Domain Decomposition and Model Reduction of Systems with Local Nonlinearities

K. Sun (), R. Glowinski (), M. Heinkenschloss () and D. C. Sorensen ()
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K. Sun: Rice University, Department of Computational and Applied Mathematics, MS-134
R. Glowinski: University of Houston, Department of Mathematics
M. Heinkenschloss: Rice University, Department of Computational and Applied Mathematics, MS-134
D. C. Sorensen: Rice University, Department of Computational and Applied Mathematics, MS-134

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 389-396 from Springer

Abstract: Abstract 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.

Keywords: Proper Orthogonal Decomposition; Domain Decomposition; Model Reduction; Discontinuous Galerkin Method; Linear Time Invariant System (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_46

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