PDEs and Stencils
summary
Claim: sparsity problems are really locality problems because metadata size becomes proportional to data size. Tools auto-generate code from the PDE weak form — Firedrake, DeVito and Pyar are examples — and expose a tensor‑contraction layer where factorizations eliminate redundant recalculation, enabling thousands of lines replaced by a few pages of Python. An incremental topological sort speeds pointer‑analysis convergence. Proposed fixes are blockwise amortization and reusing elementwise schedules; adaptive meshes and moving particles still force large metadata costs.
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