Une nouvelle équation intégrale pour l'étude de la radiation scalaire dans une cavité

Abstract

We derive an integral equation of the first kind connecting the surface values and the normal derivative for a regular solution inside a closed cavity of the Helmholtz equation. This integral equation has two advantages over the usual limit form of integral equations where the field point must lie on the boundary and the kernel is singular, namely, the field point may be anywhere inside or outside the cavity, and the kernel is regular. Analytic solution of our integral equation is obtained for the special cases of monopole and of dipole sources at the center of a sphere (Dirichlet's condition). The next paper will apply this integral equation to prolate spheroidal cavities.