A new method to find the Geometrical Optics/Uniform Theory of Diffraction reflection points over Non Uniform Rational B-Splines surfaces is presented. The approach is based on the Particle Swarm Optimization (PSO) technique, and the cost function used to find the reflection points is based on Snell's law. The technique can be used as an alternative to classic minimization techniques in cases where convergence problems arise.
2. Gomez, R. , L. E. Garcia Castillo, F. Saez de Adana, and M. Salazar-Palma, "A novel hybrid FEM high frequency technique for the analysis of scattering and radiation problems," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 7, 939-956, 2004.
3. Polka, L. A., C. A. Balanis, and A. C. Polycarpou, "High-frequency methods for multiple diffraction modeling: Application and comparison," Journal of Electromagnetic Waves and Applications, Vol. 8, No. 9-10, 1223-1246, 1994.
4. Catedra, M. F., J. Perez, F. Saez de Adana, and O. Gutierrez, "Efficient ray-tracing techniques for three-dimensional analysis of propagation in mobile communications: Application to picocell and microcell scenarios," IEEE Antennas and Propagation Magazine, Vol. 40, No. 2, 15-28, 1998.
5. Rustako, A. J., N. Amitay, G. J. Owens, and R. S. Roman, "Radio propagation at microwave frequencies for line-of-sight microcellular mobile and personal communications," IEEE Transactions on Vehicular Technology, Vol. 40, No. 2, 203-210, 1991.
6. Perez, J., J. A. Saiz, O. M. Conde, R. P. Torres, M. F. Catedra, "Analysis of antennas on board arbitrary structures modeled by NURBS surfaces," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 6, 1045-1053, 1997.
7. Lozano, L., F. Saez de Adana, and M. F. Catedra, "Ray-tracing acceleration techniques to compute diffraction and double and triple e®ects in RCS prediction methods based on physical optics," PIERS Proceedings, 573-577, Tokyo, Japan, Aug. 2-5, 2006.
8. Wang, N., Y. Zhang, and C. H. Liang, "Creeping ray-tracing algorithm of UTD method based on NURBS models with the source on surface," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 1981-1990, 2006.
9. Nocedal, J., "Theory of algorithms for unconstrained optimization," Acta Numerica, Vol. 1, 199-242, Department of Electrical Engineering and Computer Science, Northwestern University,1992.
10. Byrne, L., "A first course in optimization,", 1, 494, Department of Mathematical Sciences, University of Massachusetts Lowell, 2012.
11. Ming, C., Z. Yu, and C. H. Liang, "Calculation of the field distribution near electrically large NURBS surfaces with physical optics method," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 11, 1511-1524, 2005.
12. Gonzalez, I., O. Gutierrez, F. Saez de Adana, and M. Felipe Catedra, "Computation of the scattering of arbitrary shape bodies modeled by parametric surfaces using the multilevel fast multipole method," PIERS Proceedings, 672-676, Tokyo, Japan, Aug. 2-5, 2006.
13. Adana, F. S., O. Gutierrez, I. Gonzalez, J. Perez, and M. F. Catedra, "General method for the ray tracing on convex bodies," Applied Computational Electromagnetics Society Journal, Vol. 16, No. 1, 20-26, 2001.
14. Shewchuk, R., "An introduction to the conjugate gradient method without the agonizing pain,", 1, 64, School of Computer Science, Carnegie Mellon University, 1994.
15. Pytlak, R., "Conjugate gradient methods for non-convex problems," Non-convex Optimization and Its Applications, 63,108, Springer-Verlag, Berlin, Heidelberg, 2009 .
16. Trgo, A., "On numerical approximation of non-convex variational problems using stochastic optimization algorithm,", 1, 23, Department of Mathematical Sciences, Carnegie Mellon University, 1995.
17. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 2004.
18. Chamaani, S., S. A. Mirta, M. Teshnehlab, M. A. Shooredeli, V. Seydi, and , "Modified multi-objective particle swarm optimization for electromagnetic absorber design," Progress In Electromagnetics Research, Vol. 79, 353-366, 2008.
19. Poyatos, D., D. Escot, I. Montiel, I. Gonzalez, F. Saez de Adana, and M. F. Catedra, "Evaluation of particle swam optimization applied to single snapshot direction of arrival estimation," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 16, 2251-2258, 2008.
20. Rubio, A., O. Gutierrez Blanco, F. Saez de Adana, and M. F. Catedra, "Calculation of GTD/UTD reflection points over parametric surfaces using particle swarm optimization," Progress In Electromagnetics Research Symposium, 276, Prague, Czech Republic, Aug. 27-30, 2007.
21. Salakhutdinov, R., "E±cient optimization algorithms for learning,", 1, 84, Department of Computer Science, University of Toronto, 2003.
22. Salakhutdinov, R., "On the convergence of bound optimization algorithms," Proc. 19th Conference in Uncertainty in Artificial Intelligence , 509-516, University of Toronto, 2003.
23. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley and Sons, 1989.