Some realizations of a discrete Hodge operator: A reinterpretation of finite element techniques

IEEE Transactions on Magnetics

Volumn 35, Issue 3 PART 1, 1999, Pages 1494-1497

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

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

^b EDF R AND D   (France)

Author keywords

Differential forms; Finite element methods; Hodge operator

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; ELECTRIC IMPEDANCE; FINITE ELEMENT METHOD; GALERKIN METHODS; MAGNETOSTATICS; MATHEMATICAL OPERATORS; NUMERICAL METHODS;

DISCRETE HODGE OPERATOR; ELECTROMAGNETICS; WHITNEY COMPLEX;

ELECTROMAGNETIC FIELD THEORY;

EID: 0033121757     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/20.767250     Document Type: Article

References (11)

1. H. Flanders, Differential Forms with Applications to the Physical Sciences. Dover Publications, 1989.
2. T. Weiland, "Time domain electromagnetic field computation with finite difference methods," Int. J. Num. Modell., Vol. 9, pp. 295-319, 1996.
3. E. Tonti, "Algebraic topology and computational electromagnetism," in Proc. of 4th Int. Workshop on Elec. and Magn. Fields, (Marseille, France), pp. 285-294, 1998.
4. C. Mattiussi, "An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology," J. of Comp. Physics, Vol. 133, pp. 289-309, 1997.
5. J. Stillwell, Classical Topology and Combinatorial Group Theory. New York: Springer-Verlag, 1980.
6. A. Bossavit, "Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism," IEE Proc., Vol. 135, Pt. A, no. 8, pp. 493-500, 1988.
7. A. Bossavit, Computational Electromagnetism, Variational Formulations, Edge Elements, Complementarity. Boston: Academic Press, 1998.
8. R. Albanese and G. Rubinacci, "Integral formulation for 3D eddy-current computation using edge elements," IEE Proc., Vol. 135, Pt. A, no. 7, pp. 457-462, 1988.
9. A. M. Winslow, "Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh," J. Comp. Phys., Vol. 1, no. 2, pp. 149-172, 1967.
10. A. Bossavit, "How weak is the weak solution in finite element methods?," IEEE Trans. Magn., Vol. 34, no. 5, pp. 2429-2432, 1998.
11. A. Bossavit and L. Kettunen, "Yee-like schemes on a tetrahedral mesh with diagonal lumping," Int. J. Numer. Modelling, 1999. In press.