Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 241, Issue -, Pages 45-67Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2012.09.038
Keywords
Exponential integrators; Krylov projections; EpiRK methods; Stiff systems; Large scale computing
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Funding
- U.S. Department of Energy, Office of Science, Offices of Advanced Scientific Computing Research, and Biological & Environmental Research through the U.C. Merced Center for Computational Biology [DE-FG02-04ER25625]
- National Science Foundation [1115978]
- Direct For Mathematical & Physical Scien [1115978] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1115978] Funding Source: National Science Foundation
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Exponential integrators have enjoyed a resurgence of interest in recent years, but there is still limited understanding of how their performance compares with that of state-of-the-art integrators, most notably the commonly used Newton-Krylov implicit methods. In this paper we present comparative performance analysis of Krylov-based exponential, implicit and explicit integrators on a suite of stiff test problems and demonstrate that exponential integrators have computational advantages compared to the other methods, particularly as problems become larger and more stiff. We argue that the faster convergence of the Krylov iteration within exponential integrators accounts for the main proportion of the computational savings that they provide and illustrate how the structure of these methods ensures such efficiency. In addition, we demonstrate the computational advantages of the newly introduced Tokman and Loffeld (2010) [17] exponential propagation Runge-Kutta (EpiRK) fifth-order methods. The detailed analysis of the performance of the methods that is presented provides guidelines for the construction and implementation of efficient exponential methods and the quantitative comparisons inform the selection of appropriate schemes for other problems. (C) 2012 Elsevier By. All rights reserved.
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