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Parareal is an algorithm from numerical analysis and used for the solution of initial value problems. In contrast to e.g. Runge-Kutta or multi-step methods, some of the computations in Parareal can be performed in parallel and Parareal is therefore one example of a ''parallel-in-time'' integration method. While historically most efforts to parallelize the numerical solution of partial differential equations focussed on the spatial discretization, in view of the challenges from exascale computing, parallel methods for temporal discretization have been identified as a possible way to increase concurrency in numerical software.〔 〕 Because Parareal computes the numerical solution for multiple time steps in parallel, it is categorized as a ''parallel across the steps'' method. This is in contrast to approaches using ''parallelism across the method'' like parallel Runge-Kutta methods, where independent stages can be computed in parallel or ''parallel across the system'' methods like waveform relaxation. == History == Parareal can be derived as both a multigrid method in time method or as multiple shooting along the time axis. Both ideas, multigrid in time as well as adopting multiple shooting for time integration, go back to the 1980s and 1990s.〔 〕 Parareal is a widely studied method and has been used and modified for a range of different applications. Ideas to parallelize the solution of initial value problems go back even further: the first paper proposing a parallel-in-time integration method appeared in 1964.〔 〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Parareal」の詳細全文を読む スポンサード リンク
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