MFEMGeometricMultigridSolver

Overview

MFEMGeometricMultigridSolver defines a geometric multigrid preconditioner backed by mfem::GeometricMultigrid. It uses an MFEMFESpaceHierarchy to define the multigrid levels, a coarse-level solver, and one or more linear solvers as smoothers for the remaining levels.

The finest-level operator is supplied by the outer solver. Coarser level operators are rediscretized from the equation system on each hierarchy level using the requested "assembly_levels".

This solver is intended for linear, single-variable equation systems. Nonlinear equation systems and mixed bilinear form contributions are not supported.

Example Input File Syntax

[Solvers<<<{"href": "../../../syntax/Solvers/index.html"}>>>]
  [boomeramg]
    type = MFEMHypreBoomerAMG<<<{"description": "Hypre BoomerAMG solver and preconditioner for the iterative solution of MFEM equation systems.", "href": "MFEMHypreBoomerAMG.html"}>>>
    print_level<<<{"description": "Set the solver verbosity."}>>> = 0
  []
  [coarse]
    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."}>>> = boomeramg
    l_max_its<<<{"description": "Set the maximum number of iterations."}>>> = 10
    l_tol<<<{"description": "Set the relative tolerance."}>>> = 1e-2
    print_level<<<{"description": "Set the solver verbosity."}>>> = -1
  []
  [chebyshev]
    type = MFEMOperatorChebyshevSmoother<<<{"description": "Chebyshev polynomial smoother backed by mfem::OperatorChebyshevSmoother. Symmetric positive definite by construction; the maximum eigenvalue of D^{-1}A is estimated automatically via a power method. Suitable as a multigrid smoother.", "href": "MFEMOperatorChebyshevSmoother.html"}>>>
    order<<<{"description": "Degree of the Chebyshev polynomial (1-4)."}>>> = 2
  []
  [pmg]
    type = MFEMGeometricMultigridSolver<<<{"description": "Geometric (p-)multigrid preconditioner backed by mfem::GeometricMultigrid. Requires a linear equation system, an MFEMFESpaceHierarchy, and per-level smoother objects.", "href": "MFEMGeometricMultigridSolver.html"}>>>
    variable<<<{"description": "Name of the trial variable this preconditioner acts on."}>>> = concentration
    smoothers<<<{"description": "Names of LinearSolverBase objects used as smoothers on the interior levels (levels 1 to N-1). May have length 1 (used on all interior levels) or N-1 (one per interior level, ordered coarse-to-fine)."}>>> = chebyshev
    coarse_solver<<<{"description": "Name of the LinearSolverBase used on the coarsest level."}>>> = coarse
  []
  [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."}>>> = pmg
    l_tol<<<{"description": "Set the relative tolerance."}>>> = 1e-10
    l_max_its<<<{"description": "Set the maximum number of iterations."}>>> = 200
  []
[]

Input Parameters

coarse_solverName of the LinearSolverBase used on the coarsest level.
C++ Type:MFEMSolverName
Controllable:No
Description:Name of the LinearSolverBase used on the coarsest level.
smoothersNames of LinearSolverBase objects used as smoothers on the interior levels (levels 1 to N-1). May have length 1 (used on all interior levels) or N-1 (one per interior level, ordered coarse-to-fine).
C++ Type:std::vector<MFEMSolverName>
Controllable:No
Description:Names of LinearSolverBase objects used as smoothers on the interior levels (levels 1 to N-1). May have length 1 (used on all interior levels) or N-1 (one per interior level, ordered coarse-to-fine).
variableName of the trial variable this preconditioner acts on.
C++ Type:std::string
Controllable:No
Description:Name of the trial variable this preconditioner acts on.

Required Parameters

assembly_levelslegacy Assembly level for each level in the hierarchy. Valid values: 'legacy', 'full', 'element', 'partial', 'none'. May have length 1 (used on all N levels) or N.
Default:legacy
C++ Type:std::vector<std::string>
Controllable:No
Description:Assembly level for each level in the hierarchy. Valid values: 'legacy', 'full', 'element', 'partial', 'none'. May have length 1 (used on all N levels) or N.
low_order_refinedFalseSet usage of Low-Order Refined solver.
Default:False
C++ Type:bool
Controllable:No
Description:Set usage of Low-Order Refined solver.
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/solvers/pmg_diffusion.i)

(test/tests/mfem/solvers/pmg_diffusion.i)

