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A stable interpolation technique for FDTD on non-orthogonal grids. (English) Zbl 0926.65092

The authors consider a finite difference method for approximating the Maxwell equations and in particular Faraday’s law. For this, a non-orthogonal mesh is used, based upon two different local coordinate systems. By this, one deals with co- and contravariant components of the physical quantities. The main difference between orthogonal and non-orthogonal finite difference time domain (FDTD) approximations is that, in the latter one, covariant components of field quantities are transformed in contravariant components of flux quantities.
The long-term stability of the non-orthogonal FDTD method is studied by analyzing the spatial discretization which seems to be responsible for instability. A new interpolation scheme, which ensures long-term stability if the symmetry requirements for the material relations are fulfilled, is proposed. Finally, two examples illustrate the method and demonstrate their accuracy and convergence behaviour.
(Unfortunately, for the reader not involved in this area, no explanation of the abbreviation FDTD is given).
Reviewer: E.Emmrich (Berlin)

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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