A Natural BEM with non-uniform grids on the elliptic boundary and its coupling method

In this paper, for solving Poisson equation in 2-D unbounded domains, a natural BEM with non-uniform grids on the elliptic boundary is investigated, the coupling of NBEM–FEM with non-uniform grids on the elliptic artificial boundary is discussed, and the corresponding convergence theorems of the NBEM and the coupling method are proved. The moving mesh method based on the arc-length equidistribution principle is introduced into the NBEM and the coupling method respectively to solve exterior problems. Numerical examples confirm the convergence and demonstrate the advantage in accuracy and efficiency for the proposed methods.