Multilevel preconditioned QMR methods for unstructured mesh computation

We present a variant of the Quasi-Minimal Residual (QMR) algorithm of Freund and Nachtigal with a preconditioner based on the Algebraic Multilevel (AMLI) algorithm of Axelsson and Vassilevski. This combination provides an effective solution method for indefinite algebraic systems and is tested by application to finite element discretizations of the Helmholtz equation. The implementation is applicable with both h- and p-refinements, and easily extends to a parallel environment.

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