Domain decomposition techniques

MOX 64

Domain decomposition techniques

Friday 24th June 2005

Formaggia, Luca; Sala, Marzio; Saleri, Fausto

We introduce some parallel domain decomposition preconditioners for iterative solution of sparse linear systems like those arising from the approximation of partial differential equations by finite elements or finite volumes. We first give an overview of algebraic domain decomposition techniques. We then introduce a preconditioner based on a multilevel approximate Schurcomplement system. Then we present a Schwarz-based preconditioner augmented by an algebraic coarse correction operator. Being the definition of a coarse grid a difficult task on unstructured meshes, we propose a general framework to build a coarse operator by using an agglomeration procedure that operates directly on the matrix entries. Numerical results are presented aimed at assessing and comparing the effectiveness of the two methodologies. The main application will concern computational fluid dynamics (CFD), and in particular the simulation of compressible flow around aeronautical configurations.

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Formaggia, L.; Sala, M.; Saleri, F., Domain Decomposition Techniques, in Numerical Solution of Partial Differential Equations on Parallel Computers F. Bruaset, A. and Tveito, A. (ed.), Springer, 2006, 135-162