From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions
C. D. Cantwell; S. J. Sherwin; R. M. Kirby; P. H. J. Kelly
Mathematical Modelling of Natural Phenomena (2011)
- Volume: 6, Issue: 3, page 84-96
- ISSN: 0973-5348
Access Full Article
top
Abstract
topHow to cite
topCantwell, C. D., et al. "From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions." Mathematical Modelling of Natural Phenomena 6.3 (2011): 84-96. <http://eudml.org/doc/222362>.
@article{Cantwell2011,
abstract = {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. },
author = {Cantwell, C. D., Sherwin, S. J., Kirby, R. M., Kelly, P. H. J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {element; optimisation; code performance; Helmholtz equation; mesh refinement; numerical examples; spectral/ element method; discontinuous Galerkin formulation},
language = {eng},
month = {5},
number = {3},
pages = {84-96},
publisher = {EDP Sciences},
title = {From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions},
url = {http://eudml.org/doc/222362},
volume = {6},
year = {2011},
}
TY - JOUR
AU - Cantwell, C. D.
AU - Sherwin, S. J.
AU - Kirby, R. M.
AU - Kelly, P. H. J.
TI - From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/5//
PB - EDP Sciences
VL - 6
IS - 3
SP - 84
EP - 96
AB - 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.
LA - eng
KW - element; optimisation; code performance; Helmholtz equation; mesh refinement; numerical examples; spectral/ element method; discontinuous Galerkin formulation
UR - http://eudml.org/doc/222362
ER -
References
top- P. E. Bernard, J. F. Remacle, R. Comblen, V. Legat, K. Hillewaert. High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations. J. Comput. Phys., 228 (2009), No. 17, 6514–6535.
- C. D. Cantwell, S. J. Sherwin, R. M. Kirby, P. H. J. Kelly. From h to p efficiently: strategy selection for operator evaluation on hexahedral and tetrahedral elements. Computers and Fluids, 43 (2011), No. 1, 23–28.
- M. O. Deville, P. F. Fischer, E. H. Mund. High-order methods for incompressible fluid flow. Cambridge University Press, Cambridge, 2002.
- M. Dubiner. Spectral methods on triangles and other domains. J. Sci. Comp., 6 (1991), No. 4, 345-390.
- D. Gottlieb, S. A. Orszag. Numerical analysis of spectral methods: theory and applications. Society for Industrial Mathematics, 1977.
- J. S. Hesthaven, T. Warburton. Nodal high-order methods on unstructured grids:: I. time–domain solution of MaxwellŠs equations. J. Comput. Phys., 181 (2002), No. 1, 186-221.
- T. J. R. Hughes. The finite element method. Prentice-Hall, New Jersey, 1987.
- G. E. Karniadakis and S. J. Sherwin. Spectral/hp element methods for computational fluid dynamics. Oxford University Press, Oxford, second edition edition, 2005.
- U. Lee. Spectral element method in structural dynamics. Wiley, 2009.
- S. A. Orszag. Spectral methods for problems in complex geometries. Advances in computer methods for partial differential equations- III, (1979), 148-157.
- A. T. Patera. A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys., 54 (1984), No. 3, 468-488.
- S. J. Sherwin, G. E. Karniadakis. Tetrahedral hp finite elements: Algorithms and flow simulations. J. Comput. Phys., 124 (1996), 14-45.
- S. J. Sherwin. Hierarchical hp finite elements in hybrid domains. Finite Elements in Analysis and Design, 27 (1997), No 1, 109-119.
- B. F. Smith, P. Bjorstad, W. Gropp. Domain decomposition: parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, 2004.
- P. E. J. Vos, S. J. Sherwin, M. Kirby. From h to p efficiently: Implementing finite and spectral/hp element discretisations to achieve optimal performance at low and high order approximations. J. Comput. Phys., 229 (2010), 5161-5181.
- O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. The finite element method: its basis and fundamentals. Elsevier Butterworth Heinemann, 2005.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.