Iteratively-improved Robin boundary conditions for the finite element solution of scattering problems in unbounded domains

An iterative procedure is described for the Þnite-element solution of scalar scattering problems in unbounded domains. The scattering objects may have multiple connectivity, may be of di¤erent materials or with di¤erent boundary conditions. A Þctitious boundary enclosing all the objects involved is introduced. An appropriate Robin (mixed) condition is initially guessed on this boundary and is iteratively improved making use of GreenÕs formula. It will be seen that the best choice for the Robin boundary condition is an absorbing-like one. A theorem about the theoretical convergence of the procedure is demonstrated. An analytical study of the special case of a circular cylindrical scatterer is made. Comparisons are made with other methods. Some numerical examples are provided in order to illustrate and validate the procedure and to show its applicability whatever the frequency of the incident wave. Although particular emphasis is laid in the paper on electromagnetic problems, the procedure is fully applicable to other kinds of physical phenomena such as acoustic ones