High Order On Surface Radiation Boundary Conditions For Radar Cross-Section Application
Keywords:
On surface radiation boundary conditions, scattering problems, time-domain analysis, numerical analysis, bilinear transformation, radar-cross section, two and three-dimensionalAbstract
Solving problems governed by two and threedimensional wave equations in exterior domains are a complex task. There are techniques to reduce the computational complexities, one such technique is On-Surface Radiation Boundary Conditions (OSRBC). There have been recent interests in revisiting this technique for two and three-dimensional problems [1]. In this paper, we explore the implementation of a new high order OSRBC based on the high order local boundary conditions introduced by [2] for two and three dimensions to solve the wave equation in unbounded domains. In most cases, it is difficult to construct exact solutions. For comparisons of numerical solutions, we use solutions obtained from large domains as approximate exact solutions. The implementation involves a two step novel approach to handle time derivatives. First, the governing equations and boundary conditions are converted to Laplace transform domain. Then, based on bilinear transformation the procedure was converted to z domain which simplified the implementation process. In particular, this process leads to higher accuracy compared to the different types of finite difference schemes used to approximate the first and second order partial derivative in the new high order OSRBC and the auxiliary functions that define the high order boundary conditions. A series of numerical tests demonstrate the accuracy and efficiency of the new high order OSRBC for two and three-dimensional problems. Both the long domain solutions as well as the new OSRBC solutions are compared for accuracies and useful results for radar cross-section calculations are presented.
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H. Alzubaidi, X. Antoine, and C. Chniti, “Formulation and accuracy of on-surface radiation conditions for acoustic multiple scattering problems,” Applied Mathematics and Computation, vol. 277, pp. 82–100, 2016.
T. Hagstrom and S. I. Hariharan, “A formulation of asymptotic and exact boundary conditions using local operators,” Applied Numerical Mathematics, vol. 27, no. 4, pp. 403–416, 1998.
X. Antoine, “Advances in the on-surface radiation condition method: Theory, numerics and applications,” Computational Methods for Acoustics Problems, pp. 169–194, 2008.
Y. Mao, A. Z. Elsherbeni, S. Li, and T. Jiang, “Surface impedance absorbing boundary for terminating fdtd simulations.” Applied Computational Electromagnetics Society Journal, vol. 29, no. 12, 2014.
X. Antoine, M. Darbas, and Y. Y. Lu, “An improved on-surface radiation condition for acoustic scattering problems in the high-frequency spectrum,” Comptes Rendus Mathematique, vol. 340, no. 10, pp. 769–774, 2005.
L. L. Thompson, “A review of finite-element methods for time-harmonic acoustics,” The Journal of the Acoustical Society of America, vol. 119, no. 3, pp. 1315–1330, 2006.
J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics, vol. 114, no. 2, pp. 185– 200, 1994.
I. Mahariq, M. Kuzuoglu, and I. Tarman, “On the ˘ attenuation of the perfectly matched layer in electromagnetic scattering problems with the spectral element method.” Applied Computational Electromagnetics Society Journal, vol. 29, no. 9, 2014.
J.-C. Ned´ elec, ´ Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems. Springer Science & Business Media, 2001, vol. 144.
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory. SIAM, 2013, vol. 72.
F. Ihlenburg, Finite Element Analysis of Acoustic Scattering. Springer Science & Business Media, 2006, vol. 132.
G. Kriegsmann, A. Taflove, and K. Umashankar, “A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach,” IEEE Transactions on Antennas and Propagation, vol. 35, no. 2, pp. 153–161, 1987.
G. A. Kriegsmann and T. Moore, “An application of the on-surface radiation condition to the scattering of acoustic waves by a reactively loaded sphere,” Wave Motion, vol. 10, no. 3, pp. 277–284, 1988.
A. Bayliss and E. Turkel, “Radiation boundary conditions for wave-like equations,” Communications on Pure and applied Mathematics, vol. 33, no. 6, pp. 707–725, 1980.
A. Bayliss, M. Gunzburger, and E. Turkel, “Boundary conditions for the numerical solution of elliptic equations in exterior regions,” SIAM Journal on Applied Mathematics, vol. 42, no. 2, pp. 430–451, 1982.
B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proceedings of the National Academy of Sciences, vol. 74, no. 5, pp. 1765–1766, 1977.
S. I. Hariharan and S. Sawyer, “Transform potential-theoretic method for acoustic radiation from structures,” Journal of Aerospace Engineering, vol. 18, no. 1, pp. 60–67, 2005.
J. G. Proakis and D. K. Manolakis, Digital Signal Processing (4th Edition). Prentice-Hall, Inc., 2006.
N. Berrabah, “On high order on-surface radiation boundary conditions,” 2014.
A. Al Weshah and S. Hariharan, “A fourier spectral method to solve high order on-surface radiation boundary conditions in electromagnetics,” in Electrical and Electronics Engineering Conference (JIEEEC), 2017 10th Jordanian International. IEEE, 2017, pp. 1–6.
D. Colton, Partial Differential Equations: An Introduction. Dover Publications, 2012.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Courier Corporation, 2012
