Multiplicative, Additive and Restricted Additive Optimized Schwarz Preconditioning

Details Multiplicative, Additive and Restricted Additive Optimized Schwarz Preconditioning Multiplicative, Additive and Restricted Additive Optimized Schwarz Preconditioning

2007-02-01

arxiv.org/abs/math/0702037v2

Mathematics

Numerical Analysis

25 pages

Scientific paper

We demonstrate that a small modification of the multiplicative, additive and restricted additive Schwarz preconditioner at the algebraic level, motivated by optimized Schwarz methods defined at the continuous level, leads to a significant reduction in the iteration count of the iterative solver. Numerical experiments using finite difference and spectral element discretizations of the positive definite Helmholtz problem and an idealized climate simulation illustrate the effectiveness of the new approach.

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