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, In this paper, we give an overview of several important time parallel methods including parareal, waveform relaxation and space-time Schwarz methods for solving a system arising from the discretization of the linear parabolic equations. The numerical experiments for three dimensional problems show both the multilevel additive Schwarz methods have excellent parallel scalability and both outperform the classical time stepping method when the number of processors is large.

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