Performance predictions for parallel diagonal-implicitly iterated Runge-Kutta methods

Abstract

Many simulations in the natural sciences and engineering require the numerical solution of nonlinear differential equations. For this class of numerical methods, we propose an appropriate parallel computation model on distributed memory machines that supports the prediction of execution times. As a case study, we investigate the parallel implementation of the diagonal-implicitly iterated Runge-Kutta method, a solution method for stiff systems of ordinary differential equations. An implementation on the Intel iPSC/860 confirms the accuracy of the prediction model.