Analysis and Application of an Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element Methods

In this paper, we propose and analyze an orthogonal non-polynomial nodal basis on triangles for discontinuous spectral element methods (DSEMs) for solving Maxwell's equations. It is based on the standard tensor product of the Lagrange interpolation polynomials and a “collapsing” mapping between the standard square and the standard triangle. The basis produces diagonal mass matrices for the DSEMs and is easy to implement. Numerical results for electromagnetic scattering in heterogeneous media are provided to demonstrate the exponential convergence of the proposed basis, and its application to the simulation of optical coupling by whispering gallery modes between two microcylinders is presented as well. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)