Generalized finite element method for vector electromagnetic problems

IEEE Transactions on Antennas and Propagation

Volumn 55, Issue 5, 2007, Pages 1369-1381

  Lu, Chuan ^a   Shanker, Balasubramaniam ^a  

^a Michigan State University   (United States)

Author keywords

Finite element methods (FEM); Meshless; Partial differential equations; Vector basis function

Indexed keywords

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ELECTROMAGNETIC FIELDS; FINITE ELEMENT METHOD; GALERKIN METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

VECTOR BASIS FUNCTION; VECTOR ELECTROMAGNETIC PROBLEM;

ELECTROMAGNETIC WAVES;

EID: 34249325883     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2007.895572     Document Type: Article

References (26)

1. J. M. Jin, The Finite Element Method in Electromagnetics. New York: Wiley, 2002.
2. P. Monk, Finite Element Methods for Maxwell's Equations, ser. Numerical Analysis and Scientific Computation Series. Oxford, U.K.: Oxford Univ. Press, 2003.
3. R. D. Graglia, D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propag., vol. 45, pp. 329-342, 1997.
4. W. Rachowicz and L. Demkowicz, "A Three-Dimensional HP-Adaptive Finite Element Package for Electromagnetics" TICAM Rep. 00-04, 2000.
5. M. Costabel, M. Dague, and C. Schwab, "Exponential convergence of HP-FEM for Maxwell's equations with weighted regularization in polygonal domains," Math. Models Methods in Appl. Sci. vol. 15, 2005 [Online]. Available: http://www.perso.univ-rennes1.fr/monique.dauge/core/ index.html, To Appear
6. D. Boffi, M. Costabel, M. Dague, and L. Demkowicz, Discrete Compactness for the hp Version of Rectangular Edge Finite Elements ICES Tech. Rep. 04-29, 2004.
7. I. Babuska, U. Banerjee, and U. Osborn, "Meshless and generalized FEM: A survey of some major results," in Meshfree Methods for Partial Differential Equations, M. Griebel and M. A. Sciweitzer, Eds. New York: Springer Verlag, 2002.
8. C. A. Duarte, "The HP Cloud Method," Ph.D. dissertation, Univ. Texas at Austin, Austin, 1996.
9. J. M. Melenek and I. Babuska, "The partition of unity finite element method: Basic theory and applications," Comput. Methods Appl. Mech. Eng., vol. 139, pp. 289-314, 1996.
10. I. Babuska and J. M. Melenek, "The partition of unity method," Int. J. Numer. Methods Eng., vol. 40, pp. 727-858, 1997.
11. S. N. Atluri and S. Shen, The Meshless Local Petrov Galerkin Method Forsyth, GA: Technical Science Press, 2002.
12. T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free galerkin methods," Int. J. Numer. Meth. Engng., vol. 37, pp. 229-254, 1994.
13. I. Tsukerman, "General tangentially continuous vector elements," IEEE Trans. Magn., vol. 39, pp. 1215-1218, 2003.
14. L. Proekt S. Yuferev, and I. T. N. Ida, "Method of overlapping patches for electromagnetic computation near imperfectly conducting cusps and edges," IEEE Trans. Magn.., vol. 38, pp. 649-652, 2002.
15. L. Proekt and I. Tsukerman, "Method of overlapping patches for electromagnetic computation," IEEE Trans. Magn., vol. 38, pp. 741-744, 2002.
16. J. A. Stratton, Electromagnetic Theory. New York: McGraw-Hill, 1941.
17. W. C. Chew, Waves and Fields in Inhomogeneous Media. New York: IEEE Press, 1995.
18. J. Pitkäranta, "Boundary subspaces for the finite element method with Lagrange multipliers," Numer. Math., vol. 33, pp. 273-289, 1979.
19. J. Pitkäranta, "Local stability conditions for the Babuska method of Lagrange multipliers," Math. Comput., vol. 35, pp. 1113-1129, 1980.
20. J. Pitkäranta, "The finite element method with Lagrange multipliers for domain with corners," Math. Comput., vol. 37, pp. 13-30, 1981.
21. C. Lu and B. Shanker, Development of hybrid boundary integral-generalized (partition of unity) finite element solvers for the scalar Helmholtz equation Michigan State Univ., 2005, Tech. Rep..
22. R. Stenberg, "On some techniques for approximating boundary conditions in the finite element method," J. Comput. Appl. Math., vol. 63, pp. 139-148, 1995.
23. M. Griebel and M. A. Schweitzer, Meshless Methods for Partial Differential Equations. New York: Springer Verlag, 2002.
24. J. A. Chatterjee and J. L. Volakis, "Computation of cavity resonances using edge-based finite elements," IEEE Trans. Microw. Theory Tech. vol. 40, pp. 2106-2108, 1992.
25. R. F. Harrington, Time Harmonic Fields in Electromagnetics, ser. IEEE Press Series on Electromagnetic Wave Theory. Piscataway, NJ: Wiley-IEEE Press, 2001.
26. R. D. Graglia and G. Lombardi, "Singular higher order complete vector bases for finite methods," IEEE Trans. Antennas Propag., vol. 52, pp. 1672-1685, 2004.