A massively parallel exponential integrator for advection-diffusion models

This work considers the Real Leja Points Method (ReLPM), for the exponential integration of large-scale sparse systems of ODEs, generated by Finite Element or Finite Difference discretizations of 3-D advection-diffusion models. A scalability analysis of the most important computational kernel inside the code, the parallel sparse matrix-vector product has been performed as well as an experimental study of the communication overhead. As a result of this study an optimized parallel sparse matrix-vector product routine has been implemented. The resulting code shows good scaling behavior even when using more than one thousand processors. The numerical results presented on a number of very large test cases gives experimental evidence that the ReLPM is a reliable and efficient tool for the simulation of complex hydrodynamic processes on parallel architectures.