A boundary element method recursive procedure applied to Poisson's problems

摘要

This paper describes a simple procedure to increase the accuracy of the boundary element method (BEM) results in Poisson's problems using coarse meshes. Usually, BEM values at internal points are obtained by reusing the boundary integral equation, after having calculated all variables at the nodal points on the boundary. Accuracy in results of these internal points is superior to that obtained at boundary nodes and the reason for that can be assigned to a new minimization of residuals performed. Therefore, this idea can be used to improve BEM results by means of choosing new source points on the boundary at positions different from those of the original nodes. Tests carried out with problems governed by Laplace's equation and Navier's equation were successful; thus, this procedure is now applied to Poisson's problems that allow a more comprehensive evaluation of the performance of proposed technique.