Ainsworth, Mark and Wajid, Hafiz Abdul and , Support of MA by the Engineering and Physical Sciences Research Council under grant (Funder) (2010) *Explicit discrete dispersion relations for the acoustic wave equation in d-dimensions using finite element, spectral element and optimally blended schemes.* In: Computer Methods in Mathematics. Computer Methods in Mathematics: Advanced Structured Materials, 1 (1). Springer, pp. 3-17.

## Abstract

We study the dispersive properties of the acoustic wave equation for finite element, spectral element and optimally blended schemes using tensor product elements defined on rectangular grid in d-dimensions. We prove and give analytical expressions for the discrete dispersion relations for the above mentioned schemes. We find that for a rectangular grid (a) the analytical expressions for the discrete dispersion error in higher dimensions can be obtained using one dimensional discrete dispersion error expressions; (b) the optimum value of the blending parameter is p/(p + 1) for all p ∈ ℕ and for any number of spatial dimensions; (c) the optimal scheme guarantees two additional orders of accuracy compared with both finite and spectral element schemes; and (d) the absolute accuracy of the optimally blended scheme is and times better than that of the pure finite and spectral element schemes respectively.

Item type: | Book Section |
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ID code: | 35126 |

Keywords: | acoustic wave equation , finite element analysis , spectral elements, Mathematics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 25 Oct 2011 14:50 |

Last modified: | 12 Mar 2012 11:38 |

URI: | http://strathprints.strath.ac.uk/id/eprint/35126 |

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