An iterative finite element-boundary element algorithm

A domain decomposition algorithm coupling the finite element and boundary element methods is presented in this paper. This algorithm is iterative in nature. It essentially involves subdivision of the problem domain into subregions being respectively modeled by the two methods, as well as restoration of the original problem with continuity and equilibrium being satisfied along the interface. An arbitrary displacement vector is first assigned to the interface of the boundary element subdomain. Then, the energy equivalent nodal forces of the solved interface tractions are treated as the boundary conditions for the finite element subdomain to solve for the interface displacements. The solution is achieved when these two sets of displacements converge. To speed up the rate at which the algorithm converges, a relaxation of the displacement data at the interface is employed for the next iteration. Strategies for static and dynamic choices of relaxed displacements are addressed, and the validity of the algorithm is verified by solving an example problem. Numerical solutions of the test problem obtained using the proposed algorithm are compared with solutions from the finite and boundary element methods.