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A Performance Model for Allocating the Parallelism in a Multigrid-in-Time Solver

机译:在多网格时间求解器中分配并行性的性能模型

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摘要

The traditional way to numerically solve time-dependent problems is to sequentially march through time, solving for one time step and then the next. The parallelism in this approach is limited to the spatial dimension, which is quickly exhausted, causing the gain from using more processors to solve a problem to diminish. One approach to overcome this barrier is to use methods that are parallel in time. These methods have the potential to achieve dramatically better performance compared to time-stepping approaches, but achieving this performance requires carefully choosing the amount of parallelism devoted to space versus the amount devoted to time. Here, we present a performance model that, for a multigrid-in-time solver, makes the decision on when to switch to parallel-in-time and on how much parallelism to devote to space vs. time. In our experiments, the model selects the best parallel configuration in most of our test cases and a configuration close to the best one in all other cases.
机译:用数字方法解决与时间有关的问题的传统方法是依次遍历时间,先求解一个时间步,然后求解下一个步。这种方法中的并行性仅限于空间维度,空间维度很快就用尽了,这导致使用更多处理器来解决问题的收益减少了。克服此障碍的一种方法是使用时间并行的方法。与时间步长方法相比,这些方法有可能获得显着更好的性能,但是要实现此性能,需要仔细选择专用于空间的并行量与专用于时间的量。在这里,我们提出了一个性能模型,对于多网格实时求解器,该模型决定何时切换到并行时间以及将多少并行性分配给空间与时间的关系。在我们的实验中,模型在大多数测试案例中选择了最佳并行配置,而在所有其他案例中均选择了接近最佳并行配置的配置。

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