Error study of boundary element calculations involving close meshes

In the numerical literature certain body shapes have been known to give rise to erroneous solutions when the standard boundary element formulation is used. A prominent example is the thin disc, for which the erroneous behaviour is termed the 'thin shape breakdown' of the boundary element method. The problem appears to be due to the two close meshes on either side of the disc.
In relation to a numerical study of sound intensity probes the need to model two closely spaced bodies has arisen. In this study it was found that the close meshes forming the gap between the spacer and the microphones in an intensity probe give rise to a breakdown similar to that of the thin disc. However, the methods used to overcome the problem for the disc case cannot be used for the gap case, and hence a study of the error for the two cases was carried out.
Two features of the behaviour of the error were found. For rough meshes, ie meshes where the element length was larger than five times the gap width or disc thickness, the solution was largely in error and showed no convergence. For finer meshes the error is dramatically reduced and normal convergence behaviour is found. The work was financially supported by the Spanish Ministry of Education and Culture and by the Danish Technical Research Council.