Am ultiresolution frequency domain (MRFD) analysis similar to the finite difference frequency domain (FDFD) method is presented. This new method is derived by the application of MoM to frequency domain Maxwell's equations while expanding the fields in terms of biorthogonal scaling functions. The dispersion characteristics of waveguiding structures are analyzed in order to demonstrate the advantages of this proposed MRFD method over the traditional FDFD scheme.
1. Steinberg, B. Z. and Y. Leviatan, "On the use of wavelet expansions in the method of moments," IEEE Trans. Antennas Propagat., Vol. 41, No. 5, 610-619, 1993. doi:10.1109/8.222280
2. Sabetfakhri, K. and L. P. B. Katehi, "Analysis of integrated millimeter-wave and submillimeter-wave waveguides using orthonormal wavelet expansions," IEEE Trans. Microwave Theory Tech., Vol. 42, No. 12, 2412-2422, 1994. doi:10.1109/22.339775
3. Wagner, R. L. and W. C. Chew, "Study of wavelets for the solution of electromagnetic integral equations," IEEE Trans. Antennas and Propagat., Vol. 43, No. 8, 802-810, 1995. doi:10.1109/8.402199
4. Wei, X. C. and E. P. Li, "Fast solution for large scale electromagnetic scattering problems using wavelet transform and its precondition," Progress In Electromagnetics Research, Vol. 38, 253-267, 2002. doi:10.2528/PIER02042602
5. Krumpholz, M. and L. P. B. Katehi, "MRTD: new timedomain schemes based on multiresolution analysis," IEEE Trans. Microwave Theory Tech., Vol. 44, No. 4, 555-571, 1996. doi:10.1109/22.491023
6. Fujii, M. and W. J. R. Hoefer, "Athree-dimensional Haar-waveletbased multiresolution analysis similar to the FDTD method â€” derivation and application," IEEE Trans. Microwave Theory Tech., Vol. 46, No. 12, 2463-2475, 1998. doi:10.1109/22.739236
7. Dogaru, T. and L. Carin, "Multiresolution time-domain using CDF biorthogonal wavelets," IEEE Trans. Microwave Theory Tech., Vol. 49, No. 5, 902-912, 2001. doi:10.1109/22.920147
8. Fujii, M. and W. J. R. Hoefer, "A wavelet formulation of the finite-difference method: Full-vector analysis of optical waveguide junctions," IEEE J. Quantum Electron., Vol. 37, No. 8, 1015-1029, 2001. doi:10.1109/3.937391
9. Cao, Q., K. K. Tamma, P. K. A. Wai, and Y. Chen, "RCS scattering analysis using the three-dimensional MRTD scheme," J. of Electromagn. Waves and Appl., Vol. 17, No. 12, 1683-1701, 2003. doi:10.1163/156939303322760218
10. Barba, I., J. Represa, M. Fujii, and W. J. R. Hoefer, "Multiresolution 2D-TLM technique using Haar wavelets," IEEE MTT-S Int. Microwave Symp. Dig., 243-246, 2000.
11. Pan, G. W., Wavelets in Electromagnetics and Device Modeling, John Wiley & Sons Inc., Hoboken, New Jersey, 2003.
12. Zhu, X., T. Dogaru, and L. Carin, "Analysis of the CDF biorthogonal MRTD method with application to PEC targets," IEEE Trans. Microwave Theory Tech., Vol. 51, No. 9, 2015-2022, 2003. doi:10.1109/TMTT.2003.815874
13. Daubechies, I., Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
14. Tretiakov, Y., S. Ogurtsov, and G. Pan, "On samplingbiorthogonal time-domain scheme based on daubechies compactly supported wavelets," Progress In Electromagnetics Research, Vol. 47, 213-234, 2004. doi:10.2528/PIER04020403
15. Pereda, J. A., A. Vegas, L. F. Velarde, and O. Gonzalez, "An FDFD eigenvalue formulation for computing port solutions in FDTD simulators," Microwave and Opt. Tech. Letters, Vol. 45, No. 4, 1-3, 2005. doi:10.1002/mop.20704
16. Lui, M. L. and Z. Chen, "Adirect computation of propagation constant using compact 2-D full-wave eigen-based finite-difference frequency-domain technique," Int. Conf. on Comp. Electromagnetics and Its Applications, 2, 1999.
17. Asi, A. and L. Shafai, "Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD," Electronics Letters, Vol. 28, 1451-1452, 1992.
18. Cangellaris, A. C., "Numerical stability and numerical dispersion of a compact 2-D/FDTD method used for the dispersion analysis of waveguides," IEEE Microwave and Guided Wave Letters, Vol. 3, 3-5, 1993. doi:10.1109/75.180672
19. Harrington, R. F., Time-harmonic Electromagnetic Fields, McGraw-Hill Book Company, Inc., York, PA, 1961.