The hypersingular single integral equation and the dielectric wedge

Abstract

The fields scattered by a finite dielectric wedge are computed, and the results obtained by using two different integral equations are compared. The unknown boundary function is either the jump eta in the normal derivative of the auxiliary field across the boundary or the jump phi in the field itself. In the latter case, one of the integrals is hypersingular. The results obtained using the two different methods are compared for a 90 degrees dielectric wedge terminated by a matching cylindrical surface. The numerical experiments indicate that the results obtained by the two quite different integral equations agree reasonably well, and it is concluded that disagreements with the static limit probably are real, that is, not due to errors in the calculations. The hypersingular integral equation may provide more accurate results because the unknown boundary function does not diverge at the edge of the wedge, although the integrals are more singular. >