A fast higher-order time-domain finite element-boundary integral method for 3-D electromagnetic scattering analysis

IEEE Transactions on Antennas and Propagation

Volumn 50, Issue 9, 2002, Pages 1192-1202

  Jiao, Dan ^a   Ergin, A Arif ^a   Shanker, Balasubramaniam ^b   Michielssen, Eric ^a   Jin, Jian Ming ^a  

^a University of Illinois at Urbana Champaign   (United States)

^b Iowa State University of Science and Technology   (United States)

Author keywords

Electromagnetic scattering; Finite element method; Higher order method; Transient analysis

Indexed keywords

ALGORITHMS; BOUNDARY ELEMENT METHOD; EVALUATION; FINITE DIFFERENCE METHOD; FUNCTIONS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; TIME DOMAIN ANALYSIS; VECTORS;

HIGHER-ORDER METHOD;

ELECTROMAGNETIC WAVE SCATTERING;

EID: 0036760507     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2002.801375     Document Type: Article

References (49)

1. P.P. Silvester and G. Pelosi, Finite Elements for Wave Electromagnetics. Piscataway, NJ: IEEE Press, 1994.
2. K.S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302-307, Mar. 1966.
3. C.L. Bennet, "A Technique for Computing Approximate Impulse Response for Conducting Bodies," Ph.D. dissertation, Purdue Univ., West Lafayette, IN, 1968.
4. R. Mittra, "Integral equation methods for transient scattering," in Transient Electromagnetic Fields, L.B. Felsen, Ed. New York: Springer-Verlag, 1976, ch. 2.
5. A.G. Tijhuis, Electromagnetic Inverse Profiling. Utrecht, Netherlands: VNU, 1987.
6. S.M. Rao and D.R. Wilton, "Transient scattering by conducting surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. 39, pp. 56-61, Jan. 1991.
7. B.P. Rynne and P.D. Smith, "Stability of time marching algorithms for the electric field integral equations," J. Electromagn. Waves Applicat., vol. 12, pp. 1181-1205, 1990.
8. P.D. Smith, "Instabilities in time marching methods for scattering: Cause and rectification," Electromagn., vol. 10, pp. 439-451, 1990.
9. D.A. Vechinski and S.M. Rao, "A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. 40, pp. 661-665, June 1992.
10. B.P. Rynne, "Stability and convergence of time marching methods in scattering problems," Int. J. Appl. Math., vol. 35, pp. 297-310, 1985.
11. M.J. Bluck and S.P. Walker, "Time-domain BIE analysis of large three dimensional electromagnetic scattering problems," IEEE Trans. Antennas Propagat., vol. 45, pp. 894-901, May 1997.
12. G. Manara, A. Monorchio, and R. Reggiannini, "A space-time discretization criterion for a stable time-marching solution of the electric field integral equation," IEEE Trans. Antennas Propagat., vol. 45, pp. 527-532, Mar. 1997.
13. S.M. Rao and T.K. Sarkar, "An efficient method to evaluate the time-domain scattering from arbitrarily shaped conducting bodies," Microwave Opt. Technol. Lett., vol. 17, pp. 321-325, 1998.
14. A.A. Ergin, B. Shanker, and E. Michielssen "Fast evaluation of transient wave fields using diagonal translation operators," J. Comp. Phys., vol. 146, pp. 157-180, 1998.
15. S.P. Walker, "Scattering analysis via time-domain integral equations: Methods to reduce the scaling of cost with frequency," IEEE Antennas Propagat. Mag., vol. 39, pp. 13-20, Oct. 1997.
16. A.A. Ergin, B. Shanker, and E. Michielssen, "The plane wave time domain algorithm for the fast analysis of transient wave phenomena," IEEE Antennas Propagat. Mag., vol. 41, no. 4, pp. 39-52, Aug. 1999.
17. B. Shanker, A.A. Ergin, K. Aygün, and E. Michielssen, "The multilevel plane wave time domain algorithm for the fast analysis of transient scattering phenomena," in Proc. IEEE Antennas Propagat. Soc., vol. 2, Orlando, FL, July 1999, pp. 1342-1346.
18. A.C. Cangellaris, C.C. Lin, and K.K. Mei, "Point-matched time-domain finite element methods for electromagnetic radiation and scattering," IEEE Trans. Antennas Propagat., vol. 35, pp. 1160-1173, Oct. 1987.
19. J.T. Elson, H. Sangani, and C.H. Chan, "An explicit time-domain method using three-dimensional Whitney elements," Microwave Opt. Technol. Lett., vol. 7, pp. 607-610, 1994.
20. T.V. Yioultsis, N.V. Kantartzis, C.S. Antonopoulos, and T.D. Tsiboukis, "A fully explicit Whitney element-time domain scheme with higher order vector finite elements for three-dimensional high frequency problems," IEEE Trans. Magn., vol. 34, pp. 3288-3291, 1998.
21. M. Feliani and F. Maradei, "Hybrid finite element solution of time dependent Maxwell's curl equations," IEEE Trans. Magn., vol. 31, pp. 1330-1335, May 1995.
22. K. Choi, S.J. Salon, K.A. Connor, L.F. Libelo, and S.Y. Hahn, "Time domain finite element analysis of high power microwave aperture antennas," IEEE Trans. Magn., vol. 31, pp. 1622-1625, May 1995.
23. M. Hano and T. Itoh, "Three-dimensional time-domain method for solving Maxwell's equations based on circumference of elements," IEEE Trans. Magn., vol. 32, pp. 946-949, May 1996.
