L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation
Name
1909.01467.pdf
Description
Submitted version
Size
9.04 MB
Format
Adobe PDF
Checksum (MD5)
1dcd6eb8dcfc987ea47dff15f63806fe
Author(s)
Taus, Matthias
Zepeda-Núñez, Leonardo
Hewett, Russell J
Demanet, Laurent
Date Issued
2020
Journal
Journal of Computational Physics
Publisher
Elsevier BV
Version
Original manuscript
Abstract
© 2020 Elsevier Inc. We present the first fast solver for the high-frequency Helmholtz equation that scales optimally in parallel for a single right-hand side. The L-sweeps approach achieves this scalability by departing from the usual propagation pattern, in which information flows in a 180∘ degree cone from interfaces in a layered decomposition. Instead, with L-sweeps, information propagates in 90∘ cones induced by a Cartesian domain decomposition (CDD). We extend the notion of accurate transmission conditions to CDDs and introduce a new sweeping strategy to efficiently track the wave fronts as they propagate through the CDD. The new approach decouples the subdomains at each wave front, so that they can be processed in parallel, resulting in better parallel scalability than previously demonstrated in the literature. The method has an overall O((N/p)logω) empirical run-time for N=nd total degrees-of-freedom in a d-dimensional problem, frequency ω, and p=O(n) processors. We introduce the algorithm and provide a complexity analysis for our parallel implementation of the solver. We corroborate all claims in several two- and three-dimensional numerical examples involving constant, smooth, and discontinuous wave speeds.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.JCP.2020.109706
