Yee-like schemes on staggered cellular grids: A synthesis between FIT and FEM approaches

IEEE Transactions on Magnetics

Volumn 36, Issue 4 PART 1, 2000, Pages 861-867

  Bossavit, Alain ^a,b   Kettunen, Lauri ^a  

^a EDF R AND D   (France)

^b TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

Differential forms; Discrete hodge operator; Dual grids; FDTD; FIT

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; INTEGRATION; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS; TIME DOMAIN ANALYSIS;

HODGE OPERATOR; YEE-LIKE METHODS;

ELECTROMAGNETIC FIELDS;

EID: 0034217635     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/20.877580     Document Type: Article

References (16)

1. T. Weiland, "Time domain electromagnetic field computation with finite difference methods," to. J. Num. Modell., vol. 9, pp. 295-319, 1996.
2. A. Bossavit and I. Mayergoyz, "Edge-elements for scattering problems," IEEE Trans. Magn., vol. 25, no. 4, pp. 2816-2821, 1989.
3. M. F. Wong, O. Picon, and V. Fouad Hanna, "A finite element method based on Whitney forms to solve Maxwel 1 equations in the time domain," IEEE Trans. Magn., vol. 31, no. 5, pp. 1622-1625, 1995.
4. J.-F. Lee and Z. Sacks, "Whitney elements time domain (WETD) methods," IEEE Trans. Magn., vol. 31, no. 3, pp. 1325-1329, 1995.
5. A. Bossavit and L. Kettunen, "Yee-like schemes on a tetrahedral mesh, with diagonal lumping," Int. J. Numer. Modell., vol. 12, pp. 129-142, 1999.
6. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell' s equations in Isotropie media," IEEE Trans. Antennas Propagat., vol. 14, pp. 302-307, May 1966.
7. A. Bossavit, "Computational electromagnetism and geometry. (2): Network constitutive laws," J. Japan Soc. Appl. Electromagn. & Mech., vol. 7, no. 3, pp. 294-301, 1999.
8. "How weak is the weak solution in finite element methods?," IEEE Trans. Magn., vol. 34, no. 5, pp. 2429-2432, 1998.
9. T. Tarhasaari, L. Kettunen, and A. Bossavit, "Some realizations of a discrete Hodge operator: A reinterpretation of finite element techniques," IEEE Trans. Magn., vol. 35, no. 3, 1998.
10. E. Tonti, "Algebraic topology and computational electromagnetism," in P roc. of 4th Int. Workshop on Elec. and Magn. Fields, Marseilles, France, 1998, pp. 285-294.
11. J. C. Maxwell, "On reciprocal figures and diagrams of forces," Phil. Mag. Series 4, vol. 27, pp. 250-261, 1864.
12. A. Bossavit, Computational Electromagnetism. Boston: Academic Press, 1998.
13. J. Bey, "Tetrahedral grid refinement," Computing, vol. 55, no. 4, pp. 355-378, 1995.
14. J. Dodziuk, "Finite-difference approach to the Hodge theory of harmonic forms," Amer. J. Math., vol. 98, no. 1, pp. 79-144, 1976.
15. W. Müller, "Analytic torsion and R-torsion of Riemannian manifolds," Advances in Mathematics, vol. 28, pp. 233-305, 1978.
16. I. Tsukerman, "A general accuracy criterion for finite element approximation," IEEE Trans. Magn., vol. 34, no. 5, pp. 2425-2428, 1993.