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Base functions and discrete constitutive relations for staggered polyhedral grids. (English) Zbl 1229.78025

Summary: An electromagnetic problem can be discretized on a pair of interlocked primal – dual grids according to discrete geometric approaches like the Finite Integration Technique (FIT) or the Cell Method (CM). The critical aspect is however the construction of the discrete counterparts of the constitutive relations assuring stability and consistency of the overall discrete system of algebraic equations. Initially only orthogonal Cartesian grids where considered; more recently primal grids of tetrahedra and oblique prisms with triangular base can be handled. With this paper a novel set of edge and face vector functions for general polyhedral primal grids is presented, complying with precise specifications which allow to construct stable and consistent discrete constitutive equations in the framework of an energetic approach.

MSC:

78M12 Finite volume methods, finite integration techniques applied to problems in optics and electromagnetic theory
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