Hierarchical basis preconditioners for first kind integral equations

Abstract

We study hierarchical basis preconditioners for the h-version Galerkin boundary element method applied to weakly singular and hypersingular integral equations of the first kind. We show that the condition numbers of the preconditioned linear systems are bounded by log²(l/h). Hence, the well known result for finite elementmethods is generalized to boundary integral operators, which are non-local operators.Extensions to non-local refinements are also discussed. Numerical experiments confirmthe theoretical results.

Keywords:

• hierarchical basis
• first kind integral equations
• efficient preconditioners
• boundary element methods

Additional information

Notes on contributors

Thanh Tran

Ernst p. Stephan

Patrick Mund