Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations
Abstract
We present a fast and approximate multifrontal solver for largescale sparse linear systems arising from finitedifference, finitevolume or finiteelement discretization of highfrequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graphdistance guided entry evaluation or randomized matrixvector multiplicationbased 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 highfrequency Helmholtz and Maxwell problems.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2007.00202
 arXiv:
 arXiv:2007.00202
 Bibcode:
 2020arXiv200700202L
 Keywords:

 Computer Science  Mathematical Software;
 Computer Science  Computational Engineering;
 Finance;
 and Science;
 15A23;
 65F50;
 65R10;
 65R20
 EPrint:
 SIAM Journal on Scientific Computing. 2021(0):S36791