BiCGStab

Source: solvers/bicgstab.py

Matrix-free BiCGStab linear solver for the implicit Newton step.

A short-recurrence alternative to GMRES (no growing Krylov basis, so a bounded per-iteration memory), two matvecs per iteration. Like GMRES it is matrix-free (applies J.v via Matvec) and configured as a Newton linear_solver. Has no restart width (the max_its budget bounds the iteration count).

Other options

max_its — int · default 1000

Maximum inner (Krylov) iterations per Newton step

abs_tol — float · default 0.0

Absolute inner-residual tolerance (0 disables the absolute test)

rel_tol — float · default 0.0001

Relative inner-residual tolerance. Loose is fine (and faster): the outer Newton re-solves each step, so an inexact inner solve still converges – tighten only for stiff/ill-conditioned systems

preconditioner — str

Preconditioner object (a [Solvers] NoPreconditioner / Jacobi / BlockJacobi / FullPreconditioner); unset = no preconditioner

cache_strategy — str · default none

Preconditioner rebuild policy across Newton iterations: none (rebuild each step) | chord (build once, reuse) | max_its (rebuild when a solve exceeds cache_max_its iterations)

cache_max_its — int · default 10

Iteration bar that triggers a preconditioner rebuild under the max_its cache strategy