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dc.contributor.authorZepeda Nunez, Leonardo Andres
dc.contributor.authorDemanet, Laurent
dc.date.accessioned2018-04-23T15:00:44Z
dc.date.available2018-04-23T15:00:44Z
dc.date.issued2015-12
dc.date.submitted2015-09
dc.identifier.issn0021-9991
dc.identifier.issn1090-2716
dc.identifier.urihttp://hdl.handle.net/1721.1/114864
dc.description.abstractWe present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as O(NL), where N is the number of volume unknowns, and L is the number of processors, as long as L grows at most like a small fractional power of N. The solver decomposes the domain into layers, and uses transmission conditions in boundary integral form to explicitly define "polarized traces", i.e., up- and down-going waves sampled at interfaces. Local direct solvers are used in each layer to precompute traces of local Green's functions in an embarrassingly parallel way (the offline part), and incomplete Green's formulas are used to propagate interface data in a sweeping fashion, as a preconditioner inside a GMRES loop (the online part). Adaptive low-rank partitioning of the integral kernels is used to speed up their application to interface data. The method uses second-order finite differences. The complexity scalings are empirical but motivated by an analysis of ranks of off-diagonal blocks of oscillatory integrals. They continue to hold in the context of standard geophysical community models such as BP and Marmousi 2, where convergence occurs in 5 to 10 GMRES iterations. While the parallelism in this paper stems from decomposing the domain, we do not explore the alternative of parallelizing the systems solves with distributed linear algebra routines. Keywords: Domain decomposition; Helmholtz equation; Integral equations; High-frequency; Fast methodsen_US
dc.description.sponsorshipUnited States. Air Force Office of Scientific Research (Grant FA9550-15-1-0078)en_US
dc.description.sponsorshipUnited States. Office of Naval Research (Grant N00014-13-1-0403)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant DMS-1255203)en_US
dc.publisherElsevier BVen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/J.JCP.2015.11.040en_US
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivs Licenseen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.sourcearXiven_US
dc.titleThe method of polarized traces for the 2D Helmholtz equationen_US
dc.typeArticleen_US
dc.identifier.citationZepeda-Núñez, Leonardo, and Laurent Demanet. “The Method of Polarized Traces for the 2D Helmholtz Equation.” Journal of Computational Physics 308 (March 2016): 347–388 © 2015 Elsevier Incen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciencesen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorZepeda Nunez, Leonardo Andres
dc.contributor.mitauthorDemanet, Laurent
dc.relation.journalJournal of Computational Physicsen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2018-04-19T19:15:18Z
dspace.orderedauthorsZepeda-Núñez, Leonardo; Demanet, Laurenten_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0001-7052-5097
mit.licensePUBLISHER_CCen_US


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