A body-of-revolution discontinuous Galerkin time domain method based on curved mesh for Maxwell equations

Hongxin Qi, Zaigao Chen, Yu Liu and Yuheng Wang

Journal of Electromagnetic Waves and Applications, 2023, vol. 37, issue 14, 1139-1161

Abstract: Numerical simulation of body-of-revolution (BoR) or axisymmetric structures for scattering and radiation problems has a broad spectrum of technology applications in microwave and optical engineering. In this work, we propose a high-order BoR discontinuous Galerkin time-domain method (BoR-DGTD) for solving Maxwell equations in the cylindrical coordinate system. The presented approach is based on $ \sin (m\varphi ) $ sin⁡(mφ) or $ \cos (m\varphi ) $ cos⁡(mφ) (m is the mode number and φ is the azimuth) expansions for different field components and thus yields a real-valued final system of equations. It saves half of the unknowns as compared to the existing method in which all the field components are assumed to have the same φ variation, i.e. $ e^{im\varphi } $ eimφ. In contrast to the common practice of deriving variational formulation for the BoR Maxwell equations on two-dimensional grids in the meridian plane, we build it on three-dimensional coaxial toroidal subdomains. As a result, the singularity difficulty induced by the cylindrical coordinates is eliminated naturally. In addition, for BoR with curved material interfaces in the angular cross-section, a solution using curved grids in conjunction with the low-storage weight-adjusted approximation scheme is provided, which significantly enhances the simulation quality. Particularly, to achieve a set of optimized interpolation shape functions for the isoparametric transformation, an essential assistant in calculating the coefficient matrices, a heuristic procedure is developed to properly position the geometric control points on the curved grids. Some numerical experiments are conducted to demonstrate the accuracy and performance of our proposed BoR-DGTD method.

Date: 2023
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DOI: 10.1080/09205071.2023.2227609

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