Preconditioned dynamic iteration for coupled differential-algebraic systems

Abstract

The network approach to the modelling of complex technical systems results frequently is a set of differential-algebraic systems that are connected by coupling conditions. A common approach to the numerical solution of such coupled problems is based on the coupling of standard time integration, methods for the subsystems. As a unified framework for the convergence analysis of such multi-rate, multi-method or dynamic iteration approaches we study in the present paper the convergence of a dynamic iteration method with a (small) finite number of iteration steps in each window. Preconditioning is used to guarantee stability of the coupled numerical methods. The theoretical results are applied to quasilinar problems from electrical circuit simulation and to index-3 systems arising in multibody dynamics.