A massively parallel exponential integrator for advection-diffusion models

Abstract

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

RMCP: Relaxed Mixed Constraint Preconditioners for saddle point linear systems arising in geomechanics

“…We made use of an optimized parallel matrix-vector product which has been developed in [25] showing its effectiveness up to 1024 processors.…”

Exponential versus IMEX high-order time integrators for thermal convection in rotating spherical shells

“…In Table 4, some quantities are shown to give some idea of the time scales corresponding to the different cases consid- 12 , and T 13 ) the time interval is between one and two orders of magnitude larger. Fig.…”

“…More precisely, u r is obtained with absolute and relative error tolerances ε a = ε r (see [1]), equal to 10 −13 for T 1 , to 10 −11 for T 2 , T 3 and T 13 , and to 10 −12 for T 12 . The decrease of the relative error given by Eq.…”

“…Since then, an increasing attention has been devoted to the use of this technique for stiff problems and large scale computational problems have been successfully solved by these methods, see e.g. the results in [12,13]. Recent reviews and assessment of exponential methods can be found, among others, in [14][15][16], while other applications of exponential methods to thermal convection problems can be found in [17].…”

Banded target matrices and recursive FSAI for parallel preconditioning

“…In our implementation, we made use of an optimized parallel matrix-vector product which has been developed in [17] showing its effectiveness up to 1024 processors.…”