ADR 0014: Linear algebra with a pluggable Jacobian representation

• Status: Accepted (2026-11-10)
• Date: 2026-11-10
• Deciders: Vincent Mader
• Related: RQ6, E13; ADR 0008

Context

Implicit steps need solves with I − h γ J. For p = 1 dense LU on N ≤ 800 is cheap; for p = 2 (N up to about 4000 to 16000) dense LU costs as much as the full kernel sum (thesis review section 5). Sampled kernels yield sparse Jacobians.

Decision

Jacobians are represented by an enum: Dense, Sparse (CSR, assembled from recipes), Approximate (from a dominant-pair subset), MatrixFree (Jacobian-vector products by recipe sums). Solvers: dense LU, sparse LU, GMRES/BiCGStab with simple preconditioners (diagonal, ILU(0) on the dominant-pair Jacobian). Use the faer crate for dense and sparse factorizations if it fits after the M6 check of its current API and wasm support; otherwise nalgebra for dense plus own Krylov code.

Alternatives considered

• Dense only: makes the p = 2 cost study meaningless.
• Binding LAPACK/SuiteSparse: fast, but C dependencies and no wasm.

Consequences

• E13 can compare strategies under one interface.
• Some own Krylov and preconditioner code to test (against dense solves on small problems).