Modified Helmholtz integral equation for bodies sitting on an infinite plane

This article presents a modified version of the Helmholtz integral equation for bodies sitting on an infinite plane. By using dummy integration elements on the bottom surface, the coefficient C(P) of the Helmholtz integral equation can be evaluated by a closed contour. Two different integral forms for C(P) are derived for P off the infinite plane and on the infinite plane, respectively. Numerical results for radiation and scattering from bodies of several different shapes sitting on a rigid, infinite plane are given to verify this formulation.