PVODE, an ODE solver for parallel computers

PVODE is a general-purpose solver for ordinary differential equation (ODE) systems that implements methods for both stiff and nonstiff systems. The co de is designed for single-program multiple-data environments. It is written in ANSI standard C, with a highly modular structure. The version being dis tributed uses the message-passing interface (MPI) system for communication. In the stiff case, PVODE uses a backward differentiation formula method co mbined with preconditioned GMRES iteration. Parallelism is achieved by dist ributing the ODE solution vector into user-specified segments and paralleli zing a set of vector kernels accordingly. For PDE-based ODE systems, we pro vide a module that generates a band block-diagonal preconditioner for use w ith the GMRES iteration. We also provide a set of interfaces to accommodate Fortran applications. The paper includes a stiff example problem and test results on a Cray-T3D with three different message-passing systems. PVODE i s publicly available.