Methods for limiting the calculation area during problem solving by the finite difference method

Authors: S. A. Marković, J. M. Cvetić, T. D. Koledin

Keywords: boundary conditions; finite difference method; open space; numerically exact

Abstract:

By using the integro-differential approach and classical boundary conditions (such as Dirichlet’s, Neumann’s or the very rarely used Cauchy boundary condition) for solving the two-dimensional problems in open space by the finite difference method, it is possible to – in the numerically exact way – close the calculation area to finite distance. Thus, one of great limitations of the finite difference method is overcome.

References:

[1] S. J. Farlow, Partial differential equations for scientists and engineers, New York, J.Wiley and Sons, 1982. [2] R. H. Gordon, S. H. Fook, A finite difference approach that employs an asymptotics boundary condition on a rectangular outer boundary for modeling two-dimensional transmissonal line structures, IEEE Trans Microwave Theory Tech., Vol.41, No 8, Aug 1993. pp.1280–1286. [3] Z. Haznadar, M. Lovrenjak, The field calculation by using the finite difference method (in croatian), Zagreb, Elektrotehnika, No 5, 1971. pp. 33–47. [4] J. Jin, The finite element method in electromagnetics, New York, J.Wiley and Sons, 1993. [5] H. Okubo, M. Ikeda, M. Honda, T. Yanari, Electric field analysis by combination method, IEEE trans., Vol. PAS-101, No 10, Oct.1982. pp.4039–4048. [6] H. Okubo, M. Ikeda, M. Honda, S. Menju, Combination method for electric field calculation, Third Inter. Symp. on High Voltage Engineering, Milan, 28-31. Aug. 1979. paper 23.14. [7] B. D. Popović, Electromagnetics (in serbian), Beograd, Grad-evinska knjiga, 1980. [8] H. Singer, H. Steinbigler, P. Weiss, A charge simulation method for the calculation of high voltage fields, IEEE Trans. Pow. App, Sys, PAS -95. pp. 1660–1668. 1974. [9] H. Steinbigler, Combined application of finite element method and charge simulation method for the computation of electric fields, Third Int. Symp. On High voltage Engineering. Milan. 28-31. Aug. 1979. paper 11.11. [10] C. G. Williams, G. K. Cambrell, Efficient numerical solution of unbounded fields problems, Electronics letters, Vol.8. No 7, 4th May 1972. pp. 247–248. [11] O.C. Zienkiewicz, K. Morgan, Finite elements and approximation, New York, J. Wiley and Sons, 1983.