An Efficient Spectral-Galerkin Approximation and Error Analysis for Maxwell Transmission Eigenvalue Problems in Spherical Geometries

作者：An, Jing^*; Zhang, Zhimin

来源：Journal of Scientific Computing, 2018, 75(1): 157-181.

DOI：10.1007/s10915-017-0528-2

• Maxwell transmission eigenvalue problems
• Spherical geometry
• TE and TM modes
• Spectral-Galerkin approximation
• Error analysis

We propose and analyze an efficient spectral-Galerkin approximation for the Maxwell transmission eigenvalue problem in spherical geometry. Using a vector spherical harmonic expansion, we reduce the problem to a sequence of equivalent one-dimensional TE and TM modes that can be solved individually in parallel. For the TE mode, we derive associated generalized eigenvalue problems and corresponding pole conditions. Then we introduce weighted Sobolev spaces based on the pole condition and prove error estimates for the generalized eigenvalue problem. The TM mode is a coupled system with four unknown functions, which is challenging for numerical calculation. To handle it, we design an effective algorithm using Legendre-type vector basis functions. Finally, we provide some numerical experiments to validate our theoretical results and demonstrate the efficiency of the algorithms.

• 出版日期2018-4
• 单位贵州师范大学; 北京计算科学研究中心