SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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On construction of customized efficient exponential integrators for large stiff systems of ODEs

M. Tokman, J. Loffeld and G. Rainwater

Abstract
The flexibility of the exponential propagation iterative (EPI) methods framework allows construction of exponential schemes with improved computational efficiency. We present three classes of EPI methods of Runge-Kutta type (EPIRK) - nonsplit, split and hybrid integrators. We discuss the design principles that let us develop efficient schemes of high order with low number of stages and, consequently, reduced computational cost for a given problem. Further improvements in efficiency are derived from development of adaptive Krylov and parallel versions of EPIRK integrators. A new MPI-based software package that includes implementation of exponential methods for serial and parallel computational platforms will be presented. Using a suite of test problems we illustrate performance advantages of the new schemes and software by comparing them with other exponential and implicit methods including the popular CVODE package.

Organized by         Universidad de Valladolid     IMUVA