The higher order method of moments (HMOM) has been proposed to calculate the bistatic scattering from two-dimensional (2D) perfectly electric conducting (PEC) rough surface in this paper. The electric field integral equation (EFIE) is solved through the HMOM with the hierarchical higher order basis functions which are the modified Legendre polynomials. The non-uniform rational B-spline (NURBS) surface is applied to model the plane surface related to the rough surface. Validity of this approach is shown by comparing the bistatic scattering coefficient (BSC) to that of lower order MOM (LMOM) with the Rao-Wilton-Glisson (RWG) or rooftop basis function. This approach has fewer segments in the parametric directions than the LMOM with rooftop basis, and is more efficient for the fewer unknowns and requires less memory than the LMOM with RWG basis. Properties of EM scattering from a 2D Gaussian rough surface are also exhibited and analyzed.
2. Zhu, X., Z. Zhao, W. Yang, Y. Zhang, Z. Nie, and Q. H. Liu, "Iterative time-resersal mirror method for imaging the buried object beneath rough ground surface," Progress In Electromagnetics Research, Vol. 117, 19-33, 2011.
3. Xu, P. and K. S. Chen, "Analysis of microwave emission of exponentially correlated rough soil surfaces from 1.4 GHz to 36.5 GHz," Progress In Electromagnetics Research, Vol. 108, 205-219, 2010.
4. Yang, W., Z. Q. Zhao, C. H. Qi, W. Liu, and Z. P. Nie, "Iterative hybrid method for electromagnetic scattering from a 3-D object above a 2-D random dielectric rough surface," Progress In Electromagnetics Research, Vol. 117, 435-448, 2011.
5. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, New York, 1986.
6. Voronovich, A. G. and V. U. Zavorotny, "Theoretical model for scattering of radar signals in Ku- and C-bands from a rough sea surface with breaking waves," Waves in Random Media, Vol. 11, No. 3, 247-269, 2001.
7. Tsang, L., et al., Scattering of Electromagnetic Waves: Numerical Simulations, John Wiley & Sons, New York, 2001.
8. Li, J., L. X. Guo, and H. Zeng, "FDTD method investigation on the polarimetric scattering from 2-D rough surface," Progress In Electromagnetics Research, Vol. 101, 173-188, 2010.
9. Liu, P. and Y. Q. Jin, "Numerical simulation of the doppler spectrum of a flying target above dynamic oceanic surface by using the FEM-DDM method," IEEE Trans. Antennas Propag., Vol. 53, No. 2, 825-832, 2005.
10. Harrington, R. F., Filed Computation by Moment Method, IEEE Press, New York, 1993.
11. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 409-418, 1982.
12. Wagner, R. L., J. M. Song, and W. C. Chew, "Monte carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces," IEEE Trans. Antennas Propag., Vol. 45, No. 2, 235-245, 1997.
13. Wang, A. Q., L. X. Guo, and C. Chai, "Numerical simulations of electromagnetic scattering from 2D rough surface: Geometric modeling by NURBS surface," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 10, 1315-1328, 2010.
14. Cátedra, M. F., F. Rivas, and L. Valle, "A moment method approach using frequency independent parametric meshes," IEEE Trans. Antennas Propag., Vol. 45, No. 10, 1567-1568, 1997.
15. Jorgensen, E., et al., "Higher order hierarchical legendre basis functions for electromagnetic modeling ," IEEE Trans. Antennas Propag., Vol. 52, No. 11, 2985-2995, 2004.
16. Yuan, H. B., N. Wang, and C. H. Liang, "Combining the higher order method of moments with geometric modeling by NURBS surfaces," IEEE Trans. Antennas Propag., Vol. 57, No. 11, 3558-3563, 2009.
17. Ding, W. and G. F. Wang, "Treatment of singular integrals on generalized curvilinear parametric quadrilaterals in higher order method of moments," IEEE Antennas Wireless Propag. Lett., Vol. 8, 1310-1313, 2009.
18. Jarvenpaa, S., M. Taskinen, and P. Y. Oijala, "Singularity subtraction technique for high-order polynomial vector basis functions on planar triangles," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 42-49, 2006.
19. Guo, L. X., A. Q.Wang, and J. Ma, "Study on EM scattering from 2-D target above 1-D large scale rough surface with low grazing incidence by parallel MOM based on PC clusters ," Progress In Electromagnetics Research, Vol. 89, 149-166, 2009.
20. Wang, R. and L. X. Guo, "Numerical simulations of wave scattering from two-layered rough surface," Progress In Electromagnetics Research B, Vol. 10, 63-175, 2008.
21. Guo, L. X., Y. Liang, J. Li, and Z. S. Wu, "A high order integral SPM for the conducting rough surface scattering with the tapered wave incidence TE CASE," Progress In Electromagnetics Research, Vol. 114, 333-352, 2011.
22. Li, J., B. Wei, Q. He, L. Guo, and D. Ge, "Time-domain iterative physical optics method for analysis of EM scattering from the target half buried in rough surface: PEC case," Progress In Electromagnetics Research, Vol. 121, 391-408, 2011.
23. Zhao, Y., X. W. Shi, and L. Xu, "Modeling with NURBS surfaces used for the calculation of RCS," Progress In Electromagnetics Research, Vol. 78, 49-59, 2008.
24. Eastwood, J. W. and J. G. Morgan, "Higher-order basis functions for MoM calculations," IET Sci. Meas. Technol., Vol. 2, No. 6, 379-386, 2008.
25. Song, J. M. and W. C. Chew, "Moment method solutions using parametric geometry," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 1-2, 71-83, 1995.
26. Notaros, B. M. and B. D. Popovic, "Optimized entire-domain moment-method analysis of 3D dielectric scatterers," Int J. Numerical Modelling: Electronic Networks, Devices, and Fields, Vol. 10, 177-192, 1997.
27. Zhang, Y., et al., "Parallel MOM using higher-order basis functions and PLAPACK in-core and out-of-core solvers for challenging EM simulations," IEEE Antennas and Propagation Magazine, Vol. 51, No. 5, 42-60, 2009.
28. Lai, B., H. B. Yuan, and C. H. Liang, "Analysis of nurbs surfaces modeled geometries with higher-order MoM based aim," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 5-6, 683-691, 2012.