In this paper, we introduce the Python framework PyMGRIT, which implements the multigrid-reduction-in-time (MGRIT) algorithm for solving the (non-)linear systems arising from the discretization of time-dependent problems. The MGRIT algorithm is a reduction-based iterative method that allows parallel-in-time simulations, i. e., calculating multiple time steps simultaneously in a simulation, by using a time-grid hierarchy. The PyMGRIT framework features many different variants of the MGRIT algorithm, ranging from different multigrid cycle types and relaxation schemes, as well as various coarsening strategies, including time-only and space-time coarsening, to using different time integrators on different levels in the multigrid hierachy. PyMGRIT allows serial runs for prototyping and testing of new approaches, as well as parallel runs using the Message Passing Interface (MPI). Here, we describe the implementation of the MGRIT algorithm in PyMGRIT and present the usage from both user and developer point of views. Three examples illustrate different aspects of the package, including pure time parallelism as well as space-time parallelism by coupling PyMGRIT with PETSc or Firedrake, which enable spatial parallelism through MPI.

中文翻译：

---

PyMGRIT：时间并行方法 MGRIT 的 Python 包

在本文中，我们介绍了 Python 框架 PyMGRIT，它实现了多网格时间缩减 (MGRIT) 算法，用于解决因时间相关问题的离散化而产生的（非线性）线性系统。MGRIT 算法是一种基于缩减的迭代方法，它允许并行时间模拟，即通过使用时间网格层次结构在模拟中同时计算多个时间步长。PyMGRIT 框架具有 MGRIT 算法的许多不同变体，从不同的多重网格循环类型和松弛方案，以及各种粗化策略，包括仅时间和时空粗化，到在多重网格中的不同级别使用不同的时间积分器等级制度。PyMGRIT 允许串行运行用于新方法的原型设计和测试，以及使用消息传递接口 (MPI) 的并行运行。在这里，我们描述了 PyMGRIT 中 MGRIT 算法的实现，并从用户和开发人员的角度介绍了用法。三个示例说明了该包的不同方面，包括纯时间并行性以及通过将 PyMGRIT 与 PETSc 或 Firedrake 耦合实现的时空并行性，后者通过 MPI 实现空间并行性。