Schwarz iterations for the efficient solution of screen problems with boundary elements

This paper investigates two domain decomposition algorithms for the numerical solution of boundary integral equations of the first kind. The schemes are based on theh-type boundary element Galerkin method to which the multiplicative and the additive Schwarz methods are applied. As for twodimensional problems, the rates of convergence of both methods are shown to be independent of the number of unknowns. Numerical results for standard model problems arising from Laplaces' equation with Dirichlet or Neumann boundary conditions in both two and three dimensions are discussed. A multidomain decomposition strategy is indicated by means of a screen problem in three dimensions, so as to obtain satisfactory experimental convergence rates.