subject to the boundary condition

regularity condition

and the radiation condition (Sommerfeld [75]) for , where ,

The solution
to this problem has an integral representation
given by

where is the fundamental solution of Helmholtz's equation given by

Using (3.114) and (3.116), one obtains the
hypersingular integral equation:

where stands for the finite part of a divergent integral. The hypersingular integral equation (3.118) can be regularised as (See Appendix L.4)

where stands for the Cauchy principal value of a singular integral. This regularised integral equation (3.119) is utilised for the direct computation in FM-BIEM.