Boundary Element Methods–Numerical Implementation - The Boundary Element Method with Programming - page 137

points on or inside the envelope the accuracy of integration is assured. This has been
proposed by Eberwien et al 7 .
Figure 6.7 Contours showing the location of points P i where the integration with 4 Gauss points
gives an error of 10 -3 (second subscript of I indicates that this is for a 1/r singularity)
Table 6.1 Number of Gauss points (Eberwien et al 7 )
The result is summarised in Table 6.1 as limiting values of R/L for an integration
order of 4 and 5. Experience showed that the minimum number of integration points
should not be lower than 3 and that it is more efficient to keep the maximum integration
order low. This means that we have to subdivide the region of integration, so that the
minimum ratios of R/L according to Table 6.1, are obeyed.
Cases where the point is very close to the element occur when there is a drastic
change in element size, or the boundary surfaces are very close to each other, for
example, in the case of a thin beam. Care has to be taken not to go to extremes with the
value of R/L, because we must avoid cases where points P i are too unevenly distributed
since Betti's reciprocal theorem is only satisfied at these points.
We convert Table 6.1 into a FUNCTION Ngaus which returns the number of Gauss
points according to the value of R/L.