volume | PIER Journals

2004-04-15

On Sampling-Biorthogonal Time-Domain Scheme Based on Daubechies Compactly Supported Wavelets

Youri Tretiakov,

Dr. Youri Tretiakov

IBM Microelectronics

USA

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Stanislav Ogurtsov,

Dr. Stanislav Ogurtsov

Department of Electrical Engineering

Arizona State University

USA

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George Pan

Dr. George Pan

Department of Electrical Engineering

Arizona State University

USA

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, Vol. 47, 213-234, 2004

doi:10.2528/PIER04020403

Abstract

The multi-resolution time domain (MRTD) technique for electromagnetic field equations was proposed by Krumpholz, Katehi et al., using Battle-Lemarie wavelets. The basis principle behind the MRTD is the wavelet-Galerkin time domain (WGTD) approach. Despite its effectiveness in space discretization, the complexity ofthe MRTD makes it unpopular. Recently, the WGTD was significantly simplified by Cheong et al. based on the approximate sampling property ofthe shifted versions ofthe Daubechies compactly supported wavelets. In this paper, we provide a rigorous analysis ofthe MRTD, employing positive sampling functions and their biorthogonal dual. We call our approach as the sampling biorthogonal time-domain (SBTD) technique. The introduced sampling and dual functions are both originated from Daubechies scaling functions of order 2 (referred as to D₂), and form a biorthonormal system. This biorthonormal system has exact interpolation properties and demonstrates superiority over the FDTD in terms ofmemory and speed. Numerical examples and comparisons with the traditional FDTD results are provided.

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Youri Tretiakov, Stanislav Ogurtsov, and George Pan, "On Sampling-Biorthogonal Time-Domain Scheme Based on Daubechies Compactly Supported Wavelets," , Vol. 47, 213-234, 2004.
doi:10.2528/PIER04020403

References

1. Krumpholz, M. and L.P.B. Katehi, "MRTD: New timedomain schemes based on multiresolution analysis," IEEE Trans. Microwave Theory Tech., Vol. 44, 555-571, 1996.
doi:10.1109/22.491023

2. Yee, K.S., "Numerical solution ofinitial boundary value problems involving Maxwell's equation in isotropic media," IEEE Trans. Antennas Propagat., Vol. 14, 302-307, 1996.

3. Cheong, Y. W., Y. M. Less, K. H. Ra, J. G. Kang, and C. C. Shin, "Wavelet-Galerkin scheme oftime-dep endent inhomogeneous electromagnetic problems," IEEE Microwave Guided Wave Lett., Vol. 9, 297-299, 1999.
doi:10.1109/75.779907

4. Daubechies, I., Ten Lectures on Wavelets, SIAM, 1992.

5. Sweldens, W. and R. Piessens, "Wavelet sampling techniques," Proc. Statistical Computing Section, 20-29, 1993.

6. Walter, G. G., Wavelets and Other Orthogonal Systems with Applications, CRC Press, 1994.

7. Tentzeris, E. M.R. L. Robertson, M. Krumpholz, and L. P. B. Katehi, "Application ofMR TD to printed transmission lines," Proc. Microwave Theory Tech. Soc., 573-576, 1996.

8. Sheen, D. M., S. M. Ali, M. D. Abouzahra, and J. A. Kong, "Application ofthe three-dimensional finite-difference timedomain method to the analysis ofplanar microstrip circuits," IEEE Trans. Microwave Theory Tech., Vol. 38, 849-857, 1990.
doi:10.1109/22.55775

9. Tentzeris, E. M., R. L. Robertson, J. F. Harvey, and L. P. B. Katehi, "PML absorbing boundary conditions for the characterization ofop en microwave circuits using multiresolution time-domain techniques (MRTD)," IEEE Trans. Antenna Propagat., Vol. 47, 1709-1715, 1999.
doi:10.1109/8.814951