Multiplicative Schwarz Algorithms for the Galerkin Boundary Element Method

We study the multiplicative Schwarz method for the p-version Galerkin boundary element method for a hypersingular and a weakly singular integral equation of the rst kind and for the h-version for a hypersingular integral equation of the rst kind. We prove that the rate of convergence of the multiplicative Schwarz operator is strictly less than 1 for the h-version for both two level and multilevel methods, whereas for the p-version we show that the convergence rate grows only logarithmically in p for the 2-level method. Computational results are presented for both the h-version and the p-version which support our theory.