A parallel exponential integrator for large-scale discretizations of advection-diffusion models

We propose a parallel implementation of the ReLPM (Real Leja Points Method) for the exponential integration of large sparse systems of ODEs, generated by Finite Element discretizations of 3D advection-diffusion models. The performance of our parallel exponential integrator is compared with that of a parallelized Crank-Nicolson (CN) integrator, where the local linear solver is a parallel BiCGstab accelerated with the approximate inverse preconditioner FSAI. We developed message passing codes written in Fortran 90 and using the MPI standard. Results on SP5 and CLX machines show that the parallel efficiency raised by the two algorithms is comparable. ReLPM turns out to be from 3 to 5 times faster than CN in solving realistic advection-diffusion problems, depending on the number of processors employed.