Although semi‐implicit semi‐Lagrangian spectral atmospheric models have been very successful for decades, they are believed to face big challenges in the longer term. Foremost, the spectral method relies heavily on data‐rich global communications, which may become problematic on future massively parallel machines. This paper investigates how the Helmholtz problem, as it arises in the dynamical core of a semi‐implicit non‐hydrostatic numerical weather prediction model with a mass‐based vertical coordinate and a constant‐coefficient reference state, can be solved efficiently without relying on spectral transforms, by using a multigrid‐preconditioned iterative solver instead. In the particular case of a limited‐area geometry, the convergence rate of this iterative solver can be determined a priori, which allows us to predict the required number of iterations. This knowledge is especially valuable for an atmospheric model that is used for operational weather forecasting, because it guarantees that the model runtime stays constant from one forecast to another. The a priori knowledge of the convergence rate also allows us to choose the parameters of the multigrid preconditioner optimally. Weak scalability experiments show the superior scalability of this solver with respect to a spectral solver.

中文翻译：

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具有基于质量的垂直坐标的数值天气预报模型的非光谱亥姆霍兹求解器

尽管半隐式半拉格朗日光谱大气模型已经取得了数十年的成功，但从长期来看，它们仍面临巨大挑战。最重要的是，频谱方法严重依赖于数据丰富的全局通信，这在将来的大规模并行计算机上可能会成为问题。本文研究了如何在不依赖频谱的情况下有效解决Helmholtz问题，该问题出现在具有基于质量的垂直坐标和恒定系数参考状态的半隐式非静水数值天气预报模型的动力学核心中通过使用多网格预处理的迭代求解器进行转换。在有限区域几何的特定情况下，可以先验确定此迭代求解器的收敛速度，这使我们能够预测所需的迭代次数。该知识对于用于运营天气预报的大气模型特别有价值，因为它可以确保模型运行时间在一个预测到另一个预测之间保持恒定。该先验收敛速度的知识也让我们以最佳选择多网格预参数。弱的可伸缩性实验表明，该求解器相对于频谱求解器具有出色的可伸缩性。