Efficient Representation of Multilevel QR Algorithm for Analysis of Microstrip Structures
Keywords:
Compression techniques, microstrip structure, Multilevel QR Algorithm (MLQR)Abstract
This paper presents a novel approach for the efficient solution of large-scale microstrip structures with the mixed potential integral equation (MPIE) in conjunction with the method of moments (MoM) based on the conventional Rao-Wilton-Glisson (RWG) basis functions. Although multilevel QR (MLQR) is efficient compared with direct method, it consumes more computation time and storage memory. A novel matrix compression technique is presented to recompress the sub-matrices of MLQR algorithm. The advantages of applying the novel recompression technique are illustrated by numerical results, the computation time as well as the memory requirements are compared to the conventional MLQR algorithm and the matrix decomposition algorithm-singular value decomposition (MDA-SVD). It is demonstrated that the use of proposed method can result in significant savings in computation time and memory requirements, with little or no compromise in the accuracy of the solution.
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R. F. Harrington, Field Computation by Moment Methods. Malabar, Fla.: R. E. Krieger, 1968.
S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propagat., vol. AP-30, pp. 409-418, May 1982.
E. H. Newman and D. Forrai, “Scattering from a microstrip patch,” IEEE Trans. Antennas Propagat., vol. AP-35, pp. 245~251, Mar. 1987.
K. A. Michalski and C. G. Hsu, “RCS computation of coax-loaded microstrip patch antennas of arbitrary shape,” Electromagn., vol. 14, pp. 33~62, Jan.~Mar. 1994.
K. A. Michalski and D. L. Zheng, “Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, part I: theory,” IEEE Trans. Antennas Propag., vol. 38, no. 3, pp. 335-344, 1990.
L. Gurel and M. I. Aksun, “Electromagnetic scattering solution of conducting strips in layered media using the fast multipole method,” IEEE Microwave Guided Wave Lett., vol. 6, pp. 277~279, Aug. 1996.
P. A. Macdonald and T. Itoh, “Fast simulation of microstrip structures using the fast multipole method,” Int. J. Numer. Modeling: Electron. Networks, Devices, Fields, vol. 9, pp. 345~357, 1996.
E. Michielssen and A. Boag, “A multilevel matrix decomposition algorithm for analyzing scattering from large structures,” IEEE Trans. Antennas Propag., vol. 44, no. 8, pp. 1086-1093, Aug. 1996
A. Heldring, J. M. Tamayo, J. M. Rius, and J. Parron, “Multilevel MDA-CBI for fast direct solution of large scattering and radiation problems,” IEEE AP-S International Symposium 2007, Honolulu, Hawaii, USA, 10-15 June 2007.
J. M. Rius, J. Parron, E. Ubeda, and J. Mosig, “Multilevel matrix decomposition algorithm for analysis of electrically large electromagnetic problems in 3-D,” Microw. Opt. Technol. Lett., vol. 22, no. 3, pp. 177-182, Aug. 1999.
J. Parron, G. Junkin, and J. M. Rius, “Improving the performance of the multilevel matrix decomposition algorithm for 2.5-d structures application to metamaterials,” in Proc. Antennas Propag. Soc. Int. Symp., pp. 2941-2944, July 2006.
J. Parron, J. M. Rius, and J. Mosig, “Application of the multilevel decomposition algorithm to the frequency analysis of large microstrip antenna arrays,” IEEE Trans. Magn., vol. 38, no. 2, pp. 721-724, Mar. 2002.
J. Parron, J. M. Rius, A. Heldring, E. Ubeda, and J. R. Mosig, “Analysis of microstrip antennas by multilevel matrix decomposition algorithm,” in Proc. Euro. Congress Computational Methods Applied Sciences in Engineering, Barcelona, Spain, Sept. 2000.
J. Parron, J. M. Rius, and J. Mosig, “Method of moments enhancement technique for the analysis of sierpinski pre-fractal antennas,” IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1872-1876, Aug. 2003.
J. M. Rius, A. Heldring, J. M. Tamayo, and J. Parron, “New and more efficient formulation of MLMDA for arbitrary 3D antennas and scatterers,” Antennas Propag., EuCAP The First European Conference on, pp. 1-6, 2006.
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.
J. M. Rius, A. Heldring, J. M. Tamayo, and J. Parron, “The MDA-SVD algorithm for fast direct or iterative solution of discrete integral equations,” Antennas Propag., EuCAP The Second European Conference on, pp. 1-8, 2007.
N. A. Ozdemir and J. F. Lee, “A low-rank IE-QR algorithm for matrix compression in volume integral equations,” IEEE Trans. On Magnetics, vol. 40, no. 2, pp. 1017-1020, Mar. 2004.
S. M. Seo and J. F. Lee, “A single-level low rank IE-QR algorithm for PEC scattering problems using EFIE formulation,” IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 2141-2146, Aug. 2004.
K. Z. Zhao and J. F. Lee, “A single-level dual rank IE-QR algorithm to model large microstrip antenna arrays,” IEEE Trans. Antennas Propag., vol. 52, no. 10, pp. 2580-2585, Oct. 2004.
D. Gope and V. Jandhyala, “Oct-tree-based multilevel low-rank decomposition algorithm for rapid 3-D parasitic extraction,” IEEE Trans. Computer-Aided Design, vol. 23, no. 4, pp. 1575-1580, Nov. 2004.
D. Gope and V. Jandhyala, “Efficient solution of EFIE via low-rank compression of multilevel predetermined interactions,” IEEE Trans. Antennas Propagat., vol. 53, no. 10, pp. 3324-3333, Oct. 2005.
W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast Efficient Algorithms in Computational Electromagnetics. Boston, MA: Artech House, 2001.
J. S. Zhao, W. C. Chew, C. C. Lu, E. Michielssen, and J. M. Song, “Thin-stratified medium fastmultipole algorithm for solving microstrip structures,” IEEE Trans. Microwave Theory Tech., vol. 46, pp. 395~403, Apr. 1998.
M. Bebendorf and S. Kunis, “Recompression techniques for adaptive cross approximation,” J. Integral Equations Appl., vol. 21, no. 3, pp. 331-357, 2009.
Y. Saad and M. H. Schultz, “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Statist. Comput., vol. 7, pp. 856-869, July 1986.
Y. Saad, Iterative Methods for Sparse Linear System. PWS Publishing Company, 1996.
A.-S. Liu, T.-Y. Huang, and R.-B. Wu, “A dual wideband filter design using frequency mapping and stepped-impedance resonators,” IEEE Transaction on Microwave and Theory Technology, vol. 12, pp. 2921-2929, 2008.
