Abstract | ||
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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((N)(P)), where N is the number of volume unknowns, and P is the number of processors, as long as P = O(N-1/5). This sublinear scaling is achieved by domain decomposition, not distributed linear algebra, and improves on the P = O (N-1/8) scaling reported earlier in [L. Zepeda-Nunez 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-Nunez 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. |
Year | DOI | Venue |
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2018 | 10.1137/15M104582X | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | DocType | Volume |
high-frequency,wavepropagation,Helmholtz equation,fast methods | Journal | 40 |
Issue | ISSN | Citations |
3 | 1064-8275 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Leonardo Zepeda-Núñez | 1 | 0 | 0.34 |
Laurent Demanet | 2 | 750 | 57.81 |