Multigrid solvers

Nodal projection

The following inputs are defined using the prefix nodal_proj:

	Description	Type	Default
verbose	Verbosity of multigrid solver in nodal projection.	Int	0
bottom_verbose	Verbosity of BiCGStab solver in nodal projection.	Int	0
mg_rtol	Relative tolerance in nodal projection.	Real	1.e-11
bottom_rtol	Relative tolerance of bottom solver.	Real	1.0e-4
mg_atol	Absolute tolerance in nodal projection.	Real	1.e-14
bottom_atol	Absolute tolerance of bottom solver, a negative number means it won’t be used.	Real	-1.0
maxiter	Maximum number of iterations in the nodal projection.	Int	100
bottom_maxiter	Maximum number of iterations in the nodal projection bottom solver if using bicg, cg, bicgcg, or cgbicg.	Int	100
mg_max_coarsening_level	Maximum number of coarser levels to allow in the nodal projection. If set to 0, the bottom solver will be called at the current level.	Int	100
bottom_solver	Which bottom solver to use in the nodal projection. Options: bicgcg bicgstab cg cgbicg hypre smoother	String	bicgcg
hypre_namespace	Namespace to use in the nodal projection when using hypre to control hypre specific settings. It can be any string.	String	hypre
hypre_interface	Which interface to use in the nodal projection when using hypre. Options: ij semi-structured structured	String	ij
num_pre_smooth	Number of smoother iterations when going down the V-cycle	Int	2
num_post_smooth	Number of smoother iterations when going up the V-cycle	Int	2

MAC (Marker-and-Cell) projection

The following inputs are defined using the prefix mac_proj:

	Description	Type	Default
verbose	Verbosity of multigrid solver in MAC projection.	Int	0
bottom_verbose	Verbosity of BiCGStab solver in MAC projection.	Int	0
mg_rtol	Relative tolerance in MAC projection.	Real	1.e-11
bottom_rtol	Relative tolerance of bottom solver.	Real	1.0e-4
mg_atol	Absolute tolerance in MAC projection.	Real	1.e-14
bottom_atol	Absolute tolerance of bottom solver, a negative number means it won’t be used.	Real	-1.0
maxiter	Maximum number of iterations in the MAC projection.	Int	200
maxorder	Sets the order of the cell-centered linear operator stencil at physical boundaries with Dirichlet boundary conditions and at coarse-fine boundaries. In both of these cases, the boundary value is not defined at the center of the ghost cell. The order determines the number of interior cells that are used in the extrapolation of the boundary value from the cell face to the center of the ghost cell, where the extrapolated value is then used in the regular stencil. For example, maxorder = 2 uses the boundary value and the first interior value to extrapolate to the ghost cell center and maxorder = 3 uses the boundary value and the first two interior values.	Int	3
bottom_maxiter	Maximum number of iterations in the MAC projection bottom solver if using bicg, cg, bicgcg, or cgbicg.	Int	200
mg_max_coarsening_level	aximum number of coarser levels to allow in the MAC projection If set to 0, the bottom solver will be called at the current level.	Int	100
bottom_solver	Which bottom solver to use in the MAC projection. Options: bicgcg bicgstab cg cgbicg hypre smoother	String	bicgcg
hypre_namespace	Namespace to use in the MAC projection when using hypre to control hypre specific settings. It can be any string.	String	hypre
hypre_interface	Which interface to use in the MAC projection when using hypre. Options: ij semi-structured structured	String	ij
num_pre_smooth	Number of smoother iterations when going down the V-cycle	Int	2
num_post_smooth	Number of smoother iterations when going up the V-cycle	Int	2

Diffusion

The following inputs are defined using the prefix diffusion:

	Description	Type	Default
verbose	Verbosity of linear solver for diffusion.	Int	0
bottom_verbose	Verbosity of BiCGStab solver in diffusion.	Int	0
mg_rtol	Relative tolerance in diffusion solver.	Real	1.e-11
mg_atol	Absolute tolerance in diffusion solver.	Real	1.e-14
maxiter	Maximum number of iterations in diffusion solver.	Int	100
bottom_maxiter	Maximum number of iterations in diffusion solver bottom solver if using bicg, cg, bicgcg, or cgbicg.	Int	100
mg_max_coarsening_level	Maximum number of coarser levels to allow in diffusion solver. If set to 0, the bottom solver will be called at the current level.	Int	100
bottom_solver	Which bottom solver to use for diffusion. Options: bicgcg bicgstab cg cgbigc smoother	String	bicgcg

Hypre Settings

hypre settings are specified using the following inputs which are read directly by AMReX when hypre is used as the bottom solver for the MAC and/or nodal projections. By default, these inputs are defined using the prefix hypre, however different settings for the nodal and MAC projections can be used by specifying a hypre_namespace for each solver.

