A new approach for the Modified Local Green’s Function Method applied to Poisson equation

Resumo

Originally proposed at the end of the 80 ’s, the Modified Local Green’s Function Method (MLGFM) is
an integral method that was described as a hybrid of the Finite Element Method (FEM) and the Boundary Element
Method (BEM). The method was proposed to apply the BEM methodology to problems with no knowledge of
the fundamental solution. Essentially, the MLGFM creates discrete projections of the Green’s function solving
an auxiliary domain problem, and this problem can be solved, for example, by the FEM formulation. Despite the
good convergence of the secondary variable in the boundary, the method has a major disadvantage over FEM, the
obtainment of the Green’s function projections implies in to solve the system of equations in the domain, resulting
in a great computational effort. However, this paper aims to show a new approach to the MLGFM where it is
not necessary to obtain the Green’s projections and the final equations system has the same number of degrees
of freedom as FEM and still presents high convergence for the secondary variable in the boundary. The new
formulation can be obtained directly by the weighted residual sentence and variables using the same approximation
of the original MLGFM. The processing time of the two approaches are compared and the method is applied to
Poisson Equation.