Release 0.8.0¶

SOLVAX 0.8.0 extends the matrix-free and nonlinear solver surface so that structured kinetic, transport, and PDE codes can drive implicit solves over their native state without flattening it.

Structured and distributed FGMRES¶

gmres now accepts scalar, array, and arbitrary matching-pytree operands. The pytree path builds the flexible Arnoldi basis leaf by leaf, so it never concatenates heterogeneous state with ravel_pytree and preserves leaf-level sharding for distributed applications. An optional inner_product(left, right) callback replaces the Euclidean product throughout the Arnoldi projections, residual norms, and convergence test, which is what a distributed solve needs to define one global reduction with JAX collectives. Callers that omit both a pytree operand and a custom product keep the original optimized flat-array path, and GCROT is unchanged.

Matrix-free Newton-Krylov¶

newton_krylov solves F(x) = 0 without materializing a Jacobian. Each Newton correction obtains Jacobian-vector products from jax.linearize and is solved by SOLVAX FGMRES, so array and pytree states, right preconditioning, custom inner products, and an independent nonlinear norm are all available. The nonlinear stopping test uses the true residual recomputed after the final accepted update, and the result exposes separate nonlinear and linear convergence flags [KK04].

Affine fixed points and filtered Anderson¶

affine_fixed_point_gmres treats an affine coupling map G(x) = L x + c as the matrix-free linear system (I - L) x = c, for weakly contractive couplings where fixed-point relaxation and Anderson mixing stall. anderson_mixing gained optional spectral condition filtering to drop the smallest, ill-conditioned directions from a history.

Cyclic tridiagonal solve¶

cyclic_tridiagonal_solve solves periodic tridiagonal lines through an exact Sherman-Morrison rank-one correction, a single ordinary tridiagonal solve with two stacked right-hand sides [PTVF07]. It keeps the reproducible-Thomas / fused-cuSPARSE backend selection and is fully differentiable.

Fixes¶

lu_solve_banded promotes a real right-hand side against complex factors rather than truncating its imaginary part.