FOURIER-SPLINE APPROXIMATIONS OF QUASI-STATIC ELECTROMAGNETIC FIELD WITH LOCALLY NON-UNIFORM DISTRIBUTION OF SOURCES

A.M. Afonin, A.Yu. Pautkin, A.S. Roshal
VANT. Ser.: Mat. Mod. Fiz. Rroc 1990. Вып.3. С. 40-43.

      A new efficient method for calculations on quasi-stationary electromagnetic field created by a bunch of charged particles that occupies a relatively small part of the area under investigation is proposed. To do the computations of the potentials and the fields, we used the method of partition followed by Fourier series expansion by two coordinates and implementation of spline-approximation by the third one. An analytical solution of auxiliary tasks followed by joining numerical and analytical solutions at the boundary of the bunch is used in the areas not occupied by the bunch. The method has high accuracy and is cost-effective as it does not use finite-difference approximation of derivatives and the computational grid is introduced only in the area of the bunch. The results of comparison between the analytical and numerical solutions for several benchmark problems are provided.