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# GPR Wave Propagation Model in a Complex Geoelectric Structure Using Conformal First-Order Symplectic Euler Algorithm

Man Yang1,2,3, Hongyuan Fang1,2,3,*, Juan Zhang4, Fuming Wang1,2,3, Jianwei Lei1,2,3, Heyang Jia1,2,3

College of Water Conservancy & Environmental Engineering, Zhengzhou University, Zhengzhou, 450001, China.
National Local Joint Engineering Laboratory of Major Infrastructure Testing and Rehabilitation Technology, Zhengzhou, 450001, China.
Collaborative Innovation Center of Water Conservancy and Transportation Infrastructure Safety, Zhengzhou, 450001, China.
CCCC First Highway Consultants Co.,LTD, Shanxi Province, Xi’an, 710065, China.

*Corresponding Author: Hongyuan Fang. Email: .

Computers, Materials & Continua 2019, 61(2), 793-816. https://doi.org/10.32604/cmc.2019.06042

## Abstract

Possessing advantages such as high computing efficiency and ease of programming, the Symplectic Euler algorithm can be applied to construct a ground-penetrating radar (GPR) wave propagation numerical model for complex geoelectric structures. However, the Symplectic Euler algorithm is still a difference algorithm, and for a complicated boundary, ladder grids are needed to perform an approximation process, which results in a certain amount of error. Further, grids that are too dense will seriously decrease computing efficiency. This paper proposes a conformal Symplectic Euler algorithm based on the conformal grid technique, amends the electric/magnetic field-updating equations of the Symplectic Euler algorithm by introducing the effective dielectric constant and effective permeability coefficient, and reduces the computing error caused by the ladder approximation of rectangular grids. Moreover, three surface boundary models (the underground circular void model, the undulating stratum model, and actual measurement model) are introduced. By comparing reflection waveforms simulated by the traditional Symplectic Euler algorithm, the conformal Symplectic Euler algorithm and the conformal finite difference time domain (CFDTD), the conformal Symplectic Euler algorithm achieves almost the same level of accuracy as the CFDTD method, but the conformal Symplectic Euler algorithm improves the computational efficiency compared with the CFDTD method dramatically. When the dielectric constants of the two materials vary greatly, the conformal Symplectic Euler algorithm can reduce the pseudo-waves almost by 80% compared with the traditional Symplectic Euler algorithm on average.

## Cite This Article

M. Yang, H. Fang, J. Zhang, F. Wang, J. Lei et al., "Gpr wave propagation model in a complex geoelectric structure using conformal first-order symplectic euler algorithm," Computers, Materials & Continua, vol. 61, no.2, pp. 793–816, 2019.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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