Convergence of the parallel chaotic waveform relaxation method for stiff systems (Q1861322)

Ideas for the numerical solution of stiff linear systems of ordinary differential equations are presented, where the dimension is assumed to be very large. Specifically the authors propose to use the waveform relaxation technique to decompose the full system into smaller subsystems. On a parallel computer, each subsystem is then solved on its own processor. The computation is performed in an asynchronous way, so each processor can work independently of the others. Three different concrete realizations of this concept are introduced and analyzed with respect to their convergence behaviour: A fundamental asynchronous parallel multisplitting scheme, a relaxed variant of this, and a more complex overlapping multisplitting method. Numerical examples are given.