Numerical defaults from SOLVAX

GKX delegates physics-independent numerics to SOLVAX (solvax>=0.29.0). This page lists the SOLVAX functions GKX calls and where it calls them. Physics, preconditioners, certification gates and branch selection stay in GKX.

SOLVAX function	where GKX calls it
gmres	backward-Euler implicit linear stepping (gkx.solvers_linear_implicit); the nonlinear IMEX field solve (gkx.solvers_nonlinear_imex); every shifted inner solve of shift-invert Arnoldi (gkx.solvers_linear_krylov_algorithms); the propagator fixed-point solve of the adaptive eigenpair sensitivity (gkx.objectives.core)
KrylovSolution	result type of the implicit and IMEX GMRES solves, read into ImplicitSolveStats
linear_solve	IMEX implicit solve and its implicit-function-theorem adjoint (gkx.solvers_nonlinear_imex)
tridiagonal_solve	batched Hermite-line inverse (gkx.solvers_linear_implicit), used by the implicit time-step preconditioner and by the hermite-line and field-corrected shift-invert preconditioners
block_thomas_factor_ops	Schur elimination of the z-local block in the pr3-cm preconditioner (gkx.solvers_linear_precond_pr3); GKX’s forward substitution is pinned bitwise to block_thomas_solve_ops on the same factors
estimate_rk4_timestep, adaptive_eigenpair	stable-step estimate and residual-certified propagator eigensolve behind method="adaptive" (gkx.solvers_linear_adaptive_propagator)
exponential_eigenpairs	optional exponential-Krylov filter of the adaptive eigensolve and of the differentiable eigenpair’s adjoint candidates
propagator_eigenpairs, eigenpair_reverse	candidate extraction and implicit reverse rule of the differentiable eigenpair (gkx.objectives.core; see Differentiable matrix-free eigenmodes)
sparse_operator_matrix, SpluFactorization, sparse_eigenpairs	bounded-batch sparse assembly, shifted factorization and eigenpairs of method="sparse_shift_invert" (gkx.solvers_linear_krylov)
sparse_eigenvalue	host-factored sparse eigenvalues near a shift for solver_growth_rate_from_geometry(eigensolver="sparse-direct") (gkx.objectives.core)
chunked_jacfwd	bounded-memory geometry Jacobians (gkx.geometry.autodiff_checks)

The eigensolver and sparse functions are imported inside the function that uses them, so importing GKX does not load them.

A shift-invert inner-solver comparison once published on this page is retired: it ran unpreconditioned, on a shifted system that was singular by construction, so its accuracy ranking of plain and recycled GMRES says nothing about the production solve.