Solvers¶

OpenImpala provides two solver backends for computing tortuosity, plus a legacy solver retained for comparison.

HYPRE solvers (default)¶

The primary backend uses HYPRE structured-grid solvers. Available algorithms:

Solver	Type	Best for	Python name
PCG	Krylov (CG)	Single-phase diffusion (SPD systems)	`"pcg"` or `"auto"`
FlexGMRES	Krylov	Multi-phase, non-symmetric problems	`"flexgmres"`
GMRES	Krylov	General sparse systems	`"gmres"`
BiCGSTAB	Krylov	Non-symmetric, when GMRES stalls	`"bicgstab"`
SMG	Multigrid	Small grids, direct-like convergence	`"smg"`
PFMG	Multigrid	Large grids, low memory	`"pfmg"`

Default: "auto" selects PCG, which is optimal for the single-phase steady-state diffusion problem (the Laplacian with harmonic-mean face coefficients is symmetric positive-definite).

# Use the default (PCG)
result = oi.tortuosity(data, phase=1, direction="z")

# Explicitly choose a solver
result = oi.tortuosity(data, phase=1, direction="z", solver="flexgmres")

AMReX MLMG solver¶

The matrix-free geometric multigrid solver uses AMReX’s native MLABecLaplacian operator. Advantages:

No matrix assembly — the operator is applied matrix-free
Lower memory — approximately 3x less than HYPRE’s StructMatrix
Faster setup — no algebraic multigrid (AMG) construction

Best for small-to-medium grids on shared-memory systems.

result = oi.tortuosity(data, phase=1, direction="z", solver="mlmg")

When to use which¶

Scenario	Recommended solver
Quick desktop analysis (<256^3)	`"mlmg"`
Single-phase, any size	`"auto"` (PCG)
Multi-phase with varying D	`"flexgmres"`
Large distributed MPI runs	`"pcg"` or `"pfmg"`
Debugging / comparison	`"smg"` (most robust)

Effective diffusivity tensor¶

The EffectiveDiffusivityHypre solver uses the same HYPRE backends but solves the cell problem with periodic boundary conditions. This is accessed via the C++ API or the command-line interface, not yet exposed in the high-level Python facade.

Solver parameters¶

When using the C++ interface or input files, solver behaviour is controlled via:

hypre.eps = 1.0e-9       # Convergence tolerance
hypre.maxiter = 200      # Maximum iterations