On the convergence rate of dynamic iteration for coupled problems with multiple subsystems

摘要

In multiphysical modeling coupled problems naturally occur. Each subproblem is commonly represented by a system of partial differential-algebraic equations. Applying the method of lines, this results in coupled differential-algebraic equations (DAEs). Dynamic iteration with windowing is a standard technique for the transient simulation of such systems. In contrast to the dynamic iteration of systems of ordinary differential equations, convergence for DAEs cannot be generally guaranteed unless some contraction condition is fulfilled. In the case of convergence, it is a linear one.In this paper, we quantify the convergence rate, i.e., the slope of the contraction, in terms of the window size. We investigate the convergence rate with respect to the coupling structure for DAE and ODE systems and also for two and more subsystems. We find higher rates (for certain coupling structures) than known before (that is, linear in the window size) and give sharp estimates for the rate. Furthermore it is revealed how the rate depends on the number of subsystems.