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.
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Keywords
- Proper Orthogonal Decomposition
- Domain Decomposition
- Model Reduction
- Discontinuous Galerkin Method
- Linear Time Invariant System
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© 2008 Springer-Verlag Berlin Heidelberg
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Sun, K., Glowinski, R., Heinkenschloss, M., Sorensen, D.C. (2008). Domain Decomposition and Model Reduction of Systems with Local Nonlinearities. In: Kunisch, K., Of, G., Steinbach, O. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69777-0_46
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DOI: https://doi.org/10.1007/978-3-540-69777-0_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69776-3
Online ISBN: 978-3-540-69777-0
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