A Shifted SSOR Preconditioner with Low-Rank Compression for Monostatic RCS Calculation

Authors

  • J. Chen College of Computer and Information Engineering, Hohai University, Nanjing, China , Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, Beijing, China
  • Z. Liu School of Information Engineering, East China Jiaotong University, Nanchang, China , State Key Laboratory of Millimeter Wave, Southeast University, Nanjing, China
  • B. Yong State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China
  • Z. Jiang Department of Communication Engineering, Nanjing University of Science & Technology, Nanjing, China
  • N. Cao College of Computer and Information Engineering, Hohai University, Nanjing, China

Keywords:

Adaptive cross approximation, iterative methods, low-rank property, monostatic RCS, preconditioning techniques, shifted technique.

Abstract

Computation time and memory consumption are two crucial bottlenecks for solving large dense complex linear system arising from electric field integral equations (EFIE) formulation of monostatic scattering problems. The traditional symmetric successive overrelaxation (SSOR) preconditioner, derived from the near-field matrix of the EFIE, is widely used to accelerate the convergence rate of iterative solvers. This technique can be greatly improved by modifying the near-field matrix of the EFIE with the principal value term of the magnetic field integral equation (MFIE) operator. Additionally, the adaptive cross approximation (ACA) algorithm is applied to compress the near-field interaction matrix to save memory. Numerical experiment results indicate that the novel technique can significantly reduce both the computational time and memory significantly with low cost for construction and implementation of preconditioners.

Downloads

Download data is not yet available.

References

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, 1982.

W. Chew, J. Jin, E. Midielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Boston, MA: Artech House, 2001.

J. Song, C. Lu, and W. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 10, pp. 1488-1493, 1997.

Z. Fan, M. Chen, R. Chen, and D. Ding, “An efficient parallel FE-BI algorithm for large-scale scattering problems,” ACES Journal, vol. 26, no. 10, pp. 831-840, Oct. 2011.

X. Hu, R. Chen, D. Ding, Z. Fan, and Y. Xu, “Two-step preconditioner of multilevel simple sparse method for electromagnetic scattering problems,” ACES Journal, vol. 27, no. 1, pp. 14- 21, Jan. 2012.

Z. Liu, J. Chen, and R. Chen, “An adaptive preconditioning technique using Fuzzy controller for efficient solution of electric field integral equations,” ACES Journal, vol. 26, no. 6, pp. 512- 518, June 2011.

M. Chen, R. Chen, Z. Fan, and D. Ding, “Accelerating the multilevel fast multipole method with parallel preconditioner for large-scale scattering problems,” ACES Journal, vol. 26, no. 10, pp. 815-822, Oct. 2011.

K. Sertel and J. Volakis, “Incomplete LU preconditioner for FMM implementation,” Microwave and Optical Technology Letters, vol. 26, no. 7, pp. 265-267, 2000.

E. Chow and Y. Saad, “Experimental study of ILU preconditioners for indefinite matrices,” J. of Comput. Appl. Math, vol. 86, pp. 387-414, 1997.

J. Lee, J. Zhang, and C.-C. Lu, “Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 9, pp. 2277-2287, Sep. 2004.

B. Carpentieri, “An adaptive approximate inversebased preconditioner combined with the fast multipole method for solving dense linear systems in electromagnetic scattering,” ACES Journal, vol. 24, no. 5, pp. 504-510, Oct. 2009.

Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, 1996.

R. Chen, K. Edward, N. Yung, C. Chan, and D. Fang, “Application of SSOR preconditioned conjugate gradient algorithm to edge-FEM for 3- dimensional full wave Electromagnetic boundary value problems,” IEEE Transactions on Microwave Theory and Techniques, vol. 50, no. 4, pp. 1165 -1172, April 2002.

J. Chen, Z. Liu, K. Xu, D. Ding, Z. Fan, and R. Chen, “Shifted SSOR preconditioning technique for electromagnetic wave scattering problems,” Microwave and Optical Technology Letters, vol. 51, no. 4, pp. 1035-1039, April 2009.

A. Heldring, J. Rius, J. Tamayo, J. Parron, and E. Ubeda, “Multiscale compressed block decomposition for fast direct solution of method of moments linear system,” IEEE Trans. Antennas Propag., vol. 59, no. 2, pp. 526-536, Feb. 2011.

A. Heldring, J. Rius, J. Tamayo, J. Parron, and E. Ubeda, “Fast direct solution of method of moments linear system,” IEEE Trans. Antennas Propag., vol. 55, no. 11, pp. 3220-3228, Nov. 2007.

A. Heldring, J. Rius, J. Tamayo, and J. Parron, “Compressed block-decomposition algorithm for fast capacitance extraction,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 27, no. 2, pp. 265-271, Feb. 2008.

A. Heldring, J. Rius, J. Tamayo, and J. Parron, “Multilevel MDA-CBI for fast direct solution of large scattering and radiation problems,” Antennas and Propagation Society International Symposium, 2007.

A. Heldring, J. Tamayo, J. Rius, J. Parron, and E. Ubeda, “Multiscale CBD for fast direct solution of MoM linear system,” Antennas and Propagation Society International Symposium, 2008.

Z. Jiang, Z. Fan, D. Ding, R. Chen, and K. Leung, “Preconditioned MDA-SVD-MLFMA for analysis of multi-scale problems,” ACES Journal, vol. 25, no. 11, pp. 914-925, 2010.

M. Bebendorf, “Approximation of boundary element matrices,” Numer. Math., vol. 86, no. 4, pp. 565-589, June 2000.

S. Kurz, O. Rain, and S. Rjasanow, “The adaptive cross-approximation technique for the 3-D boundary element method,” IEEE Trans. Magn., vol. 38, no. 2, pp. 421-424, March 2002.

K. Zhao, M. Vouvakis, and J. Lee, “The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems,” IEEE Trans. Electromagnetic Compatibility, vol. 47, no. 4, pp. 763-773, Nov. 2005.

Z. Liu, R. Chen, J. Chen, and Z. Fan, “Using adaptive cross approximation for efficient calculation of monostatic scattering with multiple incident angles,” ACES Journal, vol. 26, no. 4, pp. 325-333, April 2011.

J. Hu and Z. Nie, “Improved electric field integral equation (IEFIE) for analysis of scattering from 3- D conducting structures,” IEEE Transactions on Electromagnetic Compatibility, vol. 49, no. 3, pp. 644-648, August 2007.

P. Rui, R. Chen, Z. Fan, J. Hu, and Z. Nie, “Perturbed incomplete ILU preconditioner for efficient solution of electric field integral equations,” IET Microwave Antennas Propagation, vol. 5, no. 1, pp. 1059-1063, 2007.

Downloads

Published

2021-09-27

How to Cite

[1]
J. . Chen, Z. . Liu, B. . Yong, Z. . Jiang, and N. . Cao, “A Shifted SSOR Preconditioner with Low-Rank Compression for Monostatic RCS Calculation”, ACES Journal, vol. 28, no. 09, pp. 772–779, Sep. 2021.

Issue

2013: Vol 28 Iss 9

Section

General Submission