# 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

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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

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