Boundary Element Approximation for Maxwell's Eigenvalue Problem [Elektronische Ressource] / Jiping Xin. Betreuer: C. Wieners

Boundary Element Approximation forMaxwell’s Eigenvalue ProblemZur Erlangung des akademischen Grades einesDOKTORS DER NATURWISSENSCHAFTENvon der Fakult¨at fur¨ Mathematik desKarlsruher Institut fur¨ TechnologiegenehmigteDISSERTATIONvