论文标题
与反应扩散问题的PFASST的时空多机方法的实验比较
An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem
论文作者
论文摘要
我们考虑使用（反应）扩散问题（可能是非线性）的两种平行时间。特别是，我们考虑PFASST（时空和时间上的平行完整近似方案）以及时空多级策略。对于这两种方法，我们从连续时间依赖性问题的整体表述开始。然后，采用了PFASST的搭配形式和时间时空多机的不连续的Galerkin离散化，从而在时间节点时产生了相同的离散解决方案。在时间离散的不同顺序中，比较了两种多级策略的强尺度和弱缩放。此外，我们研究了非线性问题的各自收敛行为，并突出了定量差异。
We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multilevel strategies. For both approaches, we start from an integral formulation of the continuous time-dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization in time for the space-time multigrid are employed, resulting in the same discrete solution at the time nodes. Strong and weak scaling of both multilevel strategies is compared for varying order of the temporal discretization. Moreover, we investigate the respective convergence behavior for non-linear problems and highlight quantitative differences.
