docs(fdfd): parallel ILU(0) measured on our matrices, both halves, and not used - #150
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Closes #141, by measurement: neither half of a deterministic parallel ILU(0) pays on photonoxide's matrices, so neither is used.
The factorization (Chow & Patel 2015, doi:10.1137/140968896)
Not built, measured first (comment on #141): the multigrid's smoothers already factorize slab by slab in parallel (about 1.3 s of Diel's hierarchy), and QMR + ILU(0) on the guide spends 4.0 of 5.6 s in its iterations. Chow and Patel's own results (their Section 4.2, Table 3) need 3 to 5 synchronous sweeps on matrices far from diagonally dominant.
The triangular solves (Anzt, Chow & Dongarra 2015, doi:10.1007/978-3-662-48096-0_50)
Built and measured: each triangular solve as k synchronous Jacobi sweeps, all rows in parallel, the same bits on any number of threads; on the transposed factors exactly the transpose of the same series (D⁻¹(I − TᵀD⁻¹)ʲ = (I − D⁻¹Tᵀ)ʲD⁻¹), so QMR stays consistent. The 40³ guide (Shin and Fan's operator, stretched PMLs), QMR + ILU(0) to 1e-8, 20 threads:
3.5 times slower at best, and worse with more sweeps: the factors of an indefinite matrix with PMLs are far from diagonally dominant, and the sweeps' non-normal iteration grows before it converges, as the paper warns for such matrices.
What's in this PR
Ilu0::with_sweepsandIterativeSolver3d::with_ilu_sweepsare#[cfg(test)]), so the measurement can be repeated:SWEEP_CASE=guide cargo test --release fdfd::three::tests::ilu_sweeps -- --ignored --nocapture.cargo test --release(360 passed), clippy on both crates.