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Department of Mathematics Colloquium
Parallelism in time: Can parts of the solution later in time be computed before the solution earlier in time is known?
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Time dependent problems are often solved using time marching schemes. Such schemes remain effective on parallel computers as long as each time step is costly enough for an effective computation to communication ratio. If not, parallelism in time could alleviate the situation, but is it possible to do useful computations at future time steps before the current time step results are known? I first present several classical attempts to obtain time parallelism, including unsuccessful ones, and then show a new approach introduced in 2001 by Lions, Maday and Turinici called the parareal algorithm. While parareal can be interpreted in the classical framework of time parallel algorithms, it shows that indeed for certain problems time parallel computations are a viable strategy. |