A fast directional algorithm for high-frequency electromagnetic scattering

Journal of Computational Physics

Volumn 230, Issue 14, 2011, Pages 5471-5487

  Tsuji, Paul ^a   Ying, Lexing ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Boundary integral equations; Electromagnetic scattering; Fast algorithms; Fast multipole methods; Sparse Fourier transforms

Indexed keywords

ACOUSTIC WAVE SCATTERING; BOUNDARY INTEGRAL EQUATIONS; ELECTROMAGNETIC WAVE SCATTERING; ITERATIVE METHODS;

BOUNDARY INTEGRAL FORMULATIONS; DIRECTIONAL ALGORITHMS; ELECTROMAGNETIC SCATTERING; ELECTROMAGNETIC SCATTERING PROBLEM; FAST ALGORITHMS; FAST SOLUTIONS; FAST-MULTIPOLE METHODS; HIGH-FREQUENCY ELECTROMAGNETICS; MULTILEVEL ALGORITHM; SPARSE FOURIER TRANSFORM;

RADAR CROSS SECTION;

EID: 79955732221     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.02.013     Document Type: Article

References (32)

1. Bagci H., Andriulli F., Cools K., Olyslager F., Michielssen E. A Calderon multiplicative preconditioner for the combined field integral equation. IEEE Trans. Antennas Propag. 2009, 57(10):3387-3392.
2. Bebendorf M., Kunis S. Recompression techniques for adaptive cross approximation. J. Integral Equat. Appl. 2009, 21(3):331-357.
3. Bleszynski E., Bleszynski M., Jaroszewicz T. AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems. Radio Sci. 1996, 31(5):1225-1251.
4. Bruno O.P., Kunyansky L.A. A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications. J. Comput. Phys. 2001, 169(1):80-110.
5. Candes E., Demanet L., Ying L. A fast butterfly algorithm for the computation of Fourier integral operators. Multiscale Model. Simul. 2009, 7(4):1678-1694.
6. Canning F.X., Rogovin K. Fast direct solution of standard moment-method matrices. IEEE Trans. Antennas Propag. 1998, 40(3):15-26.
7. Cheng H., Crutchfield W.Y., Gimbutas Z., Greengard L.F., Ethridge J.F., Huang J., Rokhlin V., Yarvin N., Zhao J. A wideband fast multipole method for the Helmholtz equation in three dimensions. J. Comput. Phys. 2006, 216(1):300-325.
8. Chew W., Jin J., Michielssen E., Song J. Fast and Efficient Algorithms in Computational Electromagnetics 2001, Artech House.
9. Duffy M. Quadrature over a pyramid or cube of integrands with a singularity at a vertex. SIAM J. Numer. Anal. 1982, 19:1260-1262.
10. Engquist B., Ying L. Fast directional multilevel algorithms for oscillatory kernels. SIAM J. Sci. Comput. 2008, 29(4):1710-1737.
11. Engquist B., Ying L. A fast directional algorithm for high frequency acoustic scattering in two dimensions. Commun. Math. Sci. 2009, 7(2):327-345.
12. Gibson W. The Method of Moments in Electromagnetics 2007, Chapman and Hall.
13. Greengard L. The rapid evaluation of potential fields in particle systems. ACM Distinguished Dissertations 1988, MIT Press, Cambridge, MA.
14. Greengard L., Rokhlin V. A fast algorithm for particle simulations. J. Comput. Phys. 1987, 73(2):25-348.
15. Harrington R. Time-harmonic Electromagnetic Fields 1961, McGraw-Hill.
16. Heldring A., Tamayo J.M., Rius J.M. Fast direct solution of the combined field integral equation. URSI Int. Symp. Electromagn. Theory 2010, 524-527.
17. Kapur S., Long D. IES3: efficient electrostatic and electromagnetic simulation. IEEE Comput. Sci. Eng. 1998, 5(4):60-67.
18. Martinsson P.G., Rokhlin V. A fast direct solver for scattering problems involving elongated structures. J. Comput. Phys. 2007, 221(1):288-302.
19. Michielssen E., Boag A., Chew W.C. Scattering from elongated objects: direct solution in O(N log2 N) operations. IEE Proc. Microw. Antennas Propag. 1996, 143(4):277-283.
20. Peterson A., Ray S., Mittra R. Computational Methods for Electromagnetics 2001, Wiley-IEEE Press.
21. Phillips J., White J. A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 1997, 16(10):1059-1072.
22. Rao S., Wilton D., Glisson A. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antennas Propag. 1982, 30(3):409-418.
23. Rokhlin V. Rapid solution of integral equations of scattering theory in two dimensions. J. Comput. Phys. 1990, 86(2):414-439.
24. Seo S.M., Lee J.F. A single-level low rank IE-QR algorithm for PEC scattering problems using EFIE formulation. IEEE Trans. Antennas Propag. 2004, 52(8):2141-2146.
25. Seo S.M., Lee J.F. A fast IE-FFT algorithm for solving PEC scattering problems. IEEE Trans. Magn. 2005, 41(5):1476-1479.
26. Song J., Chew W. Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microwave Optical Technol. Lett. 1995, 10(1):14-19.
27. Song J., Lu C., Chew W. Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects. IEEE Trans. Antennas Propag. 1997, 45(10):1488-1493.
28. Wandzura S., Xiao H. Symmetric quadrature rules on a triangle. Comput. Math. Appl. 2003, 45(12):1829-1840.
29. Woo A., Wang H., Schuh M., Sanders M. Benchmark radar targets for the validation of computational electromagnetics programs. IEEE Antennas Propag. Mag. 1993, 35(1):84-89.
30. Ying L. Sparse Fourier transform via butterfly algorithm. SIAM J. Sci. Comput. 2009, 31(3):1678-1694.
31. Ying L., Biros G., Zorin D. A kernel-independent adaptive fast multipole algorithm in two and three dimensions. J. Comput. Phys. 2004, 196(2):591-626.
32. Zhu A., Adams R., Canning F. Modified simply sparse method for electromagnetic scattering by PEC. IEEE Antennas Propag. Soc. Int. Symp. 2005, 4A:427-430.