The adaptive integral method (AIM) is applied in this paper to calculate the capacitance coefficients for an arbitrarily shaped three-dimensional structure. The uniformity of multipole moment approximation is revealed theoretically and numerically; it is realized that the approach can guarantee the accuracy of AIM for computing capacitance of any structure. The memory requirement and computational complexity of the present method are less than O(N1.5) and O(N1.5 logN) for three-dimensional problems, respectively. Numerical experiments for several conducting structures demonstrate that the present method is accurate and efficient to compute capacitance of an arbitrarily shaped three-dimensional structure.
2. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat., Vol. 45, No. 10, 1488-1493, Oct. 1997.
3. Greengard, L., The Rapid Evaluation of Potential Fields in Partial Systems, MIT Press, Cambridge, MA, 1988.
4. Rokhlin, V., "Rapid solution of integral equation of scattering theory in two dimensions," J. Comput. Phys., Vol. 86, No. 2, 414-439, Feb. 1990.
5. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag., Vol. 35, No. 3, 7-12, June 1993.
6. Brandt, A., "Multilevel computations of integral transforms and partical interactions with oscillatory kernels," Comput. Phys. Commun., Vol. 65, No. 1-3, 24-38, 1991.
7. Nabors, K. and J. White, "FastCap: A multipole accelerated 3-D capacitance extraction program," IEEE Trans. Computer-Aided Design, Vol. 10, No. 11, 1447-1459, Nov. 1991.
8. Nabors, K., S. Kim, and J. White, "Fast capacitance extraction of general three-dimensional structures," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 7, 1496-1506, July 1992.
9. Kamon, M., M. J. Tsuk, and J. White, "FASTHENRY: A multipole-accelerated 3-D inductance extraction program," IEEE Trans. Microwave Theory Tech., Vol. 42, No. 9, 1750-1758, Sept. 1994.
10. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "A fast integral equation solver for electromagnetic scattering problems," IEEE APS Int. Symp. Dig., Vol. 1, 416-419, 1994.
11. 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, Sept.–Oct. 1996.
12. Phillips, J. R. and J. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Trans. Computer-Aided Design of Integrated Circuits and Syst., Vol. 16, No. 10, 1059-1072, Oct. 1997.
13. Ling, F., C. F. Wang, and J. M. Jin, "Application of adaptive integral method to scattering and radiation analysis of arbitrarily shaped planar structures," J. Electromagn. Waves Appl., Vol. 12, No. 8, 1021-1037, 1998.
14. Wang, C. F., F. Ling, J. M. Song, and J. M. Jin, "Adaptive integral solution of combined field integral equation," Microwave Opt. Tech. Lett., Vol. 19, No. 5, 321-328, Dec. 1998.
15. Smythe, W. R., Static and Dynamic Electricity, 3rd Edition, A Summa Book, Revised Printing, New York, 1989.
16. Greason, W. D., Electrostatic Discharge in Electronics, Research Studies Press Ltd., England, 1992.
17. Ruehli, A. E. and P. A. Brennan, "Efficient capacitance calculations for three-dimensional multiconductor systems," IEEE Trans. Microwave Theory Tech., Vol. 21, No. 2, 76-82, Feb. 1973.
18. Brennan, S. R., A Dictionary of Applied Physics, Vol. 2, Electricity, Macmillan, London, 1922.
19. Jaswon, M. A. and G. T. Symm, Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, London, 1977.