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Eigenanalysis of Some Preconditioned Helmholtz Problems

dc.contributor.authorElman, Howard C.en_US
dc.contributor.authorO'Leary, Dianne P.en_US
dc.description.abstractIn this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that permit the use of fast solvers. The main innovation is that the eigenvalues for two and three-dimensional domains can be calculated exactly by solving a set of one-dimensional eigenvalue problems. This permits analysis of quite large problems. For grids fine enough to resolve the solution for a given wave number, preconditioning using Neumann boundary conditions yields eigenvalues that are uniformly bounded, located in the first quadrant, and outside the unit circle. In contrast, Dirichlet boundary conditions yield eigenvalues that approach zero as the product of wave number with the mesh size is decreased. These eigenvalue properties yield the first insight into the behavior of iterative methods such as GMRES applied to these preconditioned problems. (Also cross-referenced as UMIACS-TR-98-22)en_US
dc.format.extent17647449 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3890en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-98-22en_US
dc.titleEigenanalysis of Some Preconditioned Helmholtz Problemsen_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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