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Friday, 17 December 2010 00:57 |
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From h to p Efficiently: Strategy Selection for Operator Evaluation on Hexahedral and Tetrahedral Elements
C.D. Cantwell, S.J. Sherwin, R.M. Kirby, P.H.J. Kelly. In Computers and Fluids, 2010.
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.
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