Consistent material operators for tetrahedral grids based on geometrical principles

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Abstract
This paper is focused on analysis of the properties of material operators for geometrical methods on tetrahedral grids. The stiffness matrix in electrodynamics, as well as the one in electrostatics, are mathematically proven to be the same for every material operator satisfying a condition which is sufficient for the consistency of the numerical scheme. This gives a new and better insight into the strong similarities existing between the finite element method (FEM) and the finite integration technique (FIT).A symmetrization of the microcell method, which also ensures the positive definiteness of the material operators, based on geometrical properties of tetrahedra, is proposed. Numerical results in time and frequency domain for resonant cavities are presented and compared to the FEM. Copyright © 2004 John Wiley & Sons, Ltd.

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