Original Paper
Analysis and Application of an Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element Methods
Article first published online: 24 NOV 2005
DOI: 10.1002/anac.200510007
Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Issue
1611-8189/asset/cover.gif?v=1&s=0d98d9125e8de480cc19c4d87277ee8e31ba2567 "Applied Numerical Analysis & Computational Mathematics")
Applied Numerical Analysis & Computational Mathematics
Volume 2, Issue 3, pages 326–345, December 2005
Additional Information
How to Cite
Deng, S. and Cai, W. (2005), Analysis and Application of an Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element Methods. Appl. numer. anal. comput. math., 2: 326–345. doi: 10.1002/anac.200510007
Publication History
- Issue published online: 24 NOV 2005
- Article first published online: 24 NOV 2005
- Manuscript Accepted: 28 AUG 2005
- Manuscript Revised: 15 MAY 2005
- Manuscript Received: 10 JAN 2005
- Abstract
- References
- Cited By
Keywords:
- Orthogonal nodal basis;
- spectral methods;
- discontinuous Galerkin methods
Abstract
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)