Preconditioning the 2D Helmholtz equation with polarized traces
We present a domain decomposition solver for the 2D Helmholtz equation, with a special choice of integral transmission condition that involves polarizing the waves into oneway components. This refinement of the transmission condition is the key to combining local direct solves into an efficient iter...
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Society of Exploration Geophysicists
2018
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| Online Access: | http://hdl.handle.net/1721.1/115514 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1811088537928335360 |
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| author | Zepeda Nunez, Leonardo Andres Hewett, Russell Demanet, Laurent |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Zepeda Nunez, Leonardo Andres Hewett, Russell Demanet, Laurent |
| author_sort | Zepeda Nunez, Leonardo Andres |
| collection | MIT |
| description | We present a domain decomposition solver for the 2D Helmholtz equation, with a special choice of integral transmission condition that involves polarizing the waves into oneway components. This refinement of the transmission condition is the key to combining local direct solves into an efficient iterative scheme, which can then be deployed in a highperformance computing environment. The method involves an expensive, but embarrassingly parallel precomputation of local Green's functions, and a fast online computation of layer potentials in partitioned low-rank form. The online part has sequential complexity that scales sublinearly with respect to the number of volume unknowns, even in the high-frequency regime. The favorable complexity scaling continues to hold in the context of low-order finite difference schemes for standard community models such as BP and Marmousi2, where convergence occurs in 5 to 10 GMRES iterations. |
| first_indexed | 2024-09-23T14:03:25Z |
| format | Article |
| id | mit-1721.1/115514 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T14:03:25Z |
| publishDate | 2018 |
| publisher | Society of Exploration Geophysicists |
| record_format | dspace |
| spelling | mit-1721.1/1155142022-10-01T18:55:28Z Preconditioning the 2D Helmholtz equation with polarized traces Zepeda Nunez, Leonardo Andres Hewett, Russell Demanet, Laurent Massachusetts Institute of Technology. Department of Mathematics Zepeda Nunez, Leonardo Andres Hewett, Russell Demanet, Laurent We present a domain decomposition solver for the 2D Helmholtz equation, with a special choice of integral transmission condition that involves polarizing the waves into oneway components. This refinement of the transmission condition is the key to combining local direct solves into an efficient iterative scheme, which can then be deployed in a highperformance computing environment. The method involves an expensive, but embarrassingly parallel precomputation of local Green's functions, and a fast online computation of layer potentials in partitioned low-rank form. The online part has sequential complexity that scales sublinearly with respect to the number of volume unknowns, even in the high-frequency regime. The favorable complexity scaling continues to hold in the context of low-order finite difference schemes for standard community models such as BP and Marmousi2, where convergence occurs in 5 to 10 GMRES iterations. TOTAL (Firm) United States. Air Force. Office of Scientific Research United States. Office of Naval Research National Science Foundation (U.S.) 2018-05-18T20:05:37Z 2018-05-18T20:05:37Z 2014 2018-05-17T17:52:49Z Article http://purl.org/eprint/type/ConferencePaper 1949-4645 http://hdl.handle.net/1721.1/115514 Zepeda-Núñez*, Leonardo, Russell J. Hewett, and Laurent Demanet. “Preconditioning the 2D Helmholtz Equation with Polarized Traces.” SEG Technical Program Expanded Abstracts 2014 (August 5, 2014). https://orcid.org/0000-0001-7052-5097 http://dx.doi.org/10.1190/SEGAM2014-1275.1 SEG Technical Program Expanded Abstracts 2014 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Society of Exploration Geophysicists MIT Web Domain |
| spellingShingle | Zepeda Nunez, Leonardo Andres Hewett, Russell Demanet, Laurent Preconditioning the 2D Helmholtz equation with polarized traces |
| title | Preconditioning the 2D Helmholtz equation with polarized traces |
| title_full | Preconditioning the 2D Helmholtz equation with polarized traces |
| title_fullStr | Preconditioning the 2D Helmholtz equation with polarized traces |
| title_full_unstemmed | Preconditioning the 2D Helmholtz equation with polarized traces |
| title_short | Preconditioning the 2D Helmholtz equation with polarized traces |
| title_sort | preconditioning the 2d helmholtz equation with polarized traces |
| url | http://hdl.handle.net/1721.1/115514 https://orcid.org/0000-0001-7052-5097 |
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