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arXiv · 2007.00202

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations

Yang Liu·Pieter Ghysels·Lisa Claus·Xiaoye Sherry Li
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Abstract

We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

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Yang Liu, Pieter Ghysels, Lisa Claus, Xiaoye Sherry Li. 2020-07-01. Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations. https://doi.org/10.1137/20m1349667

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