volume | PIER Journals

Abstract

In this paper, we consider the resistances and inductances extraction from finite conducting metals. To remedy the weakness of volume integral equation, we extend the usage of a surface integral equation method from analyzing finite conducting rectangular wire strip to analyzing arbitrarily shaped geometry. Moreover the multilevel Green function method (MLGFIM) with a complexity of O(N) is employed to accelerate the matrix-vector multiplications in iterations. The numerical results shows the efficacy of the proposed method.

1. Venkov, G., M. W. McCall, and D. Censor, "The theory of low-frequency wave physics revisited," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 229-249, 2007.
doi:10.1163/156939307779378763 Google Scholar

2. Tang, W., X. He, T. Pan, and Y. L. Chow, "Synthetic asymptote formulas of equivalent circuit components of square spiral inductors," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 2, 215-226, 2006.
doi:10.1163/156939306775777206 Google Scholar

3. Zheng, Q. and H. Zeng, "Multipole theory analysis of 3D magnetostatic fields," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 3, 389-397, 2006.
doi:10.1163/156939306775701768 Google Scholar

4. Babic, S. I. and C. Akyel, "New mutual inductance calculation of the magnetically coupled coils: Thin disk coil-thin wall solenoid," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1281-1290, 2006.
doi:10.1163/156939306779276794 Google Scholar

5. Morsey, J. D., V. I. Okhmatovski, and A. C. Cangellaris, "Finite-thickness conductor models for full-wave analysis of interconnects with a fast integral equation method," IEEE Trans. Advaced-packaging, Vol. 27, No. 1, 24-33, February 2004.
doi:10.1109/TADVP.2004.825459 Google Scholar

6. Wang, H. G. and P. Zhao, "Combining multilevel Green's function interpolation method with volume loop bases for inductance extraction problems," Progress In Electromagnetics Research, Vol. 80, 225-239, 2008.
doi:10.2528/PIER07102101 Google Scholar

7. Rokhlin, V., "Rapid solution of integral equation of classical potential theory," J. Comput. Phys., Vol. 60, 187-207, 1985.
doi:10.1016/0021-9991(85)90002-6 Google Scholar

8. Lu, C. C. and W. C. Chew, "A multilevel algorithm for solving boundary integral equations of wave scattering," Microw. Opt. Tech. Lett., Vol. 7, 466-470, July 1994.
doi:10.1002/mop.4650071013 Google Scholar

9. Song, J. M., C. C. Lu, W. C. Chew, and S. W. Lee, "Fast illinois solver code (FISC)," IEEE Antennas Propag. Mag., Vol. 48, 27-34, June 1998.
doi:10.1109/74.706067 Google Scholar

10. Sarkar, T. K., E. Arvas, and S. M. Rao, "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies," IEEE Trans. Antennas Propagat., Vol. 34, 635-640, May 1986.
doi:10.1109/TAP.1986.1143871 Google Scholar

11. Zhao, L., T. J. Cui, and W.-D. Li, "An efficient algorithm for EM scattering by electrically large dielectric objects using MR-QEB iterative scheme and CG-FFT method," Progress In Electromagnetics Research, Vol. 67, 341-355, 2007.
doi:10.2528/PIER06121902 Google Scholar

12. Phillips, J. R. and J. K. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Trans. Comput.-aided Des. Integr. Circuits Syst., Vol. 16, 1059-1072, October 1997.
doi:10.1109/43.662670 Google Scholar

13. Chan, C. H., C.-M. Lin, L. Tsang, and Y. F. Leung, "A sparse matrix/canonical grid method for analyzing microstrip structures," IEICE Trans. Electron., Vol. E80-C, No. 11, 1354-1359, November 1996. Google Scholar

14. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Sci., Vol. 31, 1225-1251, Sept-Oct 1996.
doi:10.1029/96RS02504 Google Scholar

15. Wang, H. G., C. H. Chan, and L. Tsang, "A new multilevel Green's function interpolation method for large scale low frequency EM simulations," IEEE Trans. Comput.-aided Des. Integr. Circuits Syst., Vol. 24, No. 9, 1427-1443, Sept. 2005.
doi:10.1109/TCAD.2005.850804 Google Scholar

16. Wang, H. G. and C. H. Chan, "The implementation of multilevel Green's function interpolation method for full-wave electromagnetic problems," IEEE Trans. Antennas Propag., Vol. 55, No. 5, 1348-1358, May 2007.
doi:10.1109/TAP.2007.895576 Google Scholar

17. Wang, H. G., C. H. Chan, L. Tsang, and K. F. Chan, "Mixture effective permittivity simulations using IMLMQRF method on preconditioned EFIE," Progress In Electromagnetics Research, Vol. 57, 285-310, 2006.
doi:10.2528/PIER05072603 Google Scholar

18. Medgyesi-Mitschang, L. N. and J. M. Putnam, "Integral equation formulations for imperfectly conducting scatters," IEEE Trans. Antennas Propag., Vol. 33, No. 2, 206-214, Feb. 1985.
doi:10.1109/TAP.1985.1143560 Google Scholar

19. Arbor, A., "A note on impedance boundary conditions," Can. J. Phys., Vol. 40, 663-666, 1962. Google Scholar

20. Gilberg, R. F. and B. A. Forouzan, Data Structures: A Pseudocode Approach with C++, Thomson Asia Pte Ltd and PPTPH, 2002.

21. Pozar, D. M., Microwave Engineering, 2nd Ed., Wiley, 1998.

22. Qian, Z. G., W. C. Chew, and R. Suaya, "Generalized impedance boundary condition for conductor modeling in surface integral equation," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 11, 2354-2364, Nov. 2007.
doi:10.1109/TMTT.2007.908678 Google Scholar

23. Zhao, J. S. and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," IEEE Trans. Antennas Propagat., Vol. 48, No. 10, 1635-1645, Oct. 2000.
doi:10.1109/8.899680 Google Scholar

24. Cui, T. J. and W. C. Chew, "Accurate analysis of wire structures from very-low frequency to microwave frequency," IEEE Trans. Antennas Propagat., Vol. 50, No. 3, 301-307, Mar. 2002.
doi:10.1109/8.999620 Google Scholar

25. Li, M.-K. and W. C. Chew, "Applying divergence-free condition in solving the volume integral equation," Progress In Electromagnetics Research, Vol. 57, 311-333, 2006.
doi:10.2528/PIER05061303 Google Scholar

26. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, No. 3, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818 Google Scholar

27. Hussein, K. F. A., "Fast computational algorithm for EFIE applied to arbitrarily-shaped conducting surfaces," Progress In Electromagnetics Research, Vol. 68, 339-357, 2007.
doi:10.2528/PIER06122502 Google Scholar

28. Hanninen, I., M. Taskinen, and J. Sarvas, "Singularity subtraction integral formulae for surface integral equations with RWG, ROOFTOP and hybrid basis functions," Progress In Electromagnetics Research, Vol. 63, 243-278, 2006.
doi:10.2528/PIER06051901 Google Scholar

29. Kamon, M., M. J. Tsuk, and J. K. White, "FASTHENRY: A multipole accelerated 3-D inductance extraction program," IEEE Trans. Microw. Theory Tech., Vol. 42, No. 9, 1750-1758, Sept. 1994.
doi:10.1109/22.310584 Google Scholar

Dr. Zhao Peng

Dr. Hao-Gang Wang