Fast Solution of Low-Frequency Problems Using Efficient Form of MLACA with Loop-Tree Basis Functions

Authors

  • Zhaoneng Jiang Hefei University of Technology, Hefei 230009
  • Xiaoyan Zhao Hefei University of Technology, Hefei 230009,
  • Ye Jiang Hefei University of Technology, Hefei 230009,
  • Xuguang Qiao Hefei University of Technology, Hefei 230009,
  • Quanquan Wang Nanjing University of Posts and Telecommunications, Nanjing 210003,

Keywords:

Compressed block decomposition (CBD), efficient form of multilevel adaptive cross approximation (EFMLACA) algorithm, low frequency

Abstract

In this paper, an efficient scheme of numerical method is proposed to solve the low frequency (LF) problems, which combines the loop-tree basis functions with an efficient form of multilevel adaptive cross approximation (EFMLACA) algorithm. It utilizes the loop-tree basis functions to divide the vector part and scalar part of the impedance matrix. Meanwhile, the scalar part is frequency normalized. Through this operation, it can avoid the low frequency breakdown problem. In order to accelerate the matrix vector multiplication, the EFMLACA algorithm is applied. Meanwhile, the compressed block decomposition (CBD) preconditioner is applied to improve the condition number of poor convergence problems. The numerical results demonstrate that the memory requirement and computation time required for a matrix vector multiplication of EFMLACA algorithm is much less than that of MLACA and ACA-SVD. Moreover, the matrix vector multiplication of EFMLACA algorithm is also much more efficient than that of low-frequency multilevel fast multipole algorithm (LF-MLFMA).

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References

M. S. Al Salameh and A. M. Olaimat, “Method of moments modelling of cylindrical microwave integrated circuits interconnections,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 17, no. 2, pp. 119- 133, 2004.

P. De Doncker, “A volume/surface potential formulation of the method of moments applied to electromagnetic scattering,” Engineering Analysis with Boundary Elements, vol. 27, no. 4, pp. 325- 331, 2003.

C. Essid, M. B. B. Salah, and A. Samet, “Hybrid spatial-spectral MoM analysis of microstrip structures,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 29, no. 4, pp. 763-772, 2016.

H. De Sterck, “Steepest descent preconditioning for nonlinear GMRES optimization,” Numerical Linear Algebra with Applications, vol. 20, no. 3, pp. 453-471, 2013.

M. K. Kim and I. Yun, “An efficient implementation of the generalized minimum residual algorithm with a new preconditioner for the boundary element method,” Engineering Analysis with Boundary Elements, vol. 35, no. 11, pp. 1214-1224, 2011.

Ö. Ergül, “Fast and accurate solutions of electromagnetics problems involving lossy dielectric objects with the multilevel fast multipole algorithm,” Engineering Analysis with Boundary Elements, vol. 36, no. 3, pp. 423-432, 2012.

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

K. Zhang and J.-M. Jin, “Parallelized multilevel fast multipole algorithm for scattering by objects with anisotropic impedance surfaces,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 28, no. 1 pp. 107- 119, 2015.

J. P. De, S. R. Gago, D. W. Kelly, O. C. Zienkiewicz, and I. Babuska, “A posteriori error analysis and adaptive processes in the finite element method: Part II—Adaptive mesh refinement,” International Journal for Numerical Methods in Engineering, vol. 19, no. 11, pp. 1621-1656, Nov. 1983.

M. Zhang, L. W. Li, and A. Y. Ma, “Analysis of scattering by a large array of waveguide-fed wideslot millimeter wave antennas using precorrectedFFT algorithm,” IEEE Microwave and Wireless Components Letters, vol. 15, no. 11, pp. 772-774, Nov. 2005.

J. Aronsson, M. Shafieipour, and V. Okhmatovski, “Solution of large multiscale EMC problems with method of moments accelerated via low-frequency MLFMA,” Electromagnetic Compatibility (EMC), 2011 IEEE International Symposium on, pp. 260- 263, 2011.

M. Bebendorf, Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems, Lecture Notes in Computational Science and Engineering, vol. 63, pp. 49-98, 2008.

J. M. Rius, J. Parron, A. Heldring, J. M. Tamayo, and E. Ubeda, “Fast iterative solution of integral equations with method of moments and matrix decomposition algorithm - singular value decomposition,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp.2314-2324, Aug. 2008.

L. Grasedyck and W. Hackbusch, “Construction and arithmetics of H-matrices,” Computing, vol. 70, no. 4, pp. 295-344, 2003.

A. Heldring, J. M. Tamayo, C. Simon, E. Ubeda, and J. M. Rius, “Sparsified adaptive cross approximation algorithm for accelerated method of moments computations,” IEEE Trans. Antennas Propag., vol. 61, no. 1, pp.240-246, Jan. 2013.

J. M. Tamayo, A. Heldring, and J. M. Rius, “Multilevel adaptive cross approximation (MLACA),” IEEE Transactions on Antennas and Propagation, vol. 59, no. 12, pp. 4600-4608, Dec. 2011.

D. Ding, S. Shen, Z. Jiang, and R. Chen, “The modified multilevel compressed block decomposition algorithms for analyzing the scattering of objects in half space,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 27, no. 1, pp. 153-163, Jan. 2014.

M. Bebendorf and S. Kunis, “Recompression techniques for adaptive cross approximation,” J. Integral Equations Appl., vol. 21, no. 3, pp. 331- 357, 2009.

T. Wan and Z. Jiang, “Multilevel compressed block decomposition-based finite element domain decomposition method for the fast analysis of finite periodic structures,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, doi: 10.1002/jnm.2194, Sep. 2016.

J.-S. Zhao and W. C. Chew, “Integral equation solution of Maxwell’s equations from zero frequency to microwave frequencies,” IEEE Trans. Antennas Propag., vol. 48, no. 10, pp.1635-1645, Oct. 2000.

M.-M. Li, H. Chen, Z. Jiang, and R. Chen, “Three dimensional low-frequency fast multipole method for analysis of electromagnetic scattering,” Chinese Journal of Radio Science, vol. 25, no. 1, pp. 127- 131, Feb. 2010.

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Published

2019-05-01

How to Cite

[1]
Zhaoneng Jiang, Xiaoyan Zhao, Ye Jiang, Xuguang Qiao, and Quanquan Wang, “Fast Solution of Low-Frequency Problems Using Efficient Form of MLACA with Loop-Tree Basis Functions”, ACES Journal, vol. 34, no. 05, pp. 746–752, May 2019.

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