Abstract
In the past few years, the number of processor cores of top ranked supercomputers has increased drastically. It is challenging to design efficient parallel algorithms that offer such a high degree of parallelism, especially for certain time-dependent problems because of the sequential nature of “time”. To increase the degree of parallelization, some parallel-in-time algorithms have been developed. In this paper, we give an overview of some recently introduced parallel-in-time methods, and present in detail the class of space-time Schwarz methods, including the standard and the restricted versions, for solving parabolic partial differential equations. Some numerical experiments carried out on a parallel computer with a large number of processor cores for three-dimensional problems are given to show the parallel scalability of the methods. In the end of the paper, we provide a comparison of the parallel-in-time algorithms with a traditional algorithm that is parallelized only in space.
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