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Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers
Behrooz Zarebavami, Ahmed H. Mahmoud, Ana Dodik, Changcheng Yuan, Serban D. Porumbescu, John D. Owens, Maryam Mehri Dehnavi, Justin Solomon
https://arxiv.org/abs/2602.00898 https://arxiv.org/pdf/2602.00898 https://arxiv.org/html/2602.00898
arXiv:2602.00898v1 Announce Type: new
Abstract: We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations, repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27x.
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