asQ: 使用ParaDiag进行并行时间有限元模拟用于地质科学模型及其他领域
asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond
AI总结：
asQ是一个基于ParaDiag方法的新型库，用于并行时间有限元模拟，特别适用于地质科学中的天气和气候模型。
摘要：
现代高性能计算机具有大规模并行性；对于许多偏微分方程应用，空间并行性在计算机能力达到之前就已饱和。并行时间方法通过同时求解多个时间步来进一步加速，以暴露额外的并行性。ParaDiag是一种基于时间域的预条件处理方法，通过傅里叶变换实现块对角化。本文介绍asQ，一个实现ParaDiag并行时间方法的新库，重点应用于地质科学，尤其是天气和气候领域。asQ基于Firedrake库，该库用于自动求解有限元模型，以及PETSc库，该库包含可扩展的线性和非线性求解器。这使asQ能够为通用有限元模型构建ParaDiag求解器，并提供多种求解策略，使测试广泛问题变得简便。我们使用准牛顿公式涵盖多种ParaDiag方法，并暴露构建更复杂方法的构建块。通过线性和非线性大气流动模型的层次结构，展示了asQ的性能和灵活性。我们证明ParaDiag可以提供有前景的加速，并且asQ是进一步发展这些方法的有力测试平台。
英文摘要：
Modern high performance computers are massively parallel; for many PDE applications spatial parallelism saturates long before the computer's capability is reached. Parallel-in-time methods enable further speedup beyond spatial saturation by solving multiple timesteps simultaneously to expose additional parallelism. ParaDiag is a particular approach to parallel-in-time based on preconditioning the simultaneous timestep system with a perturbation that allows block diagonalisation via a Fourier transform in time. In this article, we introduce asQ, a new library for implementing ParaDiag parallel-in-time methods, with a focus on applications in the geosciences, especially weather and climate. asQ is built on Firedrake, a library for the automated solution of finite element models, and the PETSc library of scalable linear and nonlinear solvers. This enables asQ to build ParaDiag solvers for general finite element models and provide a range of solution strategies, making testing a wide array of problems straightforward. We use a quasi-Newton formulation that encompasses a range of ParaDiag methods, and expose building blocks for constructing more complex methods. The performance and flexibility of asQ is demonstrated on a hierarchy of linear and nonlinear atmospheric flow models. We show that ParaDiag can offer promising speedups and that asQ is a productive testbed for further developing these methods.
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