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Convergent iterative schemes for time parallelization. (English) Zbl 1089.76038
Summary: 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.

76M12 Finite volume methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76T30 Three or more component flows
76S05 Flows in porous media; filtration; seepage
65Y05 Parallel numerical computation
Full Text: DOI
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