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A high-performance parallel implementation of the certified reduced basis method

机译：经认证的简化基础方法的高性能并行实现

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The certified reduced basis method (herein RB method) is a popular approach for model reduction of parametrized partial differential equations. In this paper we introduce new techniques that are required to efficiently implement the Offline "Construction stage" of the RB method on high-performance parallel supercomputers. This enables us to generate certified RB models for large-scale three-dimensional problems that can be evaluated on standard workstations and other "thin" computing resources with speedup of many orders of magnitude compared to the corresponding full order model. We use our implementation to perform detailed numerical studies for two computationally expensive model problems: a natural convection fluid flow problem and a "many parameter" heat transfer problem. In the heat transfer problem, we exploit the computational efficiency of the RB method to perform a detailed study of "snapshot" selection in the Greedy algorithm, and we also examine statistics of the output sensitivity derivatives to obtain a "global" view of the relative importance of the parameters.
机译：认证的缩减基方法（此处为RB方法）是用于参数化偏微分方程模型简化的一种流行方法。在本文中，我们介绍了在高性能并行超级计算机上有效实现RB方法的脱机“构造阶段”所需的新技术。这使我们能够为大型三维问题生成经过认证的RB模型，与相应的完整模型相比，这些模型可以在标准工作站和其他“瘦”计算资源上进行评估，并且速度提高了多个数量级。我们使用实现对两个计算上昂贵的模型问题进行详细的数值研究：自然对流流体流动问题和“许多参数”传热问题。在传热问题中，我们利用RB方法的计算效率对Greedy算法中的“快照”选择进行了详细研究，并且我们还检查了输出灵敏度导数的统计数据以获得相对值的“全局”视图参数的重要性。

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