On the existence of Kassab and Divo's generalized boundary integral equation formulation for isotropic heterogeneous steady state heat conduction problems

Abstract In this note, we prove that the boundary integral equation formulation for isotropic heterogeneous steady state conduction problems recently suggested Kassab and Divo is not general. We also obtain the complete integral representation for the new formulation which is of the boundary domain type instead of the boundary only type, as originally proposed by the above authors. The resulting integral equation representation possesess the same difficulty than previous BEM formulations of the problem, however the evaluation of the domain integral in the new formulations is simpler than those of previous formulations.