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Multi-Resolution Approximate Inverses

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dc.contributor.authorBridson, Roberten
dc.date.accessioned2006-08-22T14:29:16Z
dc.date.available2006-08-22T14:29:16Z
dc.date.issued1999en
dc.date.submitted1999en
dc.description.abstractThis thesis presents a new preconditioner for elliptic PDE problems on unstructured meshes. Using ideas from second generation wavelets, a multi-resolution basis is constructed to effectively compress the inverse of the matrix, resolving the sparsity vs. quality problem of standard approximate inverses. This finally allows the approximate inverse approach to scale well, giving fast convergence for Krylov subspace accelerators on a wide variety of large unstructured problems. Implementation details are discussed, including ordering and construction of factored approximate inverses, discretization and basis construction in one and two dimensions, and possibilities for parallelism. The numerical experiments in one and two dimensions confirm the capabilities of the scheme. Along the way I highlight many new avenues for research, including the connections to multigrid and other multi-resolution schemes.en
dc.formatapplication/pdfen
dc.format.extent4765248 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10012/1167
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 1999, Bridson, Robert. All rights reserved.en
dc.subjectMathematicsen
dc.subjectnumericalen
dc.subjectlinearen
dc.subjectpreconditioneren
dc.subjectellipticen
dc.subjectPDEen
dc.subjectwaveletsen
dc.titleMulti-Resolution Approximate Inversesen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentApplied Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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