Numerical approximation based on a decoupled dimensionality reduction scheme for Maxwell eigenvalue problem. (English) Zbl 1538.65474
Summary: We present a high-accuracy numerical method based on a decoupled dimensionality reduction scheme for Maxwell eigenvalue problem in spherical domains. Using the orthogonality of vector spherical harmonics and the variable separation approach, we decompose the original problem into two classes of decoupled one-dimensional TE mode and TM mode. For the TE mode, we establish a variational formulation and its discrete scheme and give the error estimations of the approximate eigenvalues and eigenfunctions. For the TM mode, it is different from TE mode which naturally meets the divergence-free condition and will not generate some spurious eigenvalues. We design a numerical algorithm based on a parameterized method to filter out the spurious eigenvalues. Finally, some numerical results are presented to confirm the theoretical results and validate the algorithms.
© 2023 John Wiley & Sons, Ltd.
© 2023 John Wiley & Sons, Ltd.
MSC:
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 78A25 | Electromagnetic theory (general) |
| 78M30 | Variational methods applied to problems in optics and electromagnetic theory |
| 78M34 | Model reduction in optics and electromagnetic theory |
| 35A15 | Variational methods applied to PDEs |
Keywords:
decoupled dimensionality reduction scheme; error estimation; Maxwell eigenvalue problem; numerical approximation; spherical domainReferences:
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