Solving singularity problems in unbounded domains by coupling of natural BEM and composite grid FEM (Q5932820)

The authors discuss the fast adaptive composite grid (FAC) method combined with a coupled finite element-boundary element procedure for approximating the solution of the Laplace equation (with a Dirichlet boundary condition) in an exterior domain. The coupling uses a circular auxiliary boundary to derive a variational problem in a bounded subdomain of the exterior domain. A composite grid is then used to discretize the finite element space and the discrete problem is solved by a FAC-steepest descent algorithm.NEWLINENEWLINENEWLINEThe method handles effectively the singularities caused by the boundary of the exterior domain and has the advantage that no boundary integral equation associated with the unbounded subdomain is solved, but instead only certain singular integrals are computed. Error estimates and convergence for the method are proved. Some numerical results are presented.