A Parallel Stiff ODE Solver based on MIRKs

A parallel, "across the method" implementation of a stiff ODE solver is presented. The construction of the methods is outlined and the main implementational issues are discussed. Performance results, using MPI on the IBM SP-2 are presented and they indicate that a speed-up between 3 and 5 typically can be obtained compared to state-of-the-art sequential codes. AMS subject classification: 65L05, 65L06, 65Y05 Keywords. Stiff ordinary differential equations, Parallel computation, Multi-implicit Runge-Kutta methods, Parallelism across the method 1. Introduction When solving stiff initial value problems the possibilities of using parallel computation "across the method" has often been discussed, [20, 19, 21, 11, 24, 7, 3], but there does however seem to be a lack of successful implementations. This paper describes the parallel implementation of a class of stiffly accurate multiimplicit Runge-Kutta methods -- MIRK methods (not to be confused with monoimplicit RK-methods [10]). The parall..