Tuning the alternating Schwarz method to theexterior problems is the subject of this paper.We present the original algorithmand we propose a modification of it, so that the solution of the subproblem involving the condition at infinityhas an explicit integral representation formulas while the solutionof the other subproblem, set in a bounded domain,is approximated by classical variational methods. We investigate many of the advantages of the newSchwarz approach: a geometrical convergence rate,an easy implementation, a substantial economyin computational costs anda satisfactory accuracy in the numerical resultsas well as their agreement with the theoretical statements.
