Article ID Journal Published Year Pages File Type
521805 Journal of Computational Physics 2012 12 Pages PDF
Abstract

We study the dispersive properties of the time harmonic Maxwell equations for optimally blended finite-spectral element scheme using tensor product elements defined on rectangular grid in d  -dimensions. We prove and give analytical expressions for the discrete dispersion relations for this scheme. 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)p/(p+1) for all p∈Np∈N and for any number of spatial dimensions; (c) analytical expressions for the discrete dispersion relations for finite element and spectral element schemes can be obtained when the value of blending parameter is chosen to be 0 and 1 respectively; (d) the optimally blended scheme guarantees two additional orders of accuracy compared with standard finite element and spectral element schemes; and (e) the absolute accuracy of the optimally blended scheme is O(p-2)O(p-2) and O(p-1)O(p-1) times better than that of the pure finite element and spectral element schemes respectively.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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