Technical Report CS0824

TR#:CS0824
Class:CS
Title: ANALYSIS OF RED-BLACK RELAXATION IN AUTOMATIC MULTIGRID SOLUTION OF NONSYMMETRIC AND INDEFINITE PROBLEMS.
Authors: Y. Shapira
PDFCS0824.pdf
Abstract: A method for computing the spectrum of the iteration matrices of the Black-Box Multigrid and the Automatic Multigrid (AutoMUG) methods (implemented with two levels and the red-black Successive Over Relaxation smoothing procedure) is presented. It is based on the construction of small invariant subspaces of the iteration matrices. For indefinite Helmholtz equations it provides a prediction of the optimal mesh size for the coarsest grid used. Numerical experiments applying the Automatic Multigrid (AutoMUG) method accelerated by a Lanczos-type method to the solution of nearly singular highly indefinite Helmholtz equations show the validity of this prediction.
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