Uma nova técnica para solução de problemas setorialmente homogêneos por meio do método dos elementos de contorno aplicada a problemas de Laplace

Abstract

The Boundary Element Method (BEM) has excellent performance in applications where the variable field is scalar and stationary. However, there is a wide range of issues in science and engineering that are difficult to solve by the BEM. Among these issues, there are the nonhomogeneous media problems, where the physical properties vary locally. In these kind of problems, the domain techniques, such as Finite Element Method (FEM), Finite Volume Method (FVM) or Finite Difference Method (FDM), present considerable advantages. However, even for these cases, it is possible to obtain consistent formulations for BEM, as the technique of sub-regions. This work presents an alternative technique within the BEM scope, for the resolution of non-homogeneous media problems given by the Laplace Equation. This new formulation is tested by simulations and compared with the sub-region technique, analytical results and other domain methods (FEM and FVM). The presented technique shows good results, indicating that the new formulation technique can be easily used and replicated in problems where the media presents non-homogeneous physical properties.