Parallel geometric multigrid for global weather prediction
Parallel geometric multigrid for global weather prediction
复制标题
用于全球天气预报的并行几何多重网格
DOI：
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发表时间：
2010
影响因子：
4.3
通讯作者：
Robert Scheichl
中科院分区：
文献类型：
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作者：
Sean Buckeridge;Robert Scheichl
这项工作的主题是一个最佳的和可扩展的并行几何多重网格求解椭圆问题的球体，至关重要的预测和数据同化工具，在英国。气象局。椭圆问题的多层次技术的最优性使他们成为这些应用程序的一个合适的选择。英国气象局使用的是球形极坐标网格，虽然结构合理，但其缺点是在极点附近产生强烈的各向异性。此外，在径向方向上更高的分辨率引入进一步的各向异性，因此修改标准的多重网格松弛和粗化程序是必要的，以保持最佳的效率。由于各向异性的强度不同，我们提出了一种非均匀策略，仅在充分各向同性的区域中粗化网格。这与径向方向上的线松弛相结合。非均匀粗化策略的成功已经用代数多重网格（AMG）方法证明。然而，在没有AMG所需的大量设置成本的情况下，我们的目标是通过几何方法超越它们。我们证明了该方法的优点与模型问题的实验，顺序和并行，并显示鲁棒性和最佳效率的方法与恒定收敛因子小于0.1。它大大优于Krylov子空间方法与一级预处理器和AMG的BoomerAMG实现在典型的网格分辨率。并行实现几乎可以在多达256个处理器上进行最佳扩展，因此准地转欧米茄方程的全局求解（最大水平分辨率约为10 km，未知数为3 × 109）大约需要60 s。版权所有© 2010约翰威利父子有限公司.
The subject of this work is an optimal and scalable parallel geometric multigrid solver for elliptic problems on the sphere, crucial to the forecasting and the data assimilation tools used at the U.K. Met office. The optimality of multilevel techniques for elliptic problems makes them a suitable choice for these applications. The Met office uses spherical polar grids which, although structured, have the drawback of creating strong anisotropies near the poles. Moreover, a higher resolution in the radial direction introduces further anisotropies, and so modifications to the standard multigrid relaxation and the coarsening procedures are necessary to retain optimal efficiency. As the strength of anisotropy varies, we propose a non‐uniform strategy, coarsening the grid only in regions that are sufficiently isotropic. This is combined with line relaxation in the radial direction. The success of non‐uniform coarsening strategies has been demonstrated with algebraic multigrid (AMG) methods. Without the large setup costs required by AMG, however, we aim to surpass them with the geometric approach. We demonstrate the advantages of the method with experiments on model problems, both sequentially and in parallel, and show robustness and optimal efficiency of the method with constant convergence factors of less than 0.1. It substantially outperforms Krylov subspace methods with one‐level preconditioners and the BoomerAMG implementation of AMG on typical grid resolutions. The parallel implementation scales almost optimally on up to 256 processors, so that a global solve of the quasi‐geostrophic omega‐equation with a maximum horizontal resolution of about 10 km and 3 × 109 unknowns takes about 60 s. Copyright © 2010 John Wiley & Sons, Ltd.