24. A. Bossavit and I. Mayergoyz, "Edge elements for scattering problems," IEEE Trans. Magn., vol. 25, pp. 2816-2821, July 1989.
25. M.F. Wong, O. Picon, and V.F. Hanna, "A finite-element method based on Whitney forms to solve Maxwell equations in the time-domain," IEEE Trans. Magn., vol. 31, pp. 1618-1621, May 1995.
26. K. Mahadevan and R. Mittra, "Radar cross section computation of inhomogeneous scatterers using edge-based finite element methods in frequency and time domains," Radio Sci., vol. 28, pp. 1181-1193, Nov.-Dec. 1993.
27. D.R. Lynch and K.D. Panlsen, "Time-domain integration of the Maxwell equations on finite elements," IEEE Trans. Antennas Propagat., vol. 38, pp. 1933-1942, Dec. 1990.
28. G. Mur, "The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media," IEEE Trans. Magn., vol. 28, pp. 1130-1133, Mar. 1992.
29. J.F. Lee and Z. Sacks, "Whitney elements time domain (WETD) methods," IEEE Trans. Magn., vol. 31, pp. 1325-1329, May 1995.
30. J.F. Lee, "WETD-a finite-element time-domain approach for solving Maxwell's equations," IEEE Microwave Guided Wave Lett., vol. 4, pp. 11-13, Jan. 1994.
31. S.D. Gedney and U. Navsariwala, "An unconditionally stable finite-element time-domain solution of the vector wave equation," IEEE Microwave Guided Wave Lett., vol. 5, pp. 332-334, May 1995.
32. D.A. White, "Orthogonal vector basis functions for time domain finite element solution of the vector wave equation," IEEE Trans. Magn., vol. 35, pp. 1458-1461, May 1999.
33. J.M. Jin, M. Zunoubi, K.C. Donepudi, and W.C. Chew, "Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method," Comput. Methods Appl. Mech. Engr., vol. 169, pp. 279-296, 1999.
34. J.F. Lee, R. Lee, and A.C. Cangellaris, "Time-domain finite element methods," IEEE Trans. Antennas Propagat., vol. 45, pp. 430-442, Mar. 1997.
35. J.R. Brauer, R. Mittra, and J.F. Lee, "Absorbing boundary condition for vector and scalar potentials arising in electromagnetic finite element analysis in frequency and time domains," in Proc. IEEE Antennas Propagat. Soc. Int. Symp. Dig., ON, Canada, June 1991, pp. 1224-1227.
36. K. Mahadevan, R. Mittra, D. Rowse, and J. Murphy, "Edge-based finite element frequency and time domain algorithms for RCS computation," in Proc. IEEE Antennas Propagat Soc. Int. Symp. Dig., vol. 3, 1993, pp. 1680-1683.
37. T. Roy, T.K. Sarkar, A.R. Djordjevic, and M. Salazar-Palma, "Time-domain analysis of TM scattering from conducting cylinders using a hybrid method," IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1471-1477, Oct. 1998.
38. D. Jiao, M. Lu, E. Michielssen, and J.M. Jin, "A fast time-domain finite element-boundary integral method for electromagnetic analysis," IEEE Trans. Antennas Propagat., vol. 49, pp. 1453-1461, Oct. 2000, submitted for publication.
39. J.M. Jin, The Finite Element Method in Electromagnetics. New York: Wiley, 1993.
40. W.P. Carpes Jr., L. Pichon, and A. Razek, "A 3D finite element method for the modeling of bounded and unbounded electromagnetic problems in the time domain," Int. J. Numer. Model., vol. 13, pp. 527-540, 2000.
41. D. Jiao and J.M. Jin, "A general approach for the stability analysis of the time-domain finite-element method," in Proc. IEEE Antennas Propagat. Soc. Int. Symp. Dig., vol. 4, Boston, MA, July 2001, pp. 506-509.
42. R.D. Graglia, D.R. Wilton, and A.F. Peterson, "Higher order inter-polatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propagat., vol. 45, pp. 329-341, Mar. 1997.
43. B. Shanker, A.A. Ergin, K. Aygün, and E. Michielssen, "Computation of transient scattering from electrically large scatterers using the plane wave time domain algorithm," in Proc. IEEE Antennas Propagat. Soc. Int. Symp. Dig., vol. 2, Atlanta, GA, June 1998, pp. 948-951.
44. B. Shanker, A.A. Ergin, and E. Michielssen, "Plane-wave time-domain acceleration of exact radiation boundary, conditions in FDTD analysis of electromagnetic phenomena," IEEE Trans. Antennas and Propagat., 2000, submitted for publication.
45. B. Shanker, A.A. Ergin, K. Aygün, and E. Michielssen, "Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm," IEEE Trans. Antennas Propagat., vol. 48, pp. 510-523, Apr. 2000.
46. C.E. Reuter, E.T. Thiele, and A. Taflove, "Validation and extension to three-dimensions of the Berenger PML absorbing boundary condition for FDTD meshes," IEEE Microwave Guided Wave Lett., vol. 4, pp. 268-270, Aug. 1994.
47. P.R. Amestoy and I.S. Duff, "Vectorization of a multiprocessor multifrontal code," Int. J. Supercomput. Appl., vol. 3, pp. 41-59, 1989.
48. T.A. Davis and I.S. Duff, "An unsymmetric-pattern multifrontal methods for parallel sparse LU factorization," SIAM J. Matrix Anal. Appl., vol. 18, no. 1, pp. 140-158, 1997.
49. J.W.H. Liu, "The multifrontal method for sparse matrix solution: Theory and practice," SIAM Rev., vol. 34, pp. 82-109, 1992.