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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 32 > pp. 45-64
## 'GENERALIZED FINITE DIFFERENCES' IN COMPUTATIONAL ELECTROMAGNETICSBy A. Bossavit
Abstract:
The geometrical approach to Maxwell's equations promotes a way to discretize them that can be dubbed "Generalized Finite Differences", which has been realized independently in several computing codes. The main features of this method are the use of two grids in duality, the "metric-free" formulation of the main equations (Amp`ere and Faraday), and the concentration of metric information in the discrete representation of the Hodge operator. The specific role that finite elements have to play in such an approach is emphasized, and a rationale for Whitney forms is proposed, showing why they are the finite elements of choice.
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9. Hyman, J. M. and M. Shashkov, "Natural discretizations for the divergence, gradient, and curl on logically rectangular grids," 10. Lee, J.-F. and Z. Sacks, "Whitney elements time domain (WETD) methods," 11. Maxwell, J. C., "On reciprocal figures and diagrams of forces," 12. Muller, W., "Analytic torsion and R-torsion of Riemannian manifolds," 13. Nicolaides, R. and D.-Q. Wang, "Convergence analysis of a covolume scheme for Maxwell’s equations in three dimensions," 14. Post, E. J., "The constitutive map and some of its ramifications," 15. Silvester, P. and M. V. K. Chari, "Finite element solution of saturable magnetic field problems," 16. Taflove, A., 17. Teixeira, F. L. and W. C. Chew, "Lattice electromagnetic theory from a topological viewpoint," 18. Tonti, E., "Algebraic topology and computational electromagnetism," 19. Weiland, T., "Time domain electromagnetic field computation with finite difference methods," 20. Weiland, T., "Maxwell’s grid equations," 21. Whitney, H., 22. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," |

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