Explicit discrete dispersion relations for the acoustic wave equation in d-dimensions using finite element, spectral element and optimally blended schemes

Ainsworth, Mark and Wajid, Hafiz Abdul 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. (https://doi.org/10.1007/978-3-642-05241-5_1)

Full text not available in this repository.Request a copy

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.

CORE (COnnecting REpositories)