CALCULATIONS IN MATHEMATICA ON LOW-FREQUENCY DIFFRACTION BY A CIRCULAR DISK

Abstract

This paper is devoted to the symbolic calculation of the scattering coefficient in diffraction by a circular disk, by the use of Mathematica. Three diffraction problems are considered: scalar diffraction by an acoustically soft disk, scalar diffraction by an acoustically hard disk, and electromagnetic diffraction by a perfectly conducting disk. In the low-frequency approximation, the solutions of these problems are in the form of expansions in powers of ka, where a is the radius of the disk and k is the wave number. The emphasis is on the low-frequency expansion for the scattering coefficient, of which several terms are determined exactly with the help of Mathematica. [Vol. 11, No. 1 (1996), pp 47-56, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]