Stabilized overlapping modular time integration of coupled differential-algebraic equations

Abstract

The modeling of technical systems often leads to differential equations that are coupled by constraints. This results in a set of coupled differential-algebraic equations (DAEs). For efficiency concerns the full system of DAEs is split in several subsystems. The solution proceeds in macro steps. In each macro step, the subsystems are solved separately by different time integration methods, while necessary data from other subsystems is approximated by extrapolation or interpolation. After each macro step, at discrete predefined or adaptively defined communication points, the data is updated. The approximation of data between these communication points (for the current macro step) leads to an additional error in the time integration and may furthermore cause instability. Different from modular time integration of ordinary differential equations (ODEs), this effect cannot be fixed by reducing the stepsize below a small stability bound.In this paper we discuss a stabilization strategy for the stable modular time integration of coupled DAEs. The application of this strategy is illustrated for a simple benchmark problem.