Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation
Name
15m104582x.pdf
Description
Published version
Size
7.11 MB
Format
Adobe PDF
Checksum (MD5)
89b1f15e88f8ea750f981caffaf3331d
Author(s)
Zepeda Nunez, Leonardo Andres
Demanet, Laurent
Date Issued
June 2018
Journal
SIAM journal on scientific computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Zepeda-Núñez, Leonardo, and Laurent Demanet. "Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation." SIAM Journal on Scientific Computing 40:3 (June 2018): B944 ©2018 Author(s)
Version
Final published version
Abstract
We present a solver for the two-dimensional high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media, with online parallel complexity that scales empirically as O(NP), where N is the number of volume unknowns, and P is the number of processors, as long as P = O(N1/5). This sublinear scaling is achieved by domain decomposition, not distributed linear algebra, and improves on the P = O(N1/8) scaling reported earlier in [L. Zepeda-Núñez and L. Demanet, J. Comput. Phys., 308 (2016), pp. 347–388]. The solver relies on a two-level nested domain decomposition: a layered partition on the outer level and a further decomposition of each layer in cells at the inner level. The Helmholtz equation is reduced to a surface integral equation (SIE) posed at the interfaces between layers, efficiently solved via a nested version of the polarized traces preconditioner [L. Zepeda-Núñez and L. Demanet, J. Comput. Phys., 308 (2016), pp. 347–388]. The favorable complexity is achieved via an efficient application of the integral operators involved in the SIE.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology. Earth Resources Laboratory
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DOI of Published Version
https://doi.org/10.1137/15M104582X
