Multi-level Power Series Solution for Large Surface and Volume Electric Field Integral Equation
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https://doi.org/10.13052/2023.ACES.J.380501关键词:
H-Matrix, Method of Moments (MoM), Power Series Solution, Surface Electric Field Integral Equation, Volume Electric Field Integral Equation摘要
In this paper, we propose a new multi-level power series solution method for solving a large surface and volume electric field integral equation-based H-Matrix. The proposed solution method converges in a fixed number of iterations and is solved at each level of the H-Matrix computation. The solution method avoids the computation of a full matrix, as it can be solved independently at each level, starting from the leaf level. Solution at each level can be used as the final solution, thus saving the matrix computation time for full H-Matrix. The paper shows that the leaf level matrix computation and solution with power series gives as accurate results as the full H-Matrix iterative solver method. The method results in considerable savings time and memory savings compared to the H-Matrix iterative solver. Further, the proposed method retains the O(NlogN) solution complexity.
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参考
V. P. Padhy, Y. K. Negi, and N. Balakrishnan, “RCS enhancement due to Bragg scattering,” 2012 International Conference on Mathematical Methods in Electromagnetic Theory, Kharkiv Ukraine, pp. 443-446, IEEE, 28-30 Aug. 2012.
Y. K. Negi, V. P. Padhy and N. Balakrishnan, “RCS enhancement of concealed/hidden objects at Terahertz (THz),” 27th Annual Review of Progress in Applied Computational Electromagnetics Williamsburg, Virginia, USA, pp. 347-350, 27-31 March 2011.
A. Taflove, The Finite Difference Time Domain Method., Boston, Artech House, 1995.
R. Harrington, Field Computation by Moment Methods, Malabar, Florida, RE Krieger Publishing Company, 1982.
J.-M. Jin, The Finite Element Method in Electromagnetics, Hoboken New Jersey, John Wiley & Sons, 2015.
W. C. Chew, E. Michielssen, J. Song, and J.-M. Jin, Fast and Efficient Algorithms in Computational Electromagnetics, Norwood, MA, USA: Artech House, Inc., 2001.
E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Science, vol. 31, no. 5, pp. 1225-1251, Sept.-Oct. 1996.
J. R. Phillips and J. K. White, ‘‘A precorrected-FFT method for electrostatic analysis of complicated 3-D structures,” IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, vol. 16, no. 10, pp. 1059-1072, Oct. 1997.
S. Kapur and D. E. Long, “N-body problems: IES 3: Efficient electrostatic and electromagnetic simulation,” IEEE Computational Science and Engineering, vol. 5, no. 4, pp. 60-67, Oct.-Dec. 1998.
W. Hackbusch, “A sparse matrix arithmetic based on-matrices. Part I: Introduction to-matrices,” Computing, vol. 62, no. 2, pp. 89-108, Apr. 1999.
W. Hackbusch and B. N. Khoromskij, “A sparse H-matrix arithmetic, part II: Application to multi-dimensional problems,” Computing, vol. 64, no. 1, pp. 21-47, Feb. 2000.
Y. K. Negi, “Memory reduced half hierarchal matrix (H-matrix) for electrodynamic electric field integral equation,” Progress in Electromagnetics Research Letters, vol. 96, pp. 91-96, Feb. 2021.
Y. Saad, “ILUT: A dual threshold incomplete LU factorization,” Numerical Linear Algebra with Applications, vol. 1, no. 4, pp. 387-402, Jul.-Aug. 1994.
Y. K. Negi, N. Balakrishnan, S. M. Rao, and D. Gope, “Null-field preconditioner with selected far-field contribution for 3-D full-wave EFIE,” IEEE Transactions on Antennas and Propagation, vol. 64, no. 11, pp. 4923-4928, Nov. 2016.
Y. K. Negi, N. Balakrishnan, and S. M. Rao, “Symmetric near-field Schur’s complement preconditioner for hierarchal electric field integral equation solver,” IET Microwaves, Antennas & Propagation, vol. 14, no. 14, pp. 1846-1856, Nov. 2020.
L. Greengard, D. Gueyffier, P.-G. Martinsson, and V. Rokhlin, “Fast direct solvers for integral equations in complex three-dimensional domains,” Acta Numerica, vol. 18, pp. 243-275, May 2009.
J. Shaeffer, “Direct solve of electrically large integral equations for problem sizes to 1 M unknowns,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 8, pp. 2306-2313, Aug. 2008.
Y. K. Negi, N. Balakrishnan, and S. M. Rao, “Fast power series solution of large 3-D electrodynamic integral equation for PEC scatterers,” Applied Computational Electromagnetics Society (ACES) Journal, pp. 1301-1311, Nov. 2021.
S. M. Rao, “A new multi-level power series solution algorithm to solve electrically large electromagnetic scattering problems applicable to conducting bodies,” 2021 International Conference on Electromagnetics in Advanced Applications (ICEAA), Honolulu, HI, USA, pp. 152-152, 09-13 Aug. 2021.
S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Transactions on Antennas and Propagation, vol. 30, no. 3, pp. 409-418, May 1982.
D. Schaubert, D. Wilton, and A. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Transactions on Antennas and Propagation, vol. 32, no. 1, pp. 77-85, Jan. 1984.
M. Bebendorf, “Approximation of boundary element matrices,” Numerische Mathematik, vol. 86, pp. 565-589, Oct. 2000.
S. Kurz, O. Rain, and S. Rjasanow, “The adaptive cross-approximation technique for the 3D boundary-element method,” IEEE Transactions on Magnetics, vol. 38, no. 2, pp. 421-424, Aug. 2002.
Y. K. Negi, V. P. Padhy, and N. Balakrishnan, “Re-compressed H-matrices for fast electric field integral equation,” 2020 IEEE International Conference on Computational Electromagnetics (ICCEM), pp. 176-177, Singapore, 2020.
S. M. Rao and M. S. Kluskens, “A new power series solution approach to solving electrically large complex electromagnetic scattering problems,” Applied Computational Electromagnetics Society (ACES) Journal, pp. 1009-1019, Aug. 2021.
