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.
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 subproblems. The potential of this approach
is demonstrated for a model problem.
Keywords. Model reduction, domain decomposition, Burgers equations
PDF file of the preprint.