Domain Decomposition and Model Reduction of Systems with Local Nonlinearities

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