Abstract
We present the most classical domain decomposition methods for solving elliptic partial differential equations. The first one, the Schwarz alternative procedure, involves overlapping subregions, the two others involve non-overlapping subdomains: a conforming method, the Schur complement method, and a non-conforming method, based on introducing a Lagrange multiplier in order to enforce the continuity requirements at the interface between the subdomains.
All these methods are analyzed in terms of condensed problems on the interface.
The problem of the parallel implementation of these methods is addressed, and the results of some numerical experiments for ill conditioned three-dimensional structural analysis problems are given.
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References
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© 1990 Plenum Press, New York
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Roux, FX. (1990). Domain Decomposition Methods for Partial Differential Equations and Parallel Computing. In: Devreese, J.T., Van Camp, P.E. (eds) Scientific Computing on Supercomputers II. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0659-7_7
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DOI: https://doi.org/10.1007/978-1-4613-0659-7_7
Publisher Name: Springer, Boston, MA
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