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Fast Multipole Method for Time Domain PEEC Analysis
October-December 2003 (vol. 2 no. 4)
pp. 275-287

Abstract—High-speed electronic circuits are becoming more and more important in modern communication systems, thus leading to an increasing interest in printed circuit boards, interconnect, and packaging. Nowadays, full-wave numerical methods are widely used in order to investigate both signal integrity and electromagnetic compatibility issues arising in PCBs design. When broadband information is desired and transient effects dominate, it is more efficient using time domain numerical techniques, which may scale better than corresponding frequency-domain methods. This paper presents the derivation of the time domain partial element equivalent circuit (PEEC) method enhanced by the three-dimensional (3D) fast multipole method (FMM). It is shown that combining the full-wave time domain PEEC method with the FMM allows performing the analysis of electrically large electronic systems, which reduces both memory and CPU-time requirements. Several examples are presented confirming the capability of the proposed approach to provide a significant reduction of the computational complexity associated with the transient analysis of large systems.

[1] L.W. Nagel, SPICE: A Computer Program to Simulate Semiconductor Circuits Electronic Research Lab. Report ERL M520, Univ. of California, Berkeley, May 1975.
[2] M. Kamon, M.J. Tsuk, and J. White, "FastHenry: A Multipole-Accelerated 3D Inductance Extraction Program," IEEE Trans. Microwave Theory and Techniques, Sept. 1994, pp. 1750-1758.
[3] A.A. Ergin, B. Shanker, and E. Michielssen, The Plane-Wave Time-Domain Algorithm for the Fast Analysis of Transient Wave Phenomena IEEE Antennas and Propagation Magazine, vol. 41, no. 4, Aug. 1999.
[4] B. Shanker, A.A. Ergin, and E. Michielssen, A Multilevel Plane Wave Time Domain Algorithm for the Fast Analysis of Transient Scattering Phenomena Proc. IEEE Antennas and Propagation Soc. Int'l Symp., vol. 2, pp.1342-1345, 1999.
[5] B. Shanker, A.A. Ergin, K. Aygün, and E. Michielssen, Analysis of Transient Electromagnetic Scattering from Closed Surfaces Using a Combined Field Integral Equation IEEE Trans. Antennas and Propagation, vol. 48, no. 7, July 2000.
[6] A.E. Ruehli, Equivalent Circuit Models for Three-Dimensional Multiconductor Systems IEEE Trans. Microwave Theory Technology, vol. 22, no. 3, pp. 216-221, Mar. 1974.
[7] H. Heeb and A.E. Ruehli, Three-Dimensional Interconnect Analysis Using Partial Element Equivalent Circuit IEEE Trans. on Circuits and Systems-1: Fundamental Theory and Applications, vol. 39, no. 11, pp. 974-981, Nov. 1992.
[8] A.E. Ruehli and H. Heeb, Circuit Models for Three-Dimensional Geometries Including Dielectrics IEEE Trans. Microwave Theory Technology, vol. 40, no. 3, pp. 1507-1516, July 1992.
[9] W.T. Weeks, A.J. Jimenez, G.W. Mahoney, D. Mehta, H. Quasemzadeh, and T.R. Scott, Algorithms for ASTAP-A Network Analysis Program IEEE Trans. Circuits Theory, vol. 20, pp. 628-634, Nov. 1973.
[10] P. Restle, A. Ruehli, S.G. Walker, and G. Papadopoulos, Full-Wave PEEC Time-Domain Method for the Modeling of On-Chip Interconnects IEEE Trans. Computer-Aided Design, vol. 20, no. 7, pp. 877-887, July 2001.
[11] B. Shanker, A.A. Ergin, K. Aygün, and E. Michielssen, Analysis of Transient Electromagnetic Scattering Phenomena Using a Two-Level Plane Wave Time Domain Algorithm IEEE Trans. Antennas and Propagation, vol. 48, no. 4, pp. 510-523, Apr. 2000.
[12] L. Greengard and V. Rokhlin, A Fast Algorithm for Particle Simulations J. Computational Physics, no. 73, pp. 325-348, 1987.
[13] L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems. Cambridge, Mass.: MIT Press, 1987.
[14] L. Greengard, Fast Algorithms for Classical Physics. Cambridge, Mass.: MIT Press, 1988.
[15] G.B. Arfken and H.J. Weber, Mathematical Methods for Physicist. New York: Academic, 1995.
[16] C.A. White and M. Headgordon, Rotating Around the Quadratic Angular Momentum Barrier in Fast Multiple Method Calculation J. Chemistry and Physics, vol. 105, no. 12, pp. 5061-5067, Sept. 1996.
[17] H. Cheng, L. Greengard, and V. Rokhlin, A Fast Adaptive Multiple Algorithm in Three Dimensions J. Computational Physics, vol. 155, pp. 468-498, 1999.
[18] G. Antonini et al. Non-Orthogonal PEEC Formulation for Time and Frequency Domain EM and Circuit Modeling IEEE Trans. Elecromagnetic Compatibility, accepted for publication.
[19] C. Seberino and N. Bertram, Concise, Efficient, Three-Dimensional Fast Multiple Method for Micromagnetics IEEE Trans. Magnetics, vol. 37, no. 3, pp. 1078-1086, May 2001.

Index Terms:
Numerical methods, PEEC analysis, equivalent circuits, Fast Multipole Method.
Giulio Antonini, "Fast Multipole Method for Time Domain PEEC Analysis," IEEE Transactions on Mobile Computing, vol. 2, no. 4, pp. 275-287, Oct.-Dec. 2003, doi:10.1109/TMC.2003.1255643
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