# Diffusion solve using a p-multigrid (geometric multigrid) preconditioner.
#
# PDE:  -Laplacian(u) = f  on [0,1]^2
# Exact solution: u = sin(pi x)sin(pi y)
# Forcing:        f = 2 pi^2 sin(pi x)sin(pi y)
# BCs:            u = 0 on all four sides (exact solution is zero on boundary)
#
# Multigrid hierarchy (two levels):
#   level 0 (coarse): H1 order 1
#   level 1 (fine):   H1 order 2  - variable lives here via fespace = h1_hierarchy
#
# Solvers:
#   coarse_solver = coarse     (CG + BoomerAMG on the coarse system)
#   smoothers     = chebyshev  (Chebyshev smoother at the fine level; SPD by construction)

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

[Problem]
  type = MFEMProblem
[]

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

[FESpaceHierarchies]
  [h1_hierarchy]
    type = MFEMFESpaceHierarchy
    fespace = H1FESpace
    # One refinement entry adds the fine p=2 level, giving two total levels.
    refinements = 2
  []
[]

[Variables]
  [concentration]
    type = MFEMVariable
    fespace_hierarchy = h1_hierarchy
  []
[]

[BCs]
  [zero]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'bottom right top left'
  []
[]

[Functions]
  [u_exact]
    type = ParsedFunction
    expression = sin(pi*x)*sin(pi*y)
  []
  [forcing]
    type = ParsedFunction
    expression = 2*pi^2*sin(pi*x)*sin(pi*y)
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = concentration
  []
  [rhs]
    type = MFEMDomainLFKernel
    variable = concentration
    coefficient = forcing
  []
[]

[Solvers]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    print_level = 0
  []
  [coarse]
    type = MFEMCGSolver
    preconditioner = boomeramg
    l_max_its = 10
    l_tol = 1e-2
    print_level = -1
  []
  [chebyshev]
    type = MFEMOperatorChebyshevSmoother
    order = 2
  []
  [pmg]
    type = MFEMGeometricMultigridSolver
    variable = concentration
    smoothers = chebyshev
    coarse_solver = coarse
  []
  [main]
    type = MFEMCGSolver
    preconditioner = pmg
    l_tol = 1e-10
    l_max_its = 200
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [l2_error]
    type = MFEML2Error
    variable = concentration
    function = u_exact
  []
[]

[Outputs]
  [csv]
    type = CSV
    file_base = OutputData/PMGDiffusion
  []
[]

(test/tests/mfem/solvers/pmg_diffusion.i)

# Diffusion solve using a p-multigrid (geometric multigrid) preconditioner.
#
# PDE:  -Laplacian(u) = f  on [0,1]^2
# Exact solution: u = sin(pi x)sin(pi y)
# Forcing:        f = 2 pi^2 sin(pi x)sin(pi y)
# BCs:            u = 0 on all four sides (exact solution is zero on boundary)
#
# Multigrid hierarchy (two levels):
#   level 0 (coarse): H1 order 1
#   level 1 (fine):   H1 order 2  - variable lives here via fespace = h1_hierarchy
#
# Solvers:
#   coarse_solver = coarse     (CG + BoomerAMG on the coarse system)
#   smoothers     = chebyshev  (Chebyshev smoother at the fine level; SPD by construction)

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

[Problem]
  type = MFEMProblem
[]

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

[FESpaceHierarchies]
  [h1_hierarchy]
    type = MFEMFESpaceHierarchy
    fespace = H1FESpace
    # One refinement entry adds the fine p=2 level, giving two total levels.
    refinements = 2
  []
[]

[Variables]
  [concentration]
    type = MFEMVariable
    fespace_hierarchy = h1_hierarchy
  []
[]

[BCs]
  [zero]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'bottom right top left'
  []
[]

[Functions]
  [u_exact]
    type = ParsedFunction
    expression = sin(pi*x)*sin(pi*y)
  []
  [forcing]
    type = ParsedFunction
    expression = 2*pi^2*sin(pi*x)*sin(pi*y)
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = concentration
  []
  [rhs]
    type = MFEMDomainLFKernel
    variable = concentration
    coefficient = forcing
  []
[]

[Solvers]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    print_level = 0
  []
  [coarse]
    type = MFEMCGSolver
    preconditioner = boomeramg
    l_max_its = 10
    l_tol = 1e-2
    print_level = -1
  []
  [chebyshev]
    type = MFEMOperatorChebyshevSmoother
    order = 2
  []
  [pmg]
    type = MFEMGeometricMultigridSolver
    variable = concentration
    smoothers = chebyshev
    coarse_solver = coarse
  []
  [main]
    type = MFEMCGSolver
    preconditioner = pmg
    l_tol = 1e-10
    l_max_its = 200
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [l2_error]
    type = MFEML2Error
    variable = concentration
    function = u_exact
  []
[]

[Outputs]
  [csv]
    type = CSV
    file_base = OutputData/PMGDiffusion
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files