A Collaborative Hybrid Algorithm of WHIE-FDTD with CPML and Non-Uniform Grid for Multi-Scale Electromagnetic Structures

XIA Hanghang; HE Tingting; ZHANG Kanglong; YUAN Bo; ZHAO Peng; WANG Gaofeng

doi:10.11999/JEIT260876

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XIA Hanghang, HE Tingting, ZHANG Kanglong, YUAN Bo, ZHAO Peng, WANG Gaofeng. A Collaborative Hybrid Algorithm of WHIE-FDTD with CPML and Non-Uniform Grid for Multi-Scale Electromagnetic Structures[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260876

Citation:

XIA Hanghang, HE Tingting, ZHANG Kanglong, YUAN Bo, ZHAO Peng, WANG Gaofeng. A Collaborative Hybrid Algorithm of WHIE-FDTD with CPML and Non-Uniform Grid for Multi-Scale Electromagnetic Structures[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260876

Citation:

XIA Hanghang, HE Tingting, ZHANG Kanglong, YUAN Bo, ZHAO Peng, WANG Gaofeng. A Collaborative Hybrid Algorithm of WHIE-FDTD with CPML and Non-Uniform Grid for Multi-Scale Electromagnetic Structures[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260876

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A Collaborative Hybrid Algorithm of WHIE-FDTD with CPML and Non-Uniform Grid for Multi-Scale Electromagnetic Structures

doi: 10.11999/JEIT260876 cstr: 32379.14.JEIT260876

College of Electronic Information, Hangzhou Dianzi University, Hangzhou 310018, China

Funds: The Key Laboratory of Intelligent Computing & Signal Processing (Anhui University), Ministry of Education (2026001), The National Natural Science Foundation of China (62501211, U24A20222, 92373202), The Zhejiang Provincial Natural Science Foundation of China (LQ24F010010, LZ24F010006, LD24F010001)

Received Date: 2026-06-26
Accepted Date: 2026-11-05
Rev Recd Date: 2026-10-12

Available Online: 2026-11-14

Abstract

Abstract

The finite-difference time-domain (FDTD) method is the most representative time-domain solution algorithm in the field of computational electromagnetics. However, due to the limitations imposed by the Courant-Friedrichs-Lewy (CFL) condition, it often incurs a high computational cost when solving multi-scale problems. To fully mitigate the impact of the CFL and improve simulation efficiency, this paper proposes a hybrid algorithm solution named NG-WHIE based on the weakly hybrid implicit-explicit FDTD (WHIE-FDTD). By replacing the traditional uniform Yee grid partition with non-uniform grids (NG), only fine grid partitions are set in regions with smaller geometric dimensions. Linearly varying smooth transition grids are set in the regions between fine and coarse grids to reduce the error caused by the grid partition differences, and the convolutional perfect matching layer (CPML) boundary condition is introduced for it. It effectively truncates the reflection of electromagnetic waves after they reach the boundary, reducing the numerical oscillations caused by the reflection of electromagnetic waves. This paper processed and tested a multi-input multi-output (MIMO) patch antenna. Compared with the FDTD method, the calculation results of the high-frequency structure simulation software (HFSS) and the test results, the calculated data of the proposed method show high consistency. The results indicate that this method has extremely high accuracy and robustness, and saves a significant amount of time consumption without significantly consuming additional memory. This provides a new solution for electromagnetic field simulation problems of multi-scale structures. Objective The FDTD method is one of the most widely used time-domain numerical techniques in electromagnetic calculations. It is favored because of its direct time-domain solution and its ability to naturally handle broadband and complex electromagnetic problems. However, due to its explicit nature, the conventional FDTD algorithm is subjected to the CFL stability condition, under which the time step is coupled to the smallest spatial grid size in the computational domain. In multi-scale problems, where electrically large regions coexist with fine geometrical details requiring extremely small cells, a prohibitively small global time step is imposed by this constraint. Consequently, excessive computational time is incurred, and simulation efficiency is severely limited. To effectively mitigate the CFL bottleneck, a hybrid algorithm based on the WHIE-FDTD method is proposed in this paper. Methods The WHIE-FDTD is based on Maxwell's equations and employs an alternating explicit-implicit scheme, which overcomes the limitations imposed by CFL. Subsequently, by using different perturbation terms, different directions can be obtained as the fine direction of the electromagnetic field iteration equation. This article takes the y direction as an example. Using NG instead of the traditional uniform Yee grid partitioning enables a more scientific spatial discretization. Different-sized grids are adopted for different simulation areas. Only fine grids are used in the structurally detailed areas, while coarse grids are used in the remaining areas. Linearly varying smooth transition grids are set in the transitional areas to reduce the error introduced by the difference in grid partitioning. By introducing the CPML as the absorbing boundary condition, the problem of infinite propagation of electromagnetic waves in the open domain is truncated within a limited simulation space. At the truncation boundary, the absorbing boundary is used instead of the traditional reflective boundary to effectively suppress boundary reflection and reduce the numerical oscillations caused by electromagnetic wave reflection. Results and Discussions Taking the MIMO patch antenna as the implementation example, the numerical results show that when CFLN = 1, the S-parameter curve and radiation pattern of the WHIE-FDTD method are highly consistent with the simulation results of the FDTD method and the HFSS software, ensuring the accuracy of the WHIE-FDTD method; after introducing the NG technology, the echo loss depth measured by the NG-WHIE method is approximately 3 dB lower than that of the FDTD method, fully verifying that the NG-WHIE method has higher accuracy than the FDTD method; when CFLN = 9, the results measured by the NG-WHIE method show no divergence trend and exhibit extremely high stability. At the same time, the calculation time was reduced by approximately 61.8%, which strongly demonstrates that this method not only ensures calculation accuracy but also offers extremely high computational efficiency and robustness. Conclusions This paper presents a hybrid algorithm, NG-WHIE, based on WHIE-FDTD. By replacing the traditional uniform Yee grid with the NG technology, a more scientific spatial discretization is achieved. By introducing the Convolutionally Perfect Matching Layer (CPML) as the absorbing boundary condition, it effectively suppresses boundary reflections and reduces the numerical oscillations caused by electromagnetic wave reflections. The numerical results show that when CFLN = 1, the S-parameter curve and radiation pattern of the NG-WHIE method are highly consistent with the simulation results from the FDTD method and HFSS software, as well as actual measurements, thereby fully verifying the accuracy of the NG-WHIE method. When CFLN = 9, the results obtained by the NG-WHIE method show no divergence trend and exhibit extremely high stability. At the same time, the computation time has been reduced by approximately 61.8%, demonstrating that this method not only ensures calculation accuracy but also offers extremely high computational efficiency and good robustness.

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References(23)

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