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High-Order ADI-FDTD Schemes for Maxwell’s Equations with Material Interfaces in Two Dimensions

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Abstract

In this paper, we apply the immersed interface method (IIM) and the hierarchical derivative matching (HDM) method, respectively, to restore the accuracy of the high-order alternating direction implicit finite-difference time-domain (ADI-FDTD) scheme of the 2D Maxwell’s equations with material interfaces. For the case of discontinuous permittivity \(\varepsilon \) and continuous permeability \(\mu \), we propose four high-order schemes. Two of them are of second order in time and fourth order in space (ADI-IIM-FDTD(2,4) scheme and ADI-HDM-FDTD(2,4) scheme). Others are of fourth order both in time and space (ADI-IIM-FDTD(4,4) scheme and ADI-HDM-FDTD(4,4) scheme). For the case of discontinuous permittivity \(\varepsilon \) and permeability \(\mu \), the (2,4) scheme and the (4,4) scheme are constructed as well (ADI-HDM-FDTD-X(2,4) scheme and ADI-HDM-FDTD-X(4,4) scheme). The proposed six schemes maintain the advantages of ADI-FDTD method such as unconditional stability and computational efficiency. Numerical examples are given to verify the performance of the proposed schemes.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

W. Li’s work was supported by National Natural Science Foundation of China [Grant Numbers 11701282 and 61673011] and Natural Science Foundation of Jiangsu Province [Grant Number BK20160819].

Funding

Wanshan Li’s work was supported by National Natural Science Foundation of China (11701282 and 61673011) and Natural Science Foundation of Jiangsu Province (BK20160819).

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  1. School of Mathematics and Statistics, Nanjing University of Science and Technology, Xiaolingwei, Nanjing, 210094, China

    Na Gong & Wanshan Li

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  1. Na Gong
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Correspondence to Wanshan Li.

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Gong, N., Li, W. High-Order ADI-FDTD Schemes for Maxwell’s Equations with Material Interfaces in Two Dimensions. J Sci Comput 93, 51 (2022). https://doi.org/10.1007/s10915-022-02011-6

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  • DOI: https://doi.org/10.1007/s10915-022-02011-6

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