Acoustic boundary element method formulation with treatment of nearly singular integrands by element subdivision

It is well known that the Boundary Element Method (BEM) in its standard version cannot readily
handle situations where the calculation point is very close to a surface. These problems are
found: i) when two boundary surfaces are very close together, such as in narrow gaps and thin
bodies, and ii) when field points are calculated very close to the boundary. The difficulty is due
to the near-singularity of the integrand, which causes failure of the numerical integration over
the element. There are a number of techniques to overcome this problem, in many cases
involving a reformulation of the integrand or the whole method. On the other hand, it is also
possible to refine or improve the numerical integration, and maintain the standard BEM
formulation. In this paper a numerical technique based on element subdivision, previously
proposed by the authors, is made more general to cover most cases of interest. The subdivision
is adapted to the strength of the near-singularity and is only performed when needed, not
adding excessive calculation time and storage. The implementation is examined and verified
with test cases.