HyBIT roadmap

This roadmap describes direction, not guaranteed dates.

Published baseline

HyBIT 0.7.0 is published at immutable tag v0.7.0, commit 1fdcd6a1b8127c84306c38c3fdbad42563538ad8.

Completed in 0.7

generic algebraic two-level SPD/PCG correction;
graph/contiguous aggregation and smoothed transfer;
parallel coarse transfer and storage policies;
coarse-first resumable PCG;
prepared coarse reuse;
validated structural Graph rigid-body parallel CPU path;
release integrity/MSRV/package/ABI/real-FEM gates.

Completed on develop/0.8.0 through G7

Execution architecture

problem/execution/backend/solver/preconditioner policy architecture;
resident Krylov abstraction;
serial/Rayon resident PCG validation;
parallel CSR/Jacobi execution;
structural resident cross-check.

GeneralSquare

restarted FGMRES with separate V and Z;
reusable FGMRES workspace;
prepared GeneralSquare routing;
fixed, escalating, and budget-aware restart;
canonical prepared ILU(0);
selective row-relative pivot stabilization;
prepared ILU reuse and memory telemetry;
F1 Natural-versus-RCM ordering harness with original-system residual verification;
real nonsymmetric ordering evidence showing both a strong RCM benefit (raefsky3) and a no-benefit case (sherman5), ruling out unconditional RCM promotion;
F2 multi-matrix preflight/corpus harness with machine-readable CSV evidence;
larger real nonsymmetric venkat25 evidence showing a moderate RCM ILU(0) benefit while Jacobi remains ordering-invariant;
explicit corpus evidence that structurally missing diagonals are a common current-applicability boundary;
F3 prepared Natural/RCM ILU(0) multi-RHS harness with solver-only and end-to-end permutation accounting;
repeated 5-RHS evidence showing robust cross-RHS RCM benefit on raefsky3 but only small/timing-sensitive aggregate benefit on venkat25;
F4 serial triangular-apply/dependency profiling, with per-level and width-threshold Rayon prototypes rejected because synchronization/scheduling overhead outweighed available level parallelism.

Immediate next work

GeneralSquare robustness

GeneralSquare robustness work is closed through F7 for this 0.8 checkpoint.

Keep Jacobi as the default GeneralSquare preconditioner.
Keep canonical ILU(0) explicit/opt-in.
Keep Ilu0Fallback explicit for the missing-diagonal safety path.
Keep Natural/RCM ordering explicit; F6/F7 evidence does not justify a universal automatic selector.
Revisit automatic selection only with broader held-out validation or application-provided solve horizon / cost budget.
Treat drop-tolerance/fill, pivoting, and multilevel ILU as separate future preconditioners rather than silently changing canonical ILU(0).

ABTM topology and metadata-first execution

After the current GeneralSquare robustness sequence, reintroduce ABTM as a symbolic/topology layer rather than assuming it must replace CSR everywhere.

G1 (validated): bitmap topology algebra: AND/OR/AND-NOT/XOR, popcount, rank/select, invariants.
G2 (validated): metadata-first product pruning with candidate/executed work metrics.
G3 (validated): region growth, overlap/multiplicity, local extraction, and symbolic/numeric reuse boundaries.
G4 (validated): ABTM ILU(0) symbolic intersection and explicit production ABTM factorization path; automatic routing deferred.
G5 (validated): 3x3/6x6 block-topology characterization and explicit fixed-size dense block-CSR numerical operator; automatic CSR/B3/B6 routing deferred pending broader positive held-out evidence.
G6 (validated): ordinary scalar ABTM SpMV remains diagnostic; fixed column restrictions and graph-local restrictions use explicit prepared compact CSR, with direct or ABTM-assisted preparation selected explicitly by workload.
G7 (validated): explicit full-Rayon and task-limited prepared CSR execution; serial gather retained; automatic hardware-specific size routing deferred.
G8 (next): distributed topology, partition/halo extraction, and MPI-host integration.
G9: GPU/CubeCL-specific prepared execution after the CubeCL API stabilizes.

Track occupancy, metadata bytes, rank/select cost, bitmap operations, candidate/executed products, pruning ratio, preparation cost, and execution time. Backend promotion remains evidence-driven.

Documentation/API completeness

maintain separate user, numerical, architecture, and development docs;
keep examples runnable under gates;
add GeneralSquare selection to C/C++/Fortran only after the Rust policy is stable enough;
document report fields by solver path.

Subsequent numerical work

MINRES for SymmetricIndefinite;
genuine local spectral/GenEO-style SPD enrichment;
symbolic/topological reuse separated from numeric refactorization, with the ABTM topology track providing the structural representation experiments;
rectangular LSQR/LSMR later;
complex arithmetic later.

Parallel and large-scale work

parallel setup where worthwhile;
improve CPU sparse scheduling and NUMA/cache behavior;
GPU-resident execution after the selected CubeCL interface is stable;
GPU-suitable preconditioners rather than blindly porting serial ILU solves;
distributed-memory domain decomposition;
out-of-core state only when problem scale justifies it.

Keep release tags immutable, preserve the C ABI where practical, update language bindings together, and retain source-integrity, formatting, Clippy, MSRV, package, ABI/language, and numerical regression gates.

Non-goal

HyBIT does not claim universal sparse-solver coverage or universal performance improvement. Automatic policy changes require evidence across representative matrices.

HyBIT Documentation