New aspects of Huygens principle

Abstract

In the case of two-dimensional problems the vector field determined by Huygens' integral and its derivatives of the first and second order are continuous in the space including the surface of integration except edges and corners. In many applications, however, the determined potential, its normal derivative and those presumed by Helmholtz's formulation differ essentially. A procedure partially analytical and partially numerical is described yielding a field more exactly satisfying the presumptions.