1. A NOVEL MIXED SPECTRAL METHOD AND ERROR ESTIMATES FOR MAXWELL TRANSMISSION EIGENVALUE PROBLEMS.
- Author
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JING AN, WAIXIANG CAO, and ZHIMIN ZHANG
- Subjects
APPROXIMATION theory ,POLYNOMIAL approximation ,SPECTRAL theory ,SPHERICAL harmonics ,VECTOR valued functions ,EIGENVALUES ,COMPACT operators - Abstract
In this paper, a novel mixed spectral-Galerkin method is proposed and studied for a Maxwell transmission eigenvalue problem in a spherical domain. The method utilizes vector spherical harmonics to achieve dimension reduction. By introducing an auxiliary vector function, the original problem is rewritten as an equivalent fourth-order coupled linear eigensystem, which is further decomposed into a sequence of one-dimensional fourth-order decoupled transverse-electric (TE) and transverse-magnetic (TM) modes. Based on compact embedding theory and the spectral approximation property of compact operators, error estimates for both eigenvalue and eigenfunction approximations are established for the TE mode. For the TM mode, an efficient essential polar condition and a high-order polynomial approximation method are designed to cope with the singularity and complexity caused by the coupled boundary conditions. Numerical experiments are presented to demonstrate the efficiency and robustness of our algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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