A Comparison Between Cell-less Formulations for Domain Integrals Treat- ment in the Poisson type problem by the Boundary Element Method

Resumo

By applying the Boundary Element Method (BEM) to solve Poisson problems, besides boundary in-
tegrals, the final equation also contains a domain integral involving the inhomogeneous term. This integral can

be evaluated by discretizing the domain into cells. However, one of the main advantages of the BEM, which is
the reduction of the problem’s dimension by one order, is lost and several methods have been developed aiming
to treat these integrals without the need to do this discretization. This paper makes a comparison among three
formulations to do this: the Dual Reciprocity Method (DRM), the Multiple Reciprocity Method (MRM) and the
Radial Integration Method (RIM). The formulations and features of each method are presented as well as numeric
results obtained by their applications to some examples with known analytical solutions. The aim of this paper is
to make a critical analysis in terms of the numeric efficiency and accuracy of each technique, primarily about the
number of elements and internal points required for obtaining results inside an acceptable margin of error.