Analysis of the Parareal Time-Parallel Time-Integration method

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Article

Reference

Analysis of the Parareal Time-Parallel Time-Integration method

GANDER, Martin Jakob, VANDEWALLE, Stefan

Abstract

The parareal algorithm is a method to solve time-dependent problems parallel in time: it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time. In this paper the relation of the parareal algorithm to space-time multigrid and multiple shooting methods is first briefly discussed. The focus of the paper is on new convergence results that show superlinear convergence of the algorithm when used on bounded time intervals, and linear convergence for unbounded intervals.

GANDER, Martin Jakob, VANDEWALLE, Stefan. Analysis of the Parareal Time-Parallel Time-Integration method. SIAM Journal on Scientific Computing , 2007, vol. 29, no. 2, p.

556-578

Available at:

http://archive-ouverte.unige.ch/unige:6312

Disclaimer: layout of this document may differ from the published version.

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(70)

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(71)

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(73)

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iteration

Error

Superlinear bound

(74)

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Analysis of the Parareal Time-Parallel Time-Integration method

Article

Reference