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Yee-like schemes on a tetrahedral mesh, with diagonal lumping. (English) Zbl 0936.78011

Summary: A Galerkin edge-element solution technique for Maxwell’s equations in time domain is discussed. With proper diagonal lumping of one of the mass matrices, it can be seen as a generalization to a tetrahedral mesh and its barycentric dual of the staggered-grid finite difference scheme known nowadays as FDTD, or Yee’s scheme. A new approach to the lumping, backed by a specific convergence-proof technique, is proposed.

MSC:

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
78A25 Electromagnetic theory (general)
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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