hp Preconditioners and Adaptive Schemes for Boundary Integral Equations

Ernst P. Stephan

Dec. 4, 2001, 3:30 p.m. T 811

Galerkin boundary element solutions for first kind integral equations with the hp-version on geometrically refined meshes converge exponentially fast. However this method leads to ill-conditioned matrices and suitable preconditioners are necessary. In this talk we present (almost) optimal additive and multiplicative Schwarz preconditioners for the conjugate gradient method. We give results for weakly singular and hypersingular integral equa- tients on curves and surfaces. The analysis is based on stable subspace splittings of the ansatz spaces of piecewise linear functions and tensor products of Legendre polynomials. We further present a-posteriori error estimates and adaptive algorithms based on suitable 2-level subspace splittings. Numerical experiments for benchmarks are also given.