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A convergent algorithm for time parallelization applied to reservoir simulation. (English) Zbl 1228.76107
Kornhuber, Ralf (ed.) et al., Domain decomposition methods in science and engineering. Selected papers of the 15th international conference on domain decomposition, Berlin, Germany, July 21–25, 2003. Berlin: Springer (ISBN 3-540-22523-4/pbk). Lecture Notes in Computational Science and Engineering 40, 469-476 (2005).
Summary: Parallel methods are not usually applied to the time domain because the sequential nature of time is considered to be a handicap for the development of competitive algorithms. However, this sequential nature can also play to our advantage by ensuring convergence within a given number of iterations. The novel parallel algorithm presented in this paper acts as a predictor corrector improving both speed and accuracy with respect to the sequential solvers. Experiments using our in house fluid flow simulator in porous media, Athena, show that our parallel implementation exhibit an optimal speed up relative to the method.
For the entire collection see [Zbl 1049.65003].

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
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