Compressed Absorbing Boundary Conditions via Matrix Probing
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer stripping...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2016
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| Online Access: | http://hdl.handle.net/1721.1/100894 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1826217824493764608 |
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| author | Belanger-Rioux, R. Demanet, Laurent |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Belanger-Rioux, R. Demanet, Laurent |
| author_sort | Belanger-Rioux, R. |
| collection | MIT |
| description | Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer stripping elimination of the exterior unknowns, but the linear algebra involved is costly. We propose bypassing the elimination procedure and directly fitting the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. The result is a concise description of the absorbing boundary condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter. |
| first_indexed | 2024-09-23T17:09:44Z |
| format | Article |
| id | mit-1721.1/100894 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:09:44Z |
| publishDate | 2016 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/1008942022-09-30T00:08:10Z Compressed Absorbing Boundary Conditions via Matrix Probing Belanger-Rioux, R. Demanet, Laurent Massachusetts Institute of Technology. Department of Mathematics Demanet, Laurent Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer stripping elimination of the exterior unknowns, but the linear algebra involved is costly. We propose bypassing the elimination procedure and directly fitting the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. The result is a concise description of the absorbing boundary condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter. United States. Air Force Office of Scientific Research United States. Office of Naval Research National Science Foundation (U.S.) TOTAL (Firm) Alfred P. Sloan Foundation 2016-01-18T21:06:14Z 2016-01-18T21:06:14Z 2015-10 2015-08 Article http://purl.org/eprint/type/JournalArticle 0036-1429 1095-7170 http://hdl.handle.net/1721.1/100894 Belanger-Rioux, R., and L. Demanet. “Compressed Absorbing Boundary Conditions via Matrix Probing.” SIAM J. Numer. Anal. 53, no. 5 (January 2015): 2441–2471. © 2015 Society for Industrial and Applied Mathematics https://orcid.org/0000-0001-7052-5097 en_US http://dx.doi.org/10.1137/14095563x SIAM Journal on Numerical Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Belanger-Rioux, R. Demanet, Laurent Compressed Absorbing Boundary Conditions via Matrix Probing |
| title | Compressed Absorbing Boundary Conditions via Matrix Probing |
| title_full | Compressed Absorbing Boundary Conditions via Matrix Probing |
| title_fullStr | Compressed Absorbing Boundary Conditions via Matrix Probing |
| title_full_unstemmed | Compressed Absorbing Boundary Conditions via Matrix Probing |
| title_short | Compressed Absorbing Boundary Conditions via Matrix Probing |
| title_sort | compressed absorbing boundary conditions via matrix probing |
| url | http://hdl.handle.net/1721.1/100894 https://orcid.org/0000-0001-7052-5097 |
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