Coupling of a non-overlapping domain decomposition method for a nodal finite element method with a boundary element method

Non-overlapping domain decomposition techniques are used to solve the finite element equations and to couple them with a boundary element method. A suitable approach dealing with finite element nodes common to more than two subdomains, the so-called cross-points, endows the method with the following advantages. It yields a robust and efficient procedure to solve the equations resulting from the discretization process. Only small size finite element linear systems and a dense linear system related to a simple boundary integral equation are solved at each iteration and each of them can be solved in a stable way. We also show how to choose the parameter defining the augmented local matrices in order to improve the convergence. Several numerical simulations in 2D and 3D validating the treatment of the cross-points and illustrating the strategy to accelerate the iterative procedure are presented.