Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers
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.
Cite
@article{arxiv.2602.00898,
title = {Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers},
author = {Behrooz Zarebavami and Ahmed H. Mahmoud and Ana Dodik and Changcheng Yuan and Serban D. Porumbescu and John D. Owens and Maryam Mehri Dehnavi and Justin Solomon},
journal= {arXiv preprint arXiv:2602.00898},
year = {2026}
}