The boundary S is approximated with N flat panels with piece-wise constant
strength distributions of 
or 
,
as shown in Figure 7.
The discretized version of the integral
equation (17) is applied at the mid-points
of each panel:
where 
and
, with 
being the ``area''
of panel j.
Equation (19) is usually written in the following matrix form:
where [H] and [G] are the constant strength influence coefficients; [u] and [p] are vectors with 2N components the values of the displacements and tractions at the mid-point of each panel. The matrix equation (20) can then be rearranged and solved with respect to the unknown displacements or tractions (2N in total).
The self-influence coefficients for a constant strength distribution are given in terms of analytic expressions [8]. They are also summarized in Appendix A.1. The other influence coefficients are evaluated by using Gauss quadratures. Eight point quadrature was found to be sufficiently accurate for ``thick'', as well as for ``thin'' beams [].
It is a well known fact that low-order structural BEM's are very inaccurate in predicting either deflections or stresses, especially in the case of flexural problems [8]. This is also apparent from Figures 13 and 14 where results from applying the low-order method are shown together with results from high-order methods. It is also shown in [] that these methods are inaccurate even for trivial problems such as that of a plate in simple tension or shear. The inaccuracy of the low-order BEM's becomes even worse with decreasing beam height to span ratio. Thus, these methods are very inappropriate for hydrofoil applications.
At this point of our research the most obvious choice would be to apply a higher-order BEM, like that described in [8]. However, we decided instead to apply the ``saw-tooth'' correction approach that we described in previous sections. We did this for two reasons: (a) to maintain the relative simplicity of the low-order BEM, and (b) to avoid the special treatment of the corner points (as commonly used high-order BEM's need to do), where the formulation of the integral equation becomes cumbersome.
