This paper presents a new hybridization between MoM-GEC and a MultiResolution analysis (MR) based on the use of wavelets functions as trial functions. The proposed approach is developed to speed up convergence, alleviate calculation and then provide a considerable gain in requirements (processing time and memory storage) because it generates a sparse linear system. The approach consists in calculating the total current and input impedance on an invariant metallic pattern through two steps. The first one consists in expressing the boundary conditions of the unknown electromagnetic current with a single electrical circuit using the Generalized Equivalent Circuit method (GEC) and then deduce an electromagnetic equation based on the impedance operator. The impedance operator used here is described using the local modal basis of the waveguide enclosing the studied structure. The second step consists in approximating the total current using orthonormal periodic wavelets as testing functions and the local modal basis of the waveguide as basis functions. The proposed approach allows fast calculation of such inner products through the use of the wavelets multiresolution (MR) analysis advantages, thus significantly reducing the required CPU-time for microstrip-type structure analysis [13, 14]. A sparse matrix is generated from the application of a threshold. A sparsely filled matrix is easier to store and invert [15, 16]. Based on this approach, we study the planar structures. The obtained results show good accuracy with the method of moments. Moreover, we prove considerable improvements in CPU time and memory storage achieved by the MR-GEC approach when studying these structures.
6. Mekkioui, Z. and H. Baudrand, "A full-wave analysis of uniform microstrip leaky-wave antenna with arbitrary metallic strips," Electromagnetics, Vol. 28, No. 4, 296-314, 2008. doi:10.1080/02726340802040161
7. Aubert, H. and H. Baudrand, "L'Electromagnétisme par les schémas équivalents,", Cepaduès Editions, 2003.
8. Xiang, Z. and Y. Lu, "An effective wavelet matrix transform approach for efficient solutions of electromagnetic integral equations," IEEE Trans. Antennas Propagat., Vol. 45, Aug. 1997.
9. Loison, R., R. Gillard, J. Citerne, and G. Piton, "Application of the wavelet transform for the fast computation of a linear array of printed antennas," European Microwave Conf., Vol. 2, 301-304, Amsterdam, The Netherlands, 1998.
10. Oberschmidt, G. and A. F. Jacob, "Accelerated simulation of planar circuits by means of wavelets," European Microwave Conf., 305-310, Amsterdam, The Netherlands, 1998.
11. Wang, G. and G.-W. Pan, "Full wave analysis of microstrip expansion method," IEEE Trans. on Microw. Theory Tech., Vol. 43, No. I, 131-142, 1995. doi:10.1109/22.362998
12. Chui, C. K. and E. Quak, "Wavelets on a bounded interval,", D. Braess and C. L. Schumaker, (eds.), ``Numerical methods of approximation theory,'' Vol. 9, 53--75, 1992.
13. 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
14. Zhu, X., T. Sogaru, and L. Carin, "Three-dimensional biorthogonal multiresolution time-domain method and its application to electromagnetic scattering problems," IEEE Trans. Antennas Propagat., Vol. 51, No. 5, 1085-1092, May 2003. doi:10.1109/TAP.2003.811527
16. Aguili, T., "Modélisation des composants S. H. F planaires par la méthode des circuits équivalents généralisés,", Thesis, National Engineering School of Tunis ENIT, May 2000.
17. Wang, G., "On the utilization of periodic wavelet expansions in the moment methods," IEEE Trans. on Microw. Theory Tech., Vol. 43, No. 10, Oct. 1995.
18. Wang, G., "Application of wavelets on the interval to the analysis of thin-wire antennas and scatterers," IEEE Trans. Antennas Propagat., Vol. 45, No. 45, 885-893, May 1997. doi:10.1109/8.575642
19. Pan, G. W. and X. Zhu, "The application of fast adaptive wavelet expansion method in the computation of parameter matrices of multiple lossy transmission lines," IEEE Trans. on Microw. Theory Tech., Vol. 1, 29-32, 1994.
21. Baudrand, H., "Introduction au calcul des circuits microsondes,", Cepadues Ed., ENSEEIHT, Toulouse, 1994.
22. Boggess, F. and J. Narcowich, First Course in Wavelets with Fourier Analysis, Wiley, Oct. 2009.
23. Pan, G. W., Wavelets in Electromagnetics and Device Modeling, Wiley, New York, 2003. doi:10.1002/0471433918
24. Daubechies, "Ten lectures on wavelets,", Society for Applied Mathematics Philadelphia, Pennsylvania, 1992.
25. Beylkin, G., R. R. Coifman, and V. Rokhlin, "Fast wavelet transforms and numerical algorithms - I,", Yale Univ. Tech. Rep., YALEU/DCS/RR-696, Aug. 1989, Commun. Pure Appl. Math., Vol. XLIV, 141-183, 1991.
26. Loison, R., "Utilisation de l'analyse multirésolution dans la méthode des moments. Application à la modélisation de réseaux d'antennes imprimées,", Ph.D. Thesis, National Institute of Applied Sciences, Jan. 2000.
27. Zhu, J., "Development of sensitivity analysis and optimization for microwave circuits and antennas in the frequency domain,", Master Thesis, Mcmaster University, Amilton, Ontario, Jun. 2006.
28. N'Gongo, R. S. and H. Baudrand, "Application of wave concept iterative procedure in planar circuits," Recent Res. Devel. Microwave Theory and Technique, Vol. 1, 187-197, 1999.
29. Beylkin, G., R. Coifman, and V. Rokhlin, "Fast wavelet transforms and numerical algorithms I," Comm. Pure Appl. Math., Vol. 44, 141-183, 1991. doi:10.1002/cpa.3160440202
30. Alpert, B., R. Coifman, and V. Rokhlin, "Wavelet-like bases for the fast solution of second-kind integral equations," SIAM J. Sci. Comput., Vol. 14, No. 1, 159-184, Jan. 1993. doi:10.1137/0914010
31. Beylkin, G., R. R. Coifman, and V. Rokhlin, "Fast wavelet transforms and numerical algorithms - I,", Yale Univ. Tech. Rep., YALEU/DCS/RR-696, Aug. 1989, Commun. Pure Appl. Math., Vol. XLIV, 141-183, 1991.
32. Alpert, B., R. Coifman, and V. Rokhlin, "Wavelet-like bases for the fast solution of second-kind integral equations," SIAM J. Sci. Comput., Vol. 14, No. 1, 159-184, Jan. 1993. doi:10.1137/0914010
33. Chang, X. and L. Tsang, "Fast and broadband modeling method for multiple vias with irregular antipad in arbitrarily shaped power/ground planes in 3-D IC and packaging based on generalized foldy-lax equations," IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 4, 685-696, 2014. doi:10.1109/TCPMT.2013.2290897
34. Tsang, L. and S. Huang, "Modeling of vias sharing the same antipad in planar waveguide with boundary integral equation and group T matrix method," Progress In Electromagnetics Research, Vol. 152, 105-125, 2015. doi:10.2528/PIER15072605