MFEMFESpaceHierarchy

Overview

MFEMFESpaceHierarchy builds an mfem::ParFiniteElementSpaceHierarchy from a base MFEM finite element space. The hierarchy starts with the named coarsest FESpaces object and then applies the ordered refinements listed in "refinements".

Each refinement entry is either h, for one uniform h-refinement, or an integer polynomial order for p-refinement. P-refinement orders must increase relative to the current finest level.

The resulting hierarchy can be assigned to an MFEMVariable and used by MFEMGeometricMultigridSolver.

Example Input File Syntax

[Problem<<<{"href": "../../../syntax/Problem/index.html"}>>>]
  type = MFEMProblem
[]

[FESpaces<<<{"href": "../../../syntax/FESpaces/index.html"}>>>]
  [H1FESpace]
    type = MFEMScalarFESpace<<<{"description": "Convenience class to construct scalar finite element spaces.", "href": "MFEMScalarFESpace.html"}>>>
    fec_type<<<{"description": "Specifies the family of FE shape functions."}>>> = H1
    fec_order<<<{"description": "Order of the FE shape function to use."}>>> = FIRST
  []
[]

[FESpaceHierarchies<<<{"href": "../../../syntax/FESpaceHierarchies/index.html"}>>>]
  [h1_hierarchy]
    type = MFEMFESpaceHierarchy<<<{"description": "Builds a mfem::ParFiniteElementSpaceHierarchy from a base FESpace by applying a sequence of h-refinements ('h') and/or p-refinements (integer order strings).", "href": "MFEMFESpaceHierarchy.html"}>>>
    fespace<<<{"description": "Name of the base (coarsest-level) FESpace object."}>>> = H1FESpace
    # One refinement entry adds the fine p=2 level, giving two total levels.
    refinements<<<{"description": "Ordered sequence of refinements. Each entry is 'h' for uniform h-refinement or an integer string for p-refinement to that polynomial order (must be strictly increasing across p-entries)."}>>> = 2
  []
[]

Input Parameters

fespaceName of the base (coarsest-level) FESpace object.
C++ Type:MFEMFESpaceName
Controllable:No
Description:Name of the base (coarsest-level) FESpace object.
refinementsOrdered sequence of refinements. Each entry is 'h' for uniform h-refinement or an integer string for p-refinement to that polynomial order (must be strictly increasing across p-entries).
C++ Type:std::vector<std::string>
Controllable:No
Description:Ordered sequence of refinements. Each entry is 'h' for uniform h-refinement or an integer string for p-refinement to that polynomial order (must be strictly increasing across p-entries).

Required 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