From h to p efficiently: Strategy selection for operator evaluation on hexahedral and tetrahedral elements
From h to p efficiently: Strategy selection for operator evaluation on hexahedral and tetrahedral elements
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DOI：
10.1016/j.compfluid.2010.08.012
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发表时间：
2011-04-01
影响因子：
2.8
通讯作者：
Kelly, P. H. J.
中科院分区：
文献类型：
--
作者：
Cantwell, C. D.;Sherwin, S. J.;Kelly, P. H. J.
谱/HP元素离散化允许同时获得几何灵活性和有益的收敛特性。基本多项式阶数的选择对不同实现策略的效率有深远的影响，对于低阶谱/HP离散化，它们的性能差别很大。我们考察了仔细选择策略如何在三维多项式阶数范围内将计算成本降至最低，并比较了不同的运算符和元素形状的选择如何导致实现之间不同的盈亏平衡点。在三维空间中，较高的展开阶数会迅速导致单元内部模式的数量大幅增加，尤其是在六面体单元中。对于典型的边界-内部模式分解，这可能很快导致全局方法的性能较差，而利用元素展开的张量积结构的和因式分解技术会导致较好的性能。此外，由于有害的缓存效应和其他与机器相关的因素，增加的内存需求可能会导致实现在给定系统上表现出较差的运行时性能，即使严格的操作计数最小也是如此。0(C)2010爱思唯尔有限公司。保留所有权利。
A spectral/hp element discretisation permits both geometric flexibility and beneficial convergence properties to be attained simultaneously. The choice of elemental polynomial order has a profound effect on the efficiency of different implementation strategies with their performance varying substantially for low and high order spectral/hp discretisations. We examine how careful selection of the strategy minimises computational cost across a range of polynomial orders in three dimensions and compare how different operators, and the choice of element shape, lead to different break-even points between the implementations. In three dimensions, higher expansion orders quickly lead to a large increase in the number of element-interior modes, particularly in hexahedral elements. For a typical boundary-interior modal decomposition, this can rapidly lead to a poor performance from a global approach, while a sum-factorisation technique, exploiting the tensor-product structure of elemental expansions, leads to better performance. Furthermore, increased memory requirements may cause an implementation to show poor runtime performance on a given system, even if the strict operation count is minimal, due to detrimental caching effects and other machine-dependent factors. 0 (C) 2010 Elsevier Ltd. All rights reserved.