Closed-Form Evaluation of Potential Integrals in the Boundary Element Method

A method is presented for the closed-form evaluation of the singular and near-singular integrals
arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is
presented for the numerical evaluation of such integrals on a plane element, and used to develop
a criterion for the selection of quadrature rules. The analytical approach is based on an optimized
expansion of the Green's function for the problem, selected to limit the error to some required
tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.