volume | PIER Journals

Abstract

The second-order small-slope approximation (SSA2) is an analytical approximation method applied to electromagnetic scattering simulations on rough surfaces. However, the conventional serial SSA2 method involves a quadruple integral, and each integration requires a fast Fourier transform (FFT). As a result, the method demands very high memory and suffers from very low computational efficiency. In this paper, a parallel SSA2 method is proposed by combining region decomposition with Message Passing Interface (MPI) programming. The OpenMP technique also adopted to further improve the algorithm's performance. To avoid the frequent communication overhead caused by spectral shifting in traditional parallel FFT methods, the matrix data is carefully allocated, which effectively removes the related communication bottleneck. In addition, by using the separability of the two-dimensional (2-D) FFT, each 2-D FFT is implemented using two sequential one-dimensional (1-D) FFTs. This design limits inter-node communication to a constant upper bound. Numerical results show that when the number of computer nodes reaches 10, the parallel efficiency of the proposed method exceeds 80%, which confirms the effectiveness of the proposed method.

1. Gedney, Joseph J., Joel T. Johnson, and Robert J. Burkholder, "An analytical formulation for the coherent scattered field of a target above a randomly rough surface," IEEE Transactions on Antennas and Propagation, Vol. 73, No. 1, 329-340, 2025.
doi:10.1109/tap.2024.3505418 Google Scholar

2. Sefer, Ahmet, Ali Yapar, and Tanju Yelkenci, "Imaging of rough surfaces by RTM method," IEEE Transactions on Geoscience and Remote Sensing, Vol. 62, 1-12, 2024.
doi:10.1109/tgrs.2024.3374972 Google Scholar

3. Yoshino, Riku, Yoshihide Asakura, Keizo Inagaki, and Tetsuya Kawanishi, "300 GHz terahertz wave scattering experiment and simulation from slightly rough surfaces on dielectrics," IEICE Communications Express, Vol. 13, No. 2, 43-47, 2024.
doi:10.23919/comex.2023xbl0147 Google Scholar

4. Moss, C. D., T. M. Grzegorczyk, H. C. Han, and Jin Au Kong, "Forward-backward method with spectral acceleration for scattering from layered rough surfaces," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 3, 1006-1016, Mar. 2006.
doi:10.1109/tap.2006.869921 Google Scholar

5. Ozgun, Ozlem and Mustafa Kuzuoglu, "A domain decomposition finite-element method for modeling electromagnetic scattering from rough sea surfaces with emphasis on near-forward scattering," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 1, 335-345, Jan. 2019.
doi:10.1109/tap.2018.2874766 Google Scholar

6. Tian, Guilong, Chuanming Tong, Lu Xia, and Peng Peng, "Electromagnetic scattering from multiple moving targets above a rough surface," IEEE Geoscience and Remote Sensing Letters, Vol. 19, 1-5, 2022.
doi:10.1109/lgrs.2021.3131050 Google Scholar

7. Hao, Jing-Wei and Xin-Qing Sheng, "Accurate and efficient simulation model for the scattering from a ship on a sea-like surface," IEEE Geoscience and Remote Sensing Letters, Vol. 14, No. 12, 2375-2379, Dec. 2017.
doi:10.1109/lgrs.2017.2765342 Google Scholar

8. Di Martino, Gerardo, Alessio Di Simone, and Antonio Iodice, "Analytical formulation of scattering from anisotropic power-law spectrum surfaces: Getting rid of the cutoff wavenumber," IEEE Transactions on Geoscience and Remote Sensing, Vol. 61, 1-13, 2023.
doi:10.1109/tgrs.2023.3325722 Google Scholar

9. Raines, Ethan and Joel T. Johnson, "A study of the Kirchhoff approximation for the coherent reflection coefficient of a 1-D perfectly conducting rough surface," IEEE Geoscience and Remote Sensing Letters, Vol. 21, 1-4, 2024.
doi:10.1109/lgrs.2023.3332037 Google Scholar

10. Iodice, Antonio and Pasquale Imperatore, "A simple path to the small perturbation method for scattering from slightly rough dielectric surfaces," Remote Sensing, Vol. 16, No. 16, 3035, Aug. 2024.
doi:10.3390/rs16163035 Google Scholar

11. Di Martino, Gerardo, Alessio Di Simone, Antonio Iodice, and Daniele Riccio, "Bistatic scattering from anisotropic rough surfaces via a closed-form two-scale model," IEEE Transactions on Geoscience and Remote Sensing, Vol. 59, No. 5, 3656-3671, May 2021.
doi:10.1109/tgrs.2020.3021784 Google Scholar

12. Voronovich, A., "Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces," Waves in Random Media, Vol. 4, No. 3, 337, 1994.
doi:10.1088/0959-7174/4/3/008 Google Scholar

13. Soriano, Gabriel, Charles-Antoine Guérin, and Marc Saillard, "Scattering bytwo-dimensional rough surfaces: Comparison between the method ofmoments, Kirchhoff and small-slope approximations," Waves in Random Media, Vol. 12, No. 1, 63, Nov. 2001.
doi:10.1088/0959-7174/12/1/305 Google Scholar

14. Wang, Yanqiu and Shira L. Broschat, "A systematic study of the lowest order small slope approximation for a Pierson-Moskowitz spectrum," IEEE Geoscience and Remote Sensing Letters, Vol. 8, No. 1, 158-162, Jan. 2011.
doi:10.1109/lgrs.2010.2053193 Google Scholar

15. Wei, Peng-Bo, Min Zhang, Rong-Qing Sun, and Xiao-Feng Yuan, "Scattering studies for two-dimensional exponential correlation textured rough surfaces using small-slope approximation method," IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, No. 9, 5364-5373, Sep. 2014.
doi:10.1109/tgrs.2013.2288278 Google Scholar

16. He, Yulin, Yue Chen, Yu Mao Wu, and Peng Liu, "An improved two-scale analytical model for bistatic scattering of wind-driven sea surfaces," IEEE Geoscience and Remote Sensing Letters, Vol. 22, 1-5, 2025.
doi:10.1109/lgrs.2024.3509377 Google Scholar

17. Du, Yanlei, Junjun Yin, Shurun Tan, Jing Wang, and Jian Yang, "A numerical study of roughness scale effects on ocean radar scattering using the second-order SSA and the moment method," IEEE Transactions on Geoscience and Remote Sensing, Vol. 58, No. 10, 6874-6887, Oct. 2020.
doi:10.1109/tgrs.2020.2977368 Google Scholar

18. Voronovich, Alexander G. and Valery U. Zavorotny, "The transition from weak to strong diffuse radar bistatic scattering from rough ocean surface," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 11, 6029-6034, Nov. 2017.
doi:10.1109/tap.2017.2752219 Google Scholar

19. Shan, Jingzhe, Tianjin Liu, Jianda Xie, Kuan Yang, and Xiaojian Xu, "FFT-accelerated 3-D near-field radar image generation for objects over rough surfaces," IEEE Transactions on Antennas and Propagation, Vol. 73, No. 9, 6800-6813, Sep. 2025.
doi:10.1109/tap.2025.3571282 Google Scholar

20. Jiang, Wang-Qiang, Min Zhang, Peng-Bo Wei, and Xiao-Feng Yuan, "CUDA-based SSA method in application to calculating EM scattering from large two-dimensional rough surface," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 7, No. 4, 1372-1382, Apr. 2014.
doi:10.1109/jstars.2014.2303494 Google Scholar

21. Yamac, Yunus Emre and Ahmet Kizilay, "Scattering analyses of arbitrary roughness from 2-D perfectly conductiveperiodic surfaces with moments method," Turkish Journal of Electrical Engineering and Computer Sciences, Vol. 30, No. 3, 730-749, 2022.
doi:10.55730/1300-0632.3808 Google Scholar

22. Wei, Peng-Bo, Min Zhang, Wang-Qiang Jiang, and Ding Nie, "A new model for sand-ripple scattering based on SSA method and practical ripple profiles," IEEE Transactions on Geoscience and Remote Sensing, Vol. 54, No. 4, 2450-2459, Apr. 2016.
doi:10.1109/tgrs.2015.2501400 Google Scholar

Dr. Xiao-Yan Zhang

Dr. Luqi Wang

Dr. Hongwei He

Dr. Gang Yu