Additive Schwarz preconditioners for the h-p version boundary-element approximation to the hypersingular operator in three dimensions

Abstract

We study different preconditioners for the h-p version of the Galerkin boundary-element method when used to solve hypersingular integral equations of the first kind on a surface in ℝ³. These integral equations result from Neumann problems for the Laplace and Lamé equations in the exterior of the surface. The preconditioners are of additive Schwarz type (non-overlapping and overlapping). In all cases, we prove that the condition numbers grow at most logarithmically with the degrees of freedom.

Keywords:

• Boundary-element method
• h-p version
• Additive Schwarz
• Non-overlapping
• Overlapping

Additional information

Notes on contributors

Thanh Tran

Email: [email protected]