SIAM Journal on Scientific and Statistical Computing
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
MPI: A Message-Passing Interface Standard
MPI: A Message-Passing Interface Standard
Interpolating discrete advection-diffusion propagators at Leja sequences
Journal of Computational and Applied Mathematics
Parallel acceleration of krylov solvers by factorized approximate inverse preconditioners
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
The LEM exponential integrator for advection-diffusion-reaction equations
Journal of Computational and Applied Mathematics
Implementation of exponential Rosenbrock-type integrators
Applied Numerical Mathematics
A massively parallel exponential integrator for advection-diffusion models
Journal of Computational and Applied Mathematics
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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.