Additive schwarz methods for the H-version boundary element method

Abstract

We study additive Schwarz methods (two level and multilevel) for the h-version boundary element method. Both weakly singular and hypersingular integral equations of the first kind are considered. We prove that the condition numbers of the additive Schwarz operators are bounded independently of the number of levels and number of mesh points. Thus we show that the additive Schwarz method as a parallel preconditioner, which was originally designed for finite element discretisation of differential equations, is also an efficient solver for boundary integral operators, which are non-local operators.

Keywords:

• h-version boundary integral equation method
• additive Schwarz operator
• operator, preconditioned conjugategradient algorithm

AMS:

• 65N55
• 65N38

^*School of Mathematics, Univew South Wales, Australia

^†Institut fiir Angewandte Mathematik, University of Hannover, Germany

^*School of Mathematics, Univew South Wales, Australia

^†Institut fiir Angewandte Mathematik, University of Hannover, Germany

Notes

^*School of Mathematics, Univew South Wales, Australia

^†Institut fiir Angewandte Mathematik, University of Hannover, Germany