ON APPLICATION OF FAST AND ADAPTIVE PERIODIC BATTLE-LEMARIE WAVELETS TO MODELING OF MULTIPLE LOSSY TRANSMISSION-LINES

In this paper, the continuous operator is discretized into matrix form s by Galerkin's procedure, using periodic Battle-Lemarie wavelets as b asis/testing functions. The polynomial decomposition of wavelets is ap plied to the evaluation of matrix elements, which makes the computatio nal effort of the matrix elements no more expensive than that of metho d of moments (MoM) with conventional piecewise basis/testing functions . A new algorithm is developed employing the fast wavelet transform (F WT). Owing to localization, cancellation, and orthogonal properties of wavelets, very sparse matrices have been obtained, which are then sol ved by the LSQR iterative method. This algorithm is also adaptive in t hat one can add at will finer wavelet bases in the regions where field s vary rapidly, without any damage to the system orthogonality of the wavelet basis functions. To demonstrate the effectiveness of the new a lgorithm, we applied it to the evaluation of frequency-dependent resis tance and inductance matrices of multiple lossy transmission lines. Nu merical results agree with previously published data and laboratory me asurements. The Valid frequency range of the boundary integral equatio n results has been extended two to three decades in comparison with th e traditional MoM approach. The new algorithm has been integrated into the computer aided design tool, MagiCAD, which is used for the design and simulation of highspeed digital systems and multichip modules Pan at al. IEEE Trans. Hyb. Manuf. Technol. 15(4), 465 (1992). (C) 1997 A cademic Press.