SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Introduction to the minisymposium and to the parallelisation in time algorithms

Y. Maday

In the same spirit as the domain decomposition methods in space, time domain decomposition methods are based on a decomposition of the time interval, and then each solution trajectory is solved simultaneously in all the time subintervals using an iteration on the initial condition over each subinterval. The parareal algorithm proposed in 2001 by Lions, Maday and Turinici allowed to highlight the interest in the parallelisation in this direction. There are now several successful implementations together with convergence results that illustrate the interest of the parallelization in time is for problems when very many processors are available. The speedup -- even though not so impressive than with parallelization in space for the plain approach -- allows to reach real time leading to the name parareal (parallel in real time) of the new algorithm from 2001. Now the method is more mature, it appears better like a large framework that allows to propose new ideas working on different aspects of the different ingredients of the method. This symposium will allow to first present the frame of the parareal approach and then illustrate its application on very large problems together with attempts to cure some problems of the original algorithms and also how to combine those iterations with others in order to achieve the plain speedup available by the given number of processors.

Organized by         Universidad de Valladolid     IMUVA