MULTILEVEL ADDITIVE SCHWARZ METHOD FOR THE H-P VERSION OF THE GALERKIN BOUNDARY-ELEMENT METHOD

We study a multilevel additive Schwarz method for the h-p version of t he Galerkin boundary element method with geometrically graded meshes. Both hypersingular and weakly singular integral equations of the first kind are considered. As it is well known the h-p version with geometr ic meshes converges exponentially fast in the energy-norm. However, th e condition number of the Galerkin matrix in this case blows up expone ntially in the number of unknowns M. We prove that the condition numbe r kappa(P) of the multilevel additive Schwarz operator behaves like O( root Mlog(2) M). Asa direct consequence of this we also give the resul ts for the 2-level preconditioner and also for the h-p version with qu asi-uniform meshes. Numerical results supporting our theory are presen ted.