The Use of Inexact ODE Solver in Waveform Relaxation Methods on a Massively Parallel Computer

This paper presents the use of inexact ordinary differential equation (ODE) solver in waveform relaxation methods for solving initial value problems. Since the conventional ODE solvers are inherently sequential, the inexact ODE solver is used by taking time points from only previous waveform iteration for time integration. As a result, this method is truly massively parallel, as the equation is completely unfolded both in system and in time. Convergence analysis shows that the spectral radius of the iteration equation resulting from the "inexact" solver is the same as that from the standard method, and hence the new method is robust. The parallel implementation issues on the DECmpp 12000/Sx computer will also be discussed. Numerical results illustrate that though the number of iterations in the inexact method is increased over the exact method, as expected, the computation time is much reduced because of the large--scale parallelism. 1 Introduction Waveform Relaxation (WR) technique w..