volume | PIER Journals

Abstract

A hybrid time-domain method combing finite-difference and cell-centered finite-volume method is presented in this paper. This method is applied to solve three dimensional electromagnetic problems which involve media having finite conductivity. The fractional-step technique (FST) for FVTD scheme is applied to solve these problems. Local time-step scheme is used to enhance the efficiency of this method. Numerical results are given and compared with a reliable numerical method, which is used to show the validation of this method.

1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media ," IEEE Trans. Antennas Propagat., Vol. 14, 302-307, May 1966.
doi:10.1109/TAP.1966.1138693 Google Scholar

2. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time Domain Method, 2nd Ed., Artech House, Norwood, MA, 2000.

3. Bonnet, P., X. Ferrieres, B. L. Michielsen, P. Klotz, and J. L. Roumiguires, Time Domain Electromagnetics, Ch. 9, Academic Press, 1999.

4. Shang, J. S., "Characteristic-based algorithms for solving the Maxwell equations in the time domain," IEEE Antennas Propagat. Mag., Vol. 37, 15-25, Jun. 1995.
doi:10.1109/74.388807 Google Scholar

5. Riley, D. J. and C. D. Turner, "Local tetrahedron modeling of microelectronics using the finite-volume hybrid-grid technique,", Sandia Report, SAND95-2790, UC-706, Dec. 1995.
doi:10.1109/74.388807 Google Scholar

6. Morton, K. W., Numerical Solution of Convection-diffusion Problems, Chapman & Hall, 1996.

7. Bozza, G., D. D. Caviglia, L. Ghelardoni, and M. Pastorino, "Cell-centered finite-volume time-domain method for conducting media," IEEE Microwave and Wireless Components Letters, Vol. 20, No. 9, 477-479, Sep. 2010.
doi:10.1109/LMWC.2010.2057243 Google Scholar

8. Bommaraju, C., "Investigating finite volume time domain methods in computational electromagnetics,", Ph.D. Dissertation, Technischen University Darmstadt, Darmstadt, 2009. Google Scholar

9. Andersson, U., "Time-domain methods for the maxwell equations,", Ph.D. Dissertation, Department of Numerical Analysis and Computer Science, Royal Institute of Technology, Stockholm, 2001. Google Scholar

10. Remaki, M., "A new finite volume scheme for solving Maxwell's system," COMPEL, 913-931, 2000. Google Scholar

11. Yang, M., Y. Chen, and R. Mittra, "Hybrid finite-difference/finite-volume time-domain analysis for microwave integrated circuits with curved PEC surfaces using a nonuniform rectangular grid," IEEE Trans. Microwave Theory Tech., Vol. 48, 969-975, Jun. 2000.
doi:10.1109/22.846728 Google Scholar

12. Ferrieres, X., J.-P. Parmantier, S. Bertuol, and A. R. Ruddle, "Application of a hybrid finite difference/finite volume method to solve an automotive EMC problem," IEEE Trans. Electromagnetic Compatibility, Vol. 46, No. 4, 624-634, Nov. 2004.
doi:10.1109/TEMC.2004.837837 Google Scholar

13. Leveque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2004.

14. Haider, F., J.-P. Croisille, and B. Courbet, "Stability analysis of the cell centered finite-volume MUSCL method on un-structured grids," Numer. Math., Vol. 113, 555-600, 2009, DOI10.1007/s00211-009-0242-6.
doi:10.1007/s00211-009-0242-6 Google Scholar

15. Medgyesi-Mitschang, L. N., J. M. Putam, and M. B. Gedera, "Generalized method of moments for 3D penetrable scatters," Opt. Soc. Am. A, Vol. 11, No. 4, 1383-1398, 1994.
doi:10.1364/JOSAA.11.001383 Google Scholar

16. He, Z.-L., K. Huang, Y. Zhang, and C.-H. Liang, "A new local time-step scheme for hybrid finite difference/finite volume method," Journal of Electromagnetic Waves and Applications, Vol. 26, No. 5-, 641-652, 2012.
doi:10.1080/09205071.2012.710785 Google Scholar

Dr. Zhi-Li He

Dr. Kai Huang

Professor Chang-Hong Liang