Iterative methods for model reduction by domain decomposition |
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Authors: | M Buffoni A Iollo |
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Affiliation: | a INRIA Futurs, Equipe-Projet MC2 and Institut de Mathématiques de Bordeaux, UMR 5251 CNRS, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence Cedex, France b Dipartimento di Ingegneria Aeronautica e Spaziale, Politecnico di Torino, 10129 Torino, Italy |
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Abstract: | It is proposed a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the two subdomains. In particular, in one subdomain we discretize the governing equations by a canonical scheme, whereas in the other one we solve a reduced order model of the original problem. Different approaches to couple the low-order model to the usual discretization are presented. The effectiveness of these approaches is tested on numerical examples pertinent to non-linear model problems including Laplace equation with non-linear boundary conditions and compressible Euler equations. |
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