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A stable interpolation technique for FDTD on non‐orthogonal grids
Author(s) -
Schuhmann R.,
Weiland T.
Publication year - 1998
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/(sici)1099-1204(199811/12)11:6<299::aid-jnm314>3.0.co;2-a
Subject(s) - interpolation (computer graphics) , finite difference time domain method , mathematics , grid , multivariate interpolation , computer science , mathematical analysis , algorithm , bilinear interpolation , geometry , computer graphics (images) , physics , statistics , optics , animation
The application of the FDTD algorithm on generalized non‐orthogonal meshes, following the basic ideas of Holland (1983), has been investigated by many authors for several years now, and detailed dispersion analysis as well as convergence studies have been published. Already in 1992 also a general stability criterion was given for the time integration using the standard leap‐frog scheme (Lee et al .). Many authors, however, still propose some damped time stepping algorithms to work around unexpected instabilities in the discretization method. In this paper the origin of this type of instability is revealed, and a technique to obtain a stable discretization of Maxwell's equations on non‐orthogonal grids is proposed. To obtain more insight into the stability properties of the method, it is reformulated according to the matrix–vector notation of the Finite Integration Technique. © 1998 John Wiley & Sons, Ltd.