Rigorous, auxiliary variable-based implementation of a second-order ABC for the vector FEM

IEEE Transactions on Antennas and Propagation

Volumn 54, Issue 11, 2006, Pages 3499-3504

  Botha, Matthys M ^a   Davidson, David Bruce ^a  

^a STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

Absorbing boundary conditions (ABCs); Computational electromagnetics; Curl conforming elements; Finite element method (FEM)

Indexed keywords

BOUNDARY CONDITIONS; ELECTROMAGNETIC WAVE ABSORPTION; ELECTROMAGNETIC WAVE SCATTERING; FINITE ELEMENT METHOD; HARMONIC ANALYSIS; WAVE EQUATIONS;

ABSORBING BOUNDARY CONDITIONS; COMPUTATIONAL ELECTROMAGNETICS; CURL-CONFORMING ELEMENTS; VECTOR WAVE EQUATION;

ELECTROMAGNETIC WAVES;

EID: 33947426379     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2006.884300     Document Type: Article

References (18)

1. J.-M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. New York: Wiley, 2002.
2. M. M. Botha and J.-M. Jin, "On the variational formulation of hybrid finite element-boundary integral techniques for electromagnetic analysis," IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 3037-3047, Nov. 2004.
3. D. Givoli, "Non-reflecting boundary conditions," J. Comput. Phys., vol. 94, pp. 1-29, 1991.
4. A. Bayliss and E. Turkel, "Radiation boundary conditions forwave-like equations," Commun. Pure Appl. Math., vol. 33, pp. 707-725, 1980.
5. A. Bayliss, M. Gunzburger, and E. Turkel, "Boundary conditions for the numerical solution of elliptic equations in exterior regions," SIAM J. Appl. Mat., vol. 42, no. 2, pp. 430-451, 1982.
6. A. F. Peterson, "Absorbing boundary conditions for the vector wave equation," Microw. Opt. Technol. Lett., vol. 1, pp. 62-64, 1988.
7. J. P. Webb and V. N. Kanellopoulos, "Absorbing boundary conditions for the finite element solution of the vector wave equation," Microw. Opt. Technol. Lett., vol. 2, pp. 370-372, 1988.
8. B. Stupfel, "Absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations," IEEE Trans. Antennas Propag., vol. 42, no. 6, pp. 773-780, Jun. 1994.
9. A. Chatterjee, J. M. Jin, and J. L. Volakis, "Edge-based finite elements and vector ABCs applied to 3-D scattering," IEEE Trans. Antennas Propag., vol. 41, no. 2, pp. 221-226, Feb. 1993.
10. V. N. Kanellopoulos and J. P. Webb, "Modeling the electromagnetic field in lossy dielectrics using finite elements and vector absorbing boundary conditions," IEEE Trans. Microw. Theory Tech., vol. 43, no. 4, pp. 823-827, Apr. 1995.
11. J.-M. Jin and W. C. Chew, "Combining PML and ABC for the finite-element analysis of scattering problems," Microw. Opt. Technol. Lett., vol. 12, no. 4, pp. 192-197, Jul. 1996.
12. S. Caorsi and G. Cevini, "Assessment of the performances of first- and second-order time-domain ABCs for the truncation of finite element grids," Microw. Opt. Technol. Lett., vol. 38, no. 1, pp. 11-16, July 2003.
13. V. N. Kanellopoulos and J. P. Webb, "The importance of the surface divergence term in the finite element-vector absorbing boundary condition method," IEEE Trans. Microw. Theory Tech., vol. 43, no. 9, pp. 2168-2170, Sep. 1995.
14. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics. Oxford, U.K./New York: Oxford Univ. Press and IEEE Press, 1998.
15. V. J. Van Joolen, B. Neta, and D. Givoli, "High-order Higdon-like boundary conditions for exterior transient wave problems," Int. J. Num. Meth. Engng., vol. 63, pp. 1041-1068, 2005.
16. J. P. Webb, "Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements," IEEE Trans. Antennas Propag., vol. 47, no. 8, pp. 1244-1253, Aug. 1999.
17. J. G. Simmonds, A Brief on Tensor Analysis, ser. Undergraduate Texts in Mathematics, 2nd ed. New York: Springer-Verlag, 1994.
18. A. K. Belhora and L. Pichon, "Efficient absorbing boundary conditions for the finite element solution of 3-D scattering problems," IEEE Trans. Mag., vol. 31, no. 3, pp. 1534-1537, May 1995.