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On application of fast and adaptive periodic Battle-Lemarie wavelets for modeling of multiple lossy transmission lines. (English) Zbl 0882.65123

The paper is concerned with the boundary integral equation method for a 2D transmission line structure consisting of several conductors and one ground plane. The authors formulate a fast and adaptive algorithm using a combined nonstandard and standard wavelet decomposition method based on Battle-Lemarie wavelets of different orders. The (sparse) matrix equations are then solved by the LSQR iterative method. As a direct application, the frequency dependent inductance and resistance matrices of lossy transmission lines are evaluated.
In the numerical section of the paper, it is demonstrated that the wavelet method extends the valid frequency range of the traditional method of moments in two or three decades toward the lower end and one decade toward the higher end.

MSC:

65Z05 Applications to the sciences
65N38 Boundary element methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A30 Electro- and magnetostatics

Software:

LSQR
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Full Text: DOI

References:

[1] Pan, G.; Prentice, J.; Kahn, S.; Staniszewski, A.; Walters, W.; Gilbert, B., The simulation of high-speed, high-density digital interconnects in single chip packages and multichip modules, IEEE Trans. Comput. Hyb. Manuf. Technol., 15, 465 (1992)
[2] Benedette, J. J.; Franzier, M. W., Wavelets: Mathematics and Applications (1994), CRC Press: CRC Press Ann Arbor
[3] Alpert, B. K., Wavelets and other bases for fast numerical linear algebra, Wavelets: A Tutorial in Theory and Applications (1992), Academic Press: Academic Press New York · Zbl 0798.65127
[4] Jaffard, S.; Laurencot, Ph., Orthonormal wavelets, analysis of operators, and applications to numerical analysis, (Chui, C. K., Wavelets: A Tutorial in Theory and Applications (1992), Academic Press: Academic Press New York) · Zbl 0764.65066
[5] Glowinski, R.; Lawton, W.; Ravachol, M.; Tenenbaum, E., Wavelet solutions of linear and nonlinear elliptic, parabolic, and hyperbolic problems in one space dimension, (Glowinski, R., Computational Methods in Applied Science and Engineering (1990), SIAM: SIAM Philadelphia) · Zbl 0799.65109
[6] Beylkin, G.; Coifman, R.; Roklin, V., Fast wavelet transforms and numerical algorithm I, Commun. Pure Appl. Math., 44, 141 (1991) · Zbl 0722.65022
[7] Steinberg, B. Z.; Leviatan, Y., On the use of wavelet expansion in the method of moments, IEEE Trans. Antenna Propagat., 41, 610 (1993)
[8] Sabetfakhri, K.; Katehi, L., Analysis of integrated millimeter-wave and submillimeter-wave waveguides using orthonormal wavelet expansions, IEEE Trans. Microwave Theory Technique, 42, 2412 (1994)
[9] G. Pan, X. Zhu, 1994, The application of fast adaptive wavelet expansion method in the computation of parameter matrices of multiple lossy transmission lines, IEEE Antennas Propagat. Society Symposium, June 1994, 29, 32; G. Pan, X. Zhu, 1994, The application of fast adaptive wavelet expansion method in the computation of parameter matrices of multiple lossy transmission lines, IEEE Antennas Propagat. Society Symposium, June 1994, 29, 32
[10] Wang, G.; Pan, G., Full wave analysis of microstrip floating structures by wavelet expansion method, IEEE Trans. Microwave Theory Technique, 43, 131 (1995)
[11] Wang, G.; Pan, G.; Gilbert, B., A hybrid wavelet expansion and boundary element analysis for multiconductor transmission line in multilayered dielectric media, IEEE Trans. Microwave Tech., 43, 664 (1995)
[12] Pan, G., Orthogonal wavelets with applications in electromagnetics, IEEE Trans. Magn., 32, 975 (1996)
[13] G. Pan, J. Du, B. Gilbert, Application of intervallic wavelets to the surfare integral equations, IEEE Trans. Antennas Prop.; G. Pan, J. Du, B. Gilbert, Application of intervallic wavelets to the surfare integral equations, IEEE Trans. Antennas Prop.
[14] M. Toupikov, G. Pan, On the use of weighted wavelet expansions for integral equations on bounded intervals, IEEE Trans. Antennas Prop.; M. Toupikov, G. Pan, On the use of weighted wavelet expansions for integral equations on bounded intervals, IEEE Trans. Antennas Prop.
[15] Daubechies, I., Ten Lectures on Wavelets (1992), SIAM: SIAM Philadelphia · Zbl 0776.42018
[16] Stratton, J., Electromagnetic Theory (1941), McGraw-Hill: McGraw-Hill New York, p. 359- · JFM 67.1119.01
[17] Olyslager, F.; Zutter, D. D.; Blomme, K., Rigorous analysis of the propagation characteristics of general lossless and lossy multiconductor transmission lines in multilayered media, IEEE Trans. Microwave Theory Technique, 41, 79 (1993)
[18] Wu, R.-B.; Yang, J.-C., Boundary integral equation formulation of skin effect problems in multiconductor transmission lines, IEEE Trans. Magn., MAG-25, 3013 (1989)
[19] Tsuk, M. J.; Kong, J. A., A hybrid method for the calculation of the resistance and inductance of transmission lines with arbitrary cross sections, IEEE Trans. Microwave Theory Technique, 39, 1338 (1991)
[20] Beylkin, G.; Coifman, R.; Roklin, V., Wavelets in numerical analysis, (Ruskai, M. B., Wavelets and Their Applications (1992), Jones & Bartlett: Jones & Bartlett Boston) · Zbl 0798.65126
[21] Paige, C. C.; Sounders, M. A., LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software, 8, 43 (1982) · Zbl 0478.65016
[22] Golub, G.; Van Loan, C., Matrix Computations (1983), John Hopkins Univ. Press: John Hopkins Univ. Press Baltimore · Zbl 0559.65011
[23] Dobrowolski, J. A., Introduction to Computer Methods for Microwave Circuit Analysis and Design (1991), Artech House: Artech House Norwood
[24] Hagman, L. A.; Young, D. M., Applied Iterative Methods (1981), Academic Press: Academic Press New York
[25] Faraji-Dana, R.; Chow, Y., Edge condition of the field and a.c. resistance of a rectangular strip conductor, IEE Proc., 137, 133 (1990)
[26] Pan, G.; Olson, K.; Gilbert, B., Improved algorithmic methods for the prediction of wavefront propagation behavior in multiconductor transmission lines for high frequency digital signal processors, IEEE Trans. CAD Int. Circ. Systems, 8, 608 (1989)
[27] G. G. Walter, 1993, Wavelets and Other Orthogonal Systems with Applications, University of Wisconsin-Milwaukee; G. G. Walter, 1993, Wavelets and Other Orthogonal Systems with Applications, University of Wisconsin-Milwaukee
[28] Chui, C. K., An Introduction to Wavelets (1991), Academic Press: Academic Press New York · Zbl 0736.41010
[29] Mallat, S., A theory of multiresolution decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Mach. Intell., 11, 674 (1989) · Zbl 0709.94650
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