volume | PIER Journals

Abstract

In order to accelerate the speed of matrix-vector product (MVP) in iteration process for adaptive integral method (AIM), a virtual grids technique (VGT) with the multi-dimensional fast Fourier transform (FFT) is proposed. By adding some uniform virtual grids outside the original region, the indexes of nonzeros in the projection matrix are modified so as to eliminate the padding and unpadding procedures in MVP. The advantages of this method are that first it will not occupy any extra memory, and second it makes the Green's function vector compressed from (2N_x - 1)(2N_y - 1)(2N_z - 1) to 8(N_x - 1)(N_y - 1)(N_z - 1) because of its symmetrical block-Toeplitz property. Numerical results show that per iteration time could be reduced more than 30% by applying this method in comparison with the conventional AIM, without losing accuracy. In addition, the peak memory consumption could also be reduced because the intermediate vectors are eliminated.

1. Harrington, R. F., Field Computation by Moment Methods, Wiley-IEEE Press, New York, 1993.
doi:10.1109/9780470544631

2. Song, J., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 10, 1488-1493, October 1997.
doi:10.1109/8.633855 Google Scholar

3. Chew, W. C., T. J. Cui, and J. M. Song, "A FAFFA-MLFMA algorithm for electromagnetic scattering," IEEE Transactions on Antennas and Propagation, Vol. 50, No. 11, 1641-1649, January 2002.
doi:10.1109/TAP.2002.802162 Google Scholar

4. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Science, Vol. 31, No. 5, 1225-1251, September 1996.
doi:10.1029/96RS02504 Google Scholar

5. Yang, K. and A. E. Yilmaz, "An FFT-accelerated integral-equation solver for analyzing scattering in rectangular cavities," IEEE Transactions on Microwave Theory and Techniques, Vol. 62, No. 9, 1930-1942, September 2014.
doi:10.1109/TMTT.2014.2335176 Google Scholar

6. Wang, X., S. X. Gong, J. Ma, and C. F. Wang, "Efficient analysis of antennas mounted on largescale complex platforms using hybrid AIM-PO technique," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 3, 1517-1523, March 2014.
doi:10.1109/TAP.2013.2296326 Google Scholar

7. Wang, X., D. H. Werner, and J. P. Turpin, "Investigation of scattering properties of large-scale aperiodic tilings using a combination of the characteristic basis function and adaptive integral methods," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 6, 3149-3160, June 2013.
doi:10.1109/TAP.2013.2250474 Google Scholar

8. Ling, F., V. I. Okhmatovski, W. Harris, S. McCracken, and A. Dengi, "Large-scale broad-band parasitic extraction for fast layout verification of 3-D RF and mixed-signal on-chip structures," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 1, 264-273, January 2005.
doi:10.1109/TMTT.2004.839907 Google Scholar

9. Barrowes, B. E., F. L. Teixeira, and J. A. Kong, "Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz matrices," IEEE Transactions on Antennas and Propagation Society International Symposium, 630-633, Boston, USA, MA, July 2001. Google Scholar

Dr. Mingxuan Zheng

Dr. Huiling Zhao

Dr. Zhonghui Zhao