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Optimized Schwarz Methods

Published in SIAM Journal on Numerical Analysis. 2006, vol. 44, no. 2, p. 699-731
Abstract Optimized Schwarz methods are a new class of Schwarz methods with greatly enhanced convergence properties. They converge uniformly faster than classical Schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical Schwarz methods if the overlap is of the order of the mesh parameter, which is often the case in practical applications. They achieve this performance by using new transmission conditions between subdomains which greatly enhance the information exchange between subdomains and are motivated by the physics of the underlying problem. We analyze in this paper these new methods for symmetric positive definite problems and show their relation to other modern domain decomposition methods like the new Finite Element Tearing and Interconnect (FETI) variants.
Keywords Information exchangeNumerical analysisFinite element methodDomain decompositionGrid patternConvergence ratePreconditioningSchwarz methodBoundary value problemMultigridPartial differential equationInitial value problemConvergence acceleration
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GANDER, Martin Jakob. Optimized Schwarz Methods. In: SIAM Journal on Numerical Analysis, 2006, vol. 44, n° 2, p. 699-731. https://archive-ouverte.unige.ch/unige:6275

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Deposited on : 2010-04-20

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