable = F
  []
  [source]
    type = MFEMVectorFEDomainLFKernel
    variable = F
    vector_coefficient = f
  []
[]

[Preconditioner]
  [ADS]
    type = MFEMHypreADS
    fespace = HDivFESpace
  []
[]

[Solvers]
  [main]
    type = MFEMCGSolver
    preconditioner = ADS
    l_tol = 1e-16
    l_max_its = 1000
    print_level = 2
  []
[]

[Executioner]
  type = MFEMSteady
  device = "cpu"
[]

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

Overview
Example Input File Syntax
Input Parameters
Input Files