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Efficient Iterative Solution of the Three-Dimensional Helmholtz Equation

dc.contributor.authorElman, Howard C.en_US
dc.contributor.authorO'Leary, Dianne P.en_US
dc.description.abstractWe examine preconditioners for the discrete indefinite Helmholtz equation on a three-dimensional box-shaped domain with Sommerfeld-like boundary conditions. The preconditioners are of two types. The first is derived by discretization of a related continuous operator that differs from the original only in its boundary conditions. The second is derived by a block Toeplitz approximation to the discretized problem. The resulting preconditioning matrices allow the use of fast transform methods and differ from the discrete Helmholtz operator by an operator of low rank. We present experimental results demonstrating that when these methods are combined with Krylov subspace iteration, convergence rates depend only mildly on both the wave number and discretization mesh size. In addition, the methods display high efficiencies in an implementation on an IBM SP-2 parallel computer. (Also cross-referenced as UMIACS-TR-97-63)en_US
dc.format.extent199658 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3827en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-97-63en_US
dc.titleEfficient Iterative Solution of the Three-Dimensional Helmholtz Equationen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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