Performance of BEM superposition technique for solving sectorially heterogeneous Laplace's problems with non-regular geometry

The superposition technique is a new BEM alternative for solving sectorially heterogeneous problems in which the complete domain is divided in a surrounding homogeneous domain and other complementary sub-domains with different constitutive properties. It is an alternative to the classic BEM sub-regions technique. Results of preliminary simple problems governed by the Laplace's equation were successfully solved, using analytical solutions to performance evaluation. Thus, this paper examines the performance of the superposition technique to solve complex problems that present geometric irregularities on the boundary, such as grooves and notches, and internal inclusions. Considering the absence of analytical solutions, the Finite Element Method was used to generate the reference solutions for a suitable comparison.