Effective Model Reduction for Analysis of Distributed Parameter Systems

摘要

The first step in solving PDE models is typically model reduction through discretization of the spatial variables. When the reduced model is intended for analysis, e.g., in control design, parameter fitting or nonlinear analysis, it is crucial to obtain a reduced model of low order. In this paper we evaluate different methods for obtaining low order models of infinite dimensional models. The focus is on so-called moving mesh methods, in which the grid used for discretization is made dynamic in order to adapt to the solution. By employing results from feedback control theory, we show how the mesh controller should be designed in order to minimize the error introduced by the model reduction. Both finite difference methods as well as a finite element method, orthogonal collocation on finite elements, are considered. The results are illustrated by application to a 1-D model including convection and reaction.