  A boundary integral formulation for the solution of the Helmholtz equation is
developed in which all traditional singular behaviour in the boundary integrals
is removed analytically. The numerical precision of this approach is
illustrated with calculation of the pressure field due to radiating bodies in
acoustic wave problems. This method facilitates the use of higher order surface
elements to represent boundaries, resulting in a significant reduction in the
problem size with improved precision. Problems with extreme geometric aspect
ratios can also be handled without diminished precision. When combined with the
CHIEF method, uniqueness of the solution of the exterior acoustic problem is
assured without the need to solve hypersingular integrals.
