Convergent iterative schemes for time parallelization

Garrido, Izaskun; Lee, Barry; Fladmark, Gunnar; Espedal, Magne

doi:10.1090/S0025-5718-06-01832-1

Convergent iterative schemes for time parallelization
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by Izaskun Garrido, Barry Lee, Gunnar E. Fladmark and Magne S. Espedal;

Math. Comp. 75 (2006), 1403-1428

DOI: https://doi.org/10.1090/S0025-5718-06-01832-1

Published electronically: February 24, 2006

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Abstract:

Parallel methods are usually not applied to the time domain because of the inherit sequentialness of time evolution. But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods. In this paper, we present several such algorithms that actually exploit the sequential nature of time evolution through a predictor-corrector procedure. This sequentialness ensures convergence of a parallel predictor-corrector scheme within a fixed number of iterations. The performance of these novel algorithms, which are derived from the classical alternating Schwarz method, are illustrated through several numerical examples using the reservoir simulator Athena.

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