2011-07-30
Numerical Optimization of the Method of Auxiliary Sources by Using Level Set Technique
By
Progress In Electromagnetics Research B, Vol. 33, 203-219, 2011
Abstract
It is well-known that the choice of the auxiliary surface and the arrangement of radiation centers play a decisive role for ensuring accuracy and stability of the method of auxiliary sources (MAS). Using level set technique, a numerical scheme is proposed to determine the optimal location and amplitudes of the auxiliary sources for three-dimensional scattering problems.
Citation
Afif Bouzidi, and Taoufik Aguili, "Numerical Optimization of the Method of Auxiliary Sources by Using Level Set Technique," Progress In Electromagnetics Research B, Vol. 33, 203-219, 2011.
doi:10.2528/PIERB11060505
References

1. Popovidi-Zaridze, R., D. Karkashadze, G. Ahvlediani, and J. Khatiashvili, "Investigation of possibilities of the method of auxiliary sources in solution of two-dimensional electrodynamics problems ," Radio Tech. Electron., Vol. 22, No. 2, 1978.        Google Scholar

2. Aleksidze, M. A., Solution of Boundary Problems by Expansion Solution of Boundary Problems by Expansion, 1-350, Nauka, Moscow, 1982.

3. Aleksidze, M. A., "Fundamental Functions in Approximate Solutions of the Boundary Problems," Nauka, Moscow, 1982, 1-352.        Google Scholar

4. Kupradze, V., "About approximates solution mathematical physics problem," Success Math. Sci., Vol. 22, No. N2, 59107, 1967.        Google Scholar

5. Fikioris, G., "On two types of convergence in the method auxiliary sources," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 7, Jul. 2006.        Google Scholar

6. Anastassiu, H. T., "Error estimation of the method of auxiliary sources (MAS) for scattering from an impedance circular cylinder," Progress In Electromagnetics Research, Vol. 52, 109-128, 2005.
doi:10.2528/PIER04072101        Google Scholar

7. Popovidi-Zaridze, R. S. and Z. S. Tsverikmazashvili, "Numerical study of a diffraction problems by a modified method of nonorthogonal series," Zurnal. Vichislit. Mat. Mat. Fiz., Vol. 17, No. 2, 1977 (in Russian, English translation available, translated and reprinted by Scientific Translation Editor, Oxford, 1978).        Google Scholar

8. Zaridze, R., D. Karkashadze, G. Talakvadze, J. Khatiashvili, and Z. Tsverikmazashvili, "The method of auxiliary sources in applied electrodynamics," Proc. URSI Int. Symp. E/M Theory, 102-106, Budapest, Hungary, 1986.        Google Scholar

9. Okuno, Y., "A duality relationship between scattering field and current density calculation in the Yasuura method ," MMET, 278-281, URSI, Kharkov, Ukraine, 1994.        Google Scholar

10. Karkashadze, D. and R. Zaridze, "The method of auxiliary sources in applied electrodynamics," Latsis Symposium, Zurich, 1995.        Google Scholar

11. Osher, S. and J. A. Sethian, "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations," Journal of Computational Physics, Vol. 79, 12-49, 1988.
doi:10.1016/0021-9991(88)90002-2        Google Scholar

12. Osher, S. and R. P. Fedkiw, "Level set methods: An overview and some recent results," Journal of Computational Physics, 463-502, 2001.
doi:10.1006/jcph.2000.6636        Google Scholar

13. Sethian, J. A., "Level set methods and fast marching methods," Cambridge Monographs on Applied and Computational Mathematics, Vol. 3, Cambridge University Press, Cambridge, 1999, evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science.        Google Scholar

14. Zhao, H.-K., T. Chan, B. Merriman, and S. Osher, "A variational level set approach to multiphase motion," Journal of Computational Physics, Vol. 127, No. 1, 179-195, 1996.
doi:10.1006/jcph.1996.0167        Google Scholar

15. Mitchell, I. M., A toolbox of level set methods (version 1.1), Department of Computer Science, University of British Columbia, Vancouver, BC, Canada., 2007. [Online] Available: http://www.cs.ubc.ca/ mitchell/ToolboxLS/index.html.