Geodesic
From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions
C. D. Cantwell1 ; S. J. Sherwin2 ; R. M. Kirby3 ; P. H. J. Kelly4
1 Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
2 Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
3 School of Computing, University of Utah, Salt Lake City, Utah, USA
4 Department of Computing, Imperial College London, London, SW7 2AZ, UK
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 3, pp. 84-96.

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There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations for evaluating operators over the space of discretisations with a desired solution tolerance, we demonstrate how the optimal discretisation and operator implementation may be selected for a specified problem. Furthermore, this demonstrates the need for codes to support both low- and high-order discretisations.
DOI : 10.1051/mmnp/20116304

C. D. Cantwell 1 ; S. J. Sherwin 2 ; R. M. Kirby 3 ; P. H. J. Kelly 4

1 Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
2 Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
3 School of Computing, University of Utah, Salt Lake City, Utah, USA
4 Department of Computing, Imperial College London, London, SW7 2AZ, UK 
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C. D. Cantwell; S. J. Sherwin; R. M. Kirby; P. H. J. Kelly. From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 3, pp. 84-96. doi : 10.1051/mmnp/20116304. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116304/

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