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Domain decomposition and model reduction of systems with local nonlinearities. (English) Zbl 1157.65445

Kunisch, Karl (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69776-3/hbk). 389-396 (2008).
Summary: The goal of this paper is to combine balanced truncation model reduction and domain decomposition to derive reduced order models with guaranteed error bounds for systems of discretized partial differential equations (PDEs) with a spatially localized nonlinearities. Domain decomposition techniques are used to divide the problem into linear subproblems and small nonlinear subproblems. Balanced truncation is applied to the linear subproblems with inputs and outputs determined by the original in- and outputs as well as the interface conditions between the sub-problems. The potential of this approach is demonstrated for a model problem.
For the entire collection see [Zbl 1145.65001].

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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