SCHWARZ ITERATIONS FOR THE EFFICIENT SOLUTION OF SCREEN PROBLEMS WITHBOUNDARY ELEMENTS

This paper investigates two domain decomposition algorithms for the nu merical solution of boundary integral equations of the first kind. The schemes are based on the h-type boundary element Galerkin method to w hich the multiplicative and the additive Schwarz methods are applied. As for two-dimensional problems, the rates of convergence of both meth ods are shown to be independent of the number of unknowns. Numerical r esults for standard model problems arising from Laplaces' equation wit h Dirichlet or Neumann boundary conditions in both two and three dimen sions are discussed. A multidomain decomposition strategy is indicated by means of a screen problem in three dimensions, so as to obtain sat isfactory experimental convergence rates.