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

• Published in: IEEE transactions on magnetics Vol. 36; no. 4; pp. 861 - 867
• Main Authors: Bossavit, A., Kettunen, L.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.07.2000; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied classical electromagnetism; Convergence; Convergence of numerical methods; Differential equations; Discretization; Electromagnetism; electron and ion optics; Equivalence; Exact sciences and technology; Finite difference methods; Finite element method; Finite element methods; Force measurement; Fundamental areas of phenomenology (including applications); Law; Magnetism; Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems; Mathematical analysis; Mathematical model; Mathematical models; Maxwell equations; Moment methods; Networks; Physics; Shape; Time domain analysis; Faraday laws; Magnetostatics; Grid pattern; Time domain method; Digital simulation; Theoretical study; Maxwell equations; Numerical convergence; Finite difference method
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/20.877580

We propose an analysis (discretization techniques, convergence) of numerical schemes for Maxwell equations which use two meshes (not necessarily tetrahedral), dual to each other. Schemes of this class generalize Yee's "finite difference in time domain" method (FDTD). We distinguish network equations (the discrete equivalents of Faraday's law and Ampere's relation) which can be set up without any recourse to finite elements, and network constitutive laws, whose validity cannot be assessed without them. This establishes a complementarity between "finite integration techniques" (FIT) and the finite element method (FEM). As an example, a Yee-like method on a simplicial mesh and its so-called "orthogonal" dual, is described, and its convergence is proved.