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dc.contributor.advisorLaurent Demanet.en_US
dc.contributor.authorBélanger-Rioux, Rosalieen_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.date.accessioned2014-09-19T21:44:28Z
dc.date.available2014-09-19T21:44:28Z
dc.date.copyright2014en_US
dc.date.issued2014en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/90179
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.en_US
dc.description56en_US
dc.descriptionCataloged from student-submitted PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 101-105).en_US
dc.description.abstractAbsorbing 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 to bypass the elimination procedure, and directly fit the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. We obtain a concise description of the absorbing boundary condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter. We then obtain a fast (nearly linear in the dimension of the matrix) algorithm for the application of the absorbing boundary condition using partitioned low rank matrices. The result, modulo a precomputation, is a fast and memory-efficient compression scheme of an absorbing boundary condition for the Helmholtz equation.en_US
dc.description.statementofresponsibilityby Rosalie Bélanger-Rioux.en_US
dc.format.extent105 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleCompressed absorbing boundary conditions for the Helmholtz equationen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.oclc890207883en_US


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