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Keywords: parallelisation, time dependent problems, predictor-corrector, shooting techniques.

Abstract

In this chapter we present the current status of a method, first introduced in 2001 authored by J.-L. Lions, Y. Maday and G. Turinici that allows for parallization in time for the simulation of systems of ordinary differential equations or time dependent partial differential equations. Following the same strategy as the one that is used in domain decomposition methods for solving elliptic problems that consists of breaking the domain of computation into subdomains (with overlap or without) and solving iteratively over each subdomain independently using different processors, the "parareal in time" method proposes breaking the global problem of time evolution into a series of independent evolution problems on smaller time intervals.

The iterative algorithm is based on a predictor corrector approach that generally converges quite fast, and leads, when very many processors are available, to real time solution procedures. This reasoning led us to name this new algorithm "parareal in time" (parallel in real time).

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Computational Science, Engineering & Technology Series ISSN 1759-3158 CSETS: 24 SUBSTRUCTURING TECHNIQUES AND DOMAIN DECOMPOSITION METHODS Edited by: F. Magoulès Chapter 2 The 'Parareal in Time' Algorithm Y. Maday Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, Paris, France and Division of Applied Mathematics, Brown University, Providence, United States of America doi:10.4203/csets.24.2 purchase the full-text of this chapter Full Bibliographic Reference for this chapter Y. Maday, "The 'Parareal in Time' Algorithm", in F. Magoulès, (Editor), "Substructuring Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 2, pp 19-44, 2010. doi:10.4203/csets.24.2 Keywords: parallelisation, time dependent problems, predictor-corrector, shooting techniques. Abstract In this chapter we present the current status of a method, first introduced in 2001 authored by J.-L. Lions, Y. Maday and G. Turinici that allows for parallization in time for the simulation of systems of ordinary differential equations or time dependent partial differential equations. Following the same strategy as the one that is used in domain decomposition methods for solving elliptic problems that consists of breaking the domain of computation into subdomains (with overlap or without) and solving iteratively over each subdomain independently using different processors, the "parareal in time" method proposes breaking the global problem of time evolution into a series of independent evolution problems on smaller time intervals. The iterative algorithm is based on a predictor corrector approach that generally converges quite fast, and leads, when very many processors are available, to real time solution procedures. This reasoning led us to name this new algorithm "parareal in time" (parallel in real time). purchase the full-text of this chapter (price £25) go to the previous chapter go to the next chapter return to the table of contents return to the book description purchase this book (price £95 +P&P)
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