Computation of the diagonal matrix elements of the discretized Helmholtz integral equation

Analytic formulas are given for the diagonal matrix elements (sometimes called the ''self-terms'') which arise in discretizing the Helmholtz integral equation for acoustic radiation and scattering off an arbitrary surface. In terms of the coefficients of the first and second fundamental forms of the surface, the formulas are valid to leading order in the smallness of the surface element with respect to the characteristic dimension of the surface and the acoustic wavelength. (C) 1996 Acoustical Society of America.