Vol. 96
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2009-09-07
Analysis of Electromagnetic Scattering with Higher-Order Moment Method and NURBS Model
By
Progress In Electromagnetics Research, Vol. 96, 83-100, 2009
Abstract
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.
Citation
Zi-Liang Liu, and Juan Yang, "Analysis of Electromagnetic Scattering with Higher-Order Moment Method and NURBS Model," Progress In Electromagnetics Research, Vol. 96, 83-100, 2009.
doi:10.2528/PIER09071704
References

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.
doi:10.1109/TAP.1982.1142818

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.
doi:10.1109/TAP.1980.1142390

4. Notaros, M., B. D. Popovic, J. P. Weem, 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.
doi:10.1109/22.899977

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.
doi:10.1109/TAP.2004.833175

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.
doi:10.1002/mop.10831

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.
doi:10.1109/TAP.2004.835279

8. Vergeest, J. S. M., "CAD surface data exchange using STEP," Computer-Aided Design, Vol. 23, 269-281, May 1991.
doi:10.1016/0010-4485(91)90067-7

9. Perez, J. and M. F. Catedra, "RCS of electrically large targets modeled with NURBS surfaces," Electronics Letters, Vol. 28, 1119-1121, Jun. 1992.
doi:10.1049/el:19920706

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.
doi:10.1109/8.320747

11. Domingo, M., F. Rivas, J. Perez, et al. "Computation of the RCS of complex bodies modeled using NURBS surfaces," IEEE Antennas and Propagat. Magazine, Vol. 37, 36-47, Jun. 1995.
doi:10.1109/74.482030

12. Perez, J., J. A. Saiz, O. M. Conde, et al. "Analysis of antennas on board arbitrary structures modeled by NURBS surfaces," IEEE Trans. Antennas Propagat., Vol. 45, 1045-1053, Jun. 1997.
doi:10.1109/8.585754

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.
doi:10.1109/TAP.2006.889814

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.
doi:10.1109/8.280724

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.
doi:10.1109/TAP.2008.916935

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.
doi:10.1109/TAP.2008.926781

19. Piegl, L., "On NURBS: A survey," EEE Computer Graphics and Application, Vol. 11, No. 1, 55-71, South Florida, 1991.
doi:10.1109/38.67702

20. De Boor, C., "On calculating with B-splines," Journal of Approximation Theory, Vol. 6, 50-62, Jul. 1972.
doi:10.1016/0021-9045(72)90080-9

21. Cox, M. G., "The numerical evaluation of B-splines," IMA Journal of Applied Mathematics, Vol. 10, 134-149, 1972.
doi:10.1093/imamat/10.2.134

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.
doi:10.1137/0719090

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.