Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 96 > pp. 83-100


By Z.-L. Liu and J. Yang

Full Article PDF (1,183 KB)

A novel scheme of combining non-uniform rational B-splines (NURBS) model with higher-order moment method (HOMM) is presented. The mesh precision of conforming to practical object is a major factor for HOMM to yield accurate results. In the present paper, NURBS technique is employed to model complex objects accurately with large curved Bezier patches and no factitious geometric discontinuities are introduced between the adjoining patches. The higher-order modified Legendre basis functions are defined on Bezier patch. As a result of the combination of NURBS model with HOMM, the accuracy of results is greatly improved compared with HOMM on curved parametric quadrilateral (CPQ) model, meanwhile, the number of unknowns is much reduced. Numerical results show that NURBS-HOMM is an efficient technique with good potential to solve the electromagnetic (EM) problems of complex electrically large objects.

Z.-L. Liu and J. Yang, "Analysis of electromagnetic scattering with higher-order moment method and NURBS model," Progress In Electromagnetics Research, Vol. 96, 83-100, 2009.

1. R. F., Harrington, Field Computation by Moment Methods, Macmillan, New York, 1968.

2. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, 409-418, May 1982.

3. Glisson, W. and D. R. Wilton, "Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces," IEEE Trans. Antennas Propagat., Vol. 28, 593-603, Sep. 1980.

4. Notaros, M., et al., "Effcient large-domain MoM solutions to electrically large practical EM problems," IEEE Trans. Microw. Theory and Techniques, Vol. 49, 151-159, Jan. 2001.

5. Djordjevic, M. and B. M. Notaros, "Double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers," IEEE Trans. Antennas Propagat., Vol. 52, 2118-2129, Aug. 2004.

6. Djordjevic, M. and B. M. Notaros, "Higher-order hierarchical basis functions with improved orthogonality properties for moment-method modeling of metallic and dielectric microwave structures," Microw. Opt. Technol. Lett., Vol. 37, 83-88, Apr. 2003.

7. Jorgensen, E., J. L. Volakis, P. Meincke, and O. Breinbjerg, "Higher order hierarchical legendre basis functions for electro-magnetic modeling," IEEE Trans. Antennas Propagat., Vol. 52, 2985-2995, Nov. 2004.

8. Vergeest, J. S. M., "CAD surface data exchange using STEP," Computer-Aided Design, Vol. 23, 269-281, May 1991.

9. Perez, J. and M. F. Catedra, "RCS of electrically large targets modeled with NURBS surfaces," Electronics Letters, Vol. 28, 1119-1121, Jun. 1992.

10. Perez, J. and M. F. Catedra, "Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces," IEEE Trans. Antennas Propagat., Vol. 42, 1404-1411, Oct. 1994.

11. Domingo, M., et al., "Computation of the RCS of complex bodies modeled using NURBS surfaces," IEEE Antennas and Propagat. Magazine, Vol. 37, 36-47, Jun. 1995.

12. Perez, J., et al., "Analysis of antennas on board arbitrary structures modeled by NURBS surfaces," IEEE Trans. Antennas Propagat., Vol. 45, 1045-1053, Jun. 1997.

13. Wang, N., C. H. Liang, and H. B. Yuan, "Calculation of pattern in UTD method based on NURBS modeling with the source on surface," Opt. Technol. Lett. , Vol. 49, 2492-2498, Oct. 2007.

14. Sefi , S., "Ray tracing tools for high frequency electromagnetics simulations,", Licentiate thesis, Royal Institute of Technology of Stockholm, Sweden, May 2003.

15. Chen, M., Y. Zhang, X. W. Zhao, and C. H. Liang, "Analysis of antenna around nurbs surface with hybrid MoM-PO techniqu ," IEEE Trans. Antennas Propagat., Vol. 55, 407-413, Feb. 2007.

16. Valle, L., F. Rivas, and M. F. Catedra, "Combining the moment method with geometrical modeling by NURBS surfaces and Bezier patches," IEEE Trans. Antennas Propagat., Vol. 42, 373-381, Mar. 1994.

17. Delgado, C., M. F. Catedra, and R. Mittra, "Application of the characteristic basis function method utilizing a class of basis and testing functions defined on NURBS patches," IEEE Trans. Antennas Propagat., Vol. 56, 784-791, Mar. 2008.

18. Garcia, E., C. Delgado, I. G. Diego, and M. F. Catedra, "An iterative solution for electrically large problems combining the characteristic basis function method and the multilevel fast multipole algorithm," IEEE Trans. Antennas Propagat., Vol. 56, 2363-2371, Aug. 2008.

19. Piegl, L., "On NURBS: A survey," EEE Computer Graphics and Application, Vol. 11, No. 1, 55-71, South Florida, 1991.

20. De Boor, C., "On calculating with B-splines," Journal of Approximation Theory, Vol. 6, 50-62, Jul. 1972.

21. Cox, M. G., "The numerical evaluation of B-splines," IMA Journal of Applied Mathematics, Vol. 10, 134-149, 1972.

22. Boehm, W., "Inserting new knots into B-spline curves," Computer-Aided Design, Vol. 12, 199-201, Jul. 1980.

23. Van Bladel, J., Electromagnetic Fields, McGraw-Hill, New York, USA, 1964.

24. Duffy, M. G., "Quadrature over a pyramid or cube of integrands with a singularity at a vertex," SIAM J. Numer. Anal., Vol. 19, 1260-1262, Dec. 1982.

25. Sertel, K. and J. L. Volakis, "Method of moments solution of volume integral equations using parametric geometry," Radio Science, Vol. 37, 1-7, Jan.-Feb. 2002.

© Copyright 2014 EMW Publishing. All Rights Reserved