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) for all p is an element of 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)) and O(p(-1)) times better than that of the pure finite element and spectral element schemes respectively. (C) 2012 Elsevier Inc. All rights reserved.