Warning

• MFIX-Exa must be built with hypre enabled to use hypre as the bottom solver.

• If hypre is used for the nodal and MAC projections, then either the hypre_namespace must be left as the default (hypre) or unique name spaces must be provided for both.

• These inputs are all case-sensitive.

These inputs follow the typical approach for using hypre in MFIX-Exa where BoomerAMG is employed as a preconditioner and GMRES for the linear solver.

	Description	Type	Default
hypre_preconditioner	Type of preconditioner when using hypre. Options: none - no preconditioner BoomerAMG euclid	String	none
recompute_preconditioner	Recompute preconditioner during runs.	Bool	true
hypre_solver	Type of hypre solver. Options: BoomerAMG GMRES COGMRES LGMRES FlexGMRES BiCGSTAB PCG Hybrid	String	BoomerAMG
verbose	Verbosity of hypre.	Int	0
num_krylov	Number of iterations.	Int	50
adjust_singular_matrix	Enable if the problem to be solved has a singular matrix.	Bool	false
overwrite_existing_matrix_files	Overwrite existing matrix files.	Bool	false
write_matrix_files	Write matrix into text files.	Bool	false

The following inputs are valid when using BoomerAMG as a preconditioner or solver. They must be defined using the prefix hypre:

	Description	Type	Default
bamg_agg_interp_type	See HYPRE_BoomerAMGSetAggInterpType.	Int	4
bamg_agg_num_levels	See HYPRE_BoomerAMGSetAggNumLevels.	Int	0
bamg_agg_pmax_elmts	See HYPRE_BoomerAMGSetAggPMaxElmts.	Int	0
bamg_coarse_relax_type	See HYPRE_BoomerAMGSetCycleRelaxType.	Int	11
bamg_coarsen_type	See HYPRE_BoomerAMGSetCoarsenType.	Int	6
bamg_cycle_type	See HYPRE_BoomerAMGSetCycleType.	Int	1
bamg_down_relax_type	See HYPRE_BoomerAMGSetCycleRelaxType.	Int	11
bamg_interp_type	See HYPRE_BoomerAMGSetInterpType.	Int	0
bamg_keep_transpose	See HYPRE_BoomerAMGSetKeepTranspose.	Int	0
bamg_logging	See HYPRE_BoomerAMGSetLogging.	Int	0
bamg_max_coarse_size	See HYPRE_BoomerAMGSetMaxCoarseSize.	Int	9
bamg_max_iterations	See HYPRE_BoomerAMGSetMaxIter.	Int	1
bamg_max_levels	See HYPRE_BoomerAMGSetMaxLevels.	Int	20
bamg_min_coarse_size	See HYPRE_BoomerAMGSetMinCoarseSize.	Int	1
bamg_num_coarse_sweeps	See HYPRE_BoomerAMGSetCycleNumSweeps.	Int	1
bamg_num_down_sweeps	See HYPRE_BoomerAMGSetCycleNumSweeps.	Int	2
bamg_num_down_sweeps	See HYPRE_BoomerAMGSetCycleNumSweeps.	Int	2
bamg_num_sweeps	See HYPRE_BoomerAMGSetNumSweeps.	Int	2
bamg_num_sweeps	See HYPRE_BoomerAMGSetNumSweeps.	Int	2
bamg_num_up_sweeps	See HYPRE_BoomerAMGSetCycleNumSweeps.	Int	2
bamg_pmax_elmts	See HYPRE_BoomerAMGSetPMaxElmts.	Int	4
bamg_precond_tolerance	See HYPRE_BoomerAMGSetTol.	Real	0.0
bamg_relax_order	See HYPRE_BoomerAMGSetRelaxOrder.	Int	1
bamg_relax_type	See HYPRE_BoomerAMGSetRelaxType.	Int	6
bamg_set_restriction	See HYPRE_BoomerAMGSetRestriction.	Int	0
bamg_strong_threshold	See HYPRE_BoomerAMGSetStrongThreshold.	Real	0.57
bamg_trunc_factor	See HYPRE_BoomerAMGSetTruncFactor.	Real	0.1
bamg_up_relax_type	See HYPRE_BoomerAMGSetCycleRelaxType.	Int	11
bamg_variant	See HYPRE_BoomerAMGSetVariant.	Int	0
bamg_verbose	Set BoomerAMG verbosity.	Int	0

Note

This list is likely incomplete because the AMReX / hypre interface continues to evolve.