Domain Decomposition and Model Reduction of Systems with Local Nonlinearities

Kai Sun
Department of Computational and Applied Mathematics
Rice University

Roland Glowinski
Department of Mathematics
University of Houston

Matthias Heinkenschloss
Danny C. Sorensen
Department of Computational and Applied Mathematics
Rice University

In K. Kunisch, O. Steinbach, and G. Of (eds.), Numerical Mathematics And Advanced Applications. EUMATH 2007. Springer-Verlag, Heidelberg, 2008, pp. 389--396.


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 subproblems. The potential of this approach is demonstrated for a model problem.

Keywords. Model reduction, domain decomposition, Burgers equations

PDF file of the preprint.