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Structured Block Matrices Benchmark

Machine: Apple Silicon (darwin, aarch64), Julia 1.12.2, single-threaded.

fem2d (block size 7x7)

fem2d_solve(L=..., p=1.0), unstructured (sparse) vs structured (block-diagonal).

L Unstructured (s) GC % Memory (GiB) Structured (s) GC % Memory (GiB) Speedup Memory reduction
6 17.2 38.5 69.8 7.5 13.1 25.2 2.29x 2.77x
7 60.5 32.2 259.5 28.8 13.4 98.2 2.10x 2.64x
8 357.3 22.0 1809.8 171.3 6.2 644.2 2.09x 2.81x

fem3d (block size 64x64, k=3)

fem3d_solve(L=..., p=1.0), unstructured (sparse) vs structured (block-diagonal).

L Unstructured (s) GC % Memory (GiB) Structured (s) GC % Memory (GiB) Speedup Memory reduction
3 8.3 39.1 34.8 9.2 15.5 19.7 0.90x 1.77x
4 138.2 25.6 705.6 159.7 5.8 359.2 0.86x 1.97x

Date: 2026-02-09