Additive schwarz methods for indefinite hypersingular integral equations in R³ - the p-version

Abstract

We propose and analyze preconditioners for the p-version of the boundary element method in three dimensions. We consider indefinite hypersingular integral equations on surfaces and use quadrilateral elements for the boundary discretization. We use the GMRES method as iterative solver for the linear systems and prove for an overlapping additive Schwarz method that the number of iterations is bounded. This bound is independent of the polynomial degree of the ansatz functions and of the size of the underlying mesh. For a modified diagonal scaling, which uses special basis functions, we prove that the number of iterations grows only polylogarithmically in the polynomial degree. Here, a sufficiently fine mesh is required. Numerical results supporting the theory are presented.

Keywords:

• Boundary element method
• Schwarz methods
• preconditioning

AMS:

• 65N55
• 65N38

^*Institut f¨r Wissenschaftliche Datenverarbeitung, Universitat Bremen, Germany

^*Institut f¨r Wissenschaftliche Datenverarbeitung, Universitat Bremen, Germany

Notes

^*Institut f¨r Wissenschaftliche Datenverarbeitung, Universitat Bremen, Germany