Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations
Open Access Publications from the University of California

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

• Author(s): Liu, Yang
• Ghysels, Pieter
• Claus, Lisa
• Li, Xiaoye Sherry
• et al.

## Published Web Location

https://doi.org/10.1137/20m1349667
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.