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首页> 外文期刊>Journal of Computational Physics >Space-time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems
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Space-time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

机译：用于Boltzmann运输问题的大规模线性动力系统时空减少阶模型

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摘要

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space-time reduced order model for dynamical problems has been developed [17], where the space-time reduced order model shows an order of a hundred speed-up with a relative error of 10(-4) for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space-time reduced basis construction algorithm needs to be developed. We present the incremental space-time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space-time reduced basis is exploited, which enables the avoidance of constructing the reduced space-time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space-time reduced order models are derived. Published by Elsevier Inc.
机译：动力学问题的经典降阶模型涉及问题规模的空间缩减。然而，伴随空间缩减的时间缩减可以在不损失太多精度的情况下进一步减少问题的规模，这比仅空间缩减的速度快得多。最近，针对动力学问题开发了一种新的时空降阶模型[17]，其中对于小型学术问题，时空降阶模型显示了100阶的加速，相对误差为10（-4）。然而，为了使该方法适用于大规模问题，需要开发一种高效的时空缩减基构造算法。我们提出了增量时空缩减基构造算法。增量算法是完全并行和可扩展的。此外，利用了空时约化基中的块结构，避免了构造约化空时基。这些新技术被应用于一个具有百万和十亿自由度的大规模粒子输运模拟。数值算例表明，该算法具有可扩展性和实用性。此外，它实现了巨大的加速，保持了良好的准确性。最后，推导了纯空间模型和时空降阶模型的误差界。爱思唯尔公司出版。

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