hp-version of the boundary element method for electromagnetic problems [Elektronische Ressource] : error analysis, adaptivity, preconditioners / von Florian Leydecker

hp-version of the boundary element methodfor electromagnetic problems –error analysis, adaptivity, preconditionersVon der Fakult¨at fu¨r Mathematik und Physikder Universit¨at Hannoverzur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonDipl.-Math. Florian Leydeckergeboren am 15. Juni 1974 in Frankfurt / Main2006Referent: Prof. Dr. E. P. Stephan, Hannover UniversityKorreferent: Prof. Dr. N. Heuer, Uxbridge University, Brunel, UKTag der Promotion: 30.06.2006AbstractThis thesis deals with the hp-version for the coupling of finite elements and boundary3elements inR . We present preconditioners as well as reliable and efficient a posteriorierror estimates for the hp-version.In the first part we consider the hypersingular integral equation of the normal deriva-tive of the double layer potential on surfaces and perform the Galerkin hp-version ofthe boundary element method (BEM) on triangles. This method is known to convergerapidly for smooth aswell as for singular solutions. On theother hand the arising linearsystem is highly ill-conditioned. Hence, for an efficient solution procedure appropriatepreconditioners are necessary to reduce the number of CG-iterations. We present an it-erative substructuring method which uses the functions concentrated on the wire basketand the bubble functions in the interior of the elements separately.