A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete
Helmholtz Equations
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete
Helmholtz Equations
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Date
1999-08-27
Authors
Elman, Howard C.
Ernst, Oliver G.
O'Leary, Dianne P.
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Abstract
Standard multigrid algorithms have proven ineffective for the solution of
discretizations of Helmholtz equations. In this work we modify the standard
algorithm by adding GMRES iterations at coarse levels and as an outer
iteration. We demonstrate the algorithm's effectiveness through theoretical
analysis of a model problem and experimental results. In particular, we show
that the combined use of GMRES as a smoother and outer iteration produces an
algorithm whose performance depends relatively mildly on wave number and is
robust for normalized wave numbers as large as two hundred. For fixed wave
numbers, it displays grid-independent convergence rates and has costs
proportional to number of unknowns.
Also cross-referenced as UMIACS-TR-99-36