# Wide-Angle Claerbout Scheme for Three-Dimensional Time Domain Parabolic Equation and its CN, ADI, AGE Solutions

## Keywords:

Electromagnetic scattering, time domain parabolic equation, wide angle## Abstract

The wide-angle Claerbout scheme of three-dimensional time domain parabolic equation (Claerbout-TDPE) is derived in this paper, which can provide accurate results at angles within 25° of the paraxial direction. At first, the Crank-Nicolson (CN) type is introduced to discretize the Claerbout-TDPE. In this way, a three-dimensional EM scattering problem can be divided into a series of two-dimensional ones. Moreover, the alternating direction implicit (ADI) type is utilized to the Claerbout-TDPE. In this way, a three-dimensional EM scattering problem can be further reduced to a series of one-dimensional ones. Furthermore, the alternating group explicit (AGE) type is introduced to the Claerbout- TDPE for higher computational efficiency. Comparisons are made among the CN, ADI and AGE types in the numerical results.

## References

A. E. Barrios, “A terrain parabolic equation model for propagation in the troposphere,” IEEE Trans. Antennas and Propagation, vol. 42, no. 1, pp. 90- 98, 1994.

S. Mckee, D. P. Wall, and S. K. Wilson, “An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms,” J. Computat. Phys., vol. 126, no. 0120, pp. 64-76, 1996.

R. Martelly and R. Janaswamy, “Modeling radio transmission loss in curved, branched and roughwalled tunnels with the ADI-PE method,” IEEE Trans. Antennas and Propagation, vol. 58, no. 6, pp. 2037-2045, 2010.

A. A. Zaporozhets and M. F. Levy, “Bistatic RCS calculations with the vector parabolic equation method,” IEEE Trans. Antennas and Propagation, vol. 47, no. 11, pp. 1688-1696, 1999.

M. F. Levy and P. P. Borsboom, “Radar crosssection computations using the parabolic equation method,” Electron. Lett., vol. 32, pp. 1234-1236, 1996.

Z. He and R. S. Chen, “A novel parallel parabolic equation method for electromagnetic scatterings,” IEEE Trans. Antennas and Propagation, vol. PP, no. 99, pp. 1-1. (early access).

M. F. Levy, Parabolic Equation Methods for Electromagnetic Wave Propagation, London: The Institution of Electrical Engineers, 2000.

Z. He and R. S. Chen, “A vector meshless parabolic equation method for three-dimensional electromagnetic scatterings,” IEEE Trans. Antennas and Propagation, vol. 63, no. 6, pp. 2595-2603, 2015.

Z. He, Z. H. Fan, and R. S. Chen, “Spectral element method based parabolic equation for EM scattering problems,” Waves in Random and Complex Media, vol. 26, iss. 1, pp. 80-88, 2016.

Z. He, Z. H. Fan, D. Z. Ding, and R. S. Chen, “A vector parabolic equation method combined with MLFMM for scattering from a cavity,” Applied Computational Electromagnetics Society Journal, vol. 30, no. 5, pp. 496-502, 2015.

Z. He, T. Su, and R. S. Chen, “Vector parabolic equation method for the scattering from PEC objects in half-space,” Applied Computational Electromagnetics Society Journal, vol. 30, no. 8, pp. 877-883, 2015.

Z. He, Z. H. Fan, D. Z. Ding, and R. S. Chen, “Efficient radar cross-section computation of electrically large targets with ADI-PE method,” Electronics Letters, vol. 51, no. 4, pp. 360-362, 2015.

Z. He, Z. H. Fan, D. Z. Ding, and R. S. Chen, “GPU-accelerated ADI-PE method for the analysis of EM scatterings,” Electronics Letters, vol. 51, no. 21, pp. 1652-1654, 2015.

W. L. Siegmann, G. A. Kriegsmann, and D. Lee, “A wide-angle three-dimensional parabolic wave equation,” J. Acoust. Soc. Am., vol. 78, no. 2, pp. 659-664, 1985.

Z. X. Huang , B. Wu, W. Sha, M. S. Chen, X. L. Wu, and H. Dai, “High-order parabolic equation method for electromagnetic computation,” APMC 2008, Asia-Pacific, 2008.

M. D. Collins, “Generalization of the split-step Pade solution,” J. Acoust. Soc. Am., vol. 96, iss. 1, pp. 382-385, 1994.

Z. He and R. S. Chen, “A wide-angle ADI-PE method for EM scattering from electrically large targets,” Electromagnetics, to be published.

J. E. Murphy, “Finite-difference treatment of a time-domain parabolic equation: Theory,” The Journal of the Acoustical Society of America, vol. 77, no. 5, pp. 1958-1960, 1985.

A. V. Popov, V. V. Kopeikin, N. Y. Zhu, and F. M. Landstorfer, “Modeling EM transient propagation over irregular dispersive boundary,” Electronics Letters, vol. 38, no. 14, pp. 691-692, 2002.

N. Y. Zhu and F. M. Landstorfer, “Numerical modelling of pulse propagation in tunnels,” Frequenz, vol. 62, no. 7-8, pp. 160-163, 2008.

Y. Q. Yang and Y. L. Long, “Modeling EM pulse propagation in the troposphere based on the TDPE method,” Antennas and Wireless Propagation Letters, vol. 12, pp. 190-193, 2013.

Z. He and R. S. Chen, “Fast analysis of wide-band scattering from electrically large targets with timedomain parabolic equation method,” Computer Physics Communication, vol. 200, pp. 139-146, 2016.

Z. He and R. S. Chen, “A novel marching-on-indegree solver of time domain parabolic equation for transient EM scattering analysis,” IEEE Trans. Antennas and Propagation, vol. 64, no. 11, pp. 4905-4910, 2016.

H. H. Zhang, Q. Q. Wang, Y. F. Shi, and R. S. Chen, “Efficient marching-on-in-degree solver of time domain integral equation with adaptive cross approximation algorithm-singular value decomposition,” Applied Computational Electromagnetics Society Journal, vol. 27, no. 6, pp. 475-482, 2012.

H. H. Zhang, Z. H. Fan, and R. S. Chen, “Marchingon-in-degree solver of time-domain finite elementboundary integral method for transient electromagnetic analysis,” IEEE Transactions on Antennas and Propagation, vol. 62, no. 1, pp.319-326, 2014.

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*33*(03), 251–258. Retrieved from https://journals.riverpublishers.com/index.php/ACES/article/view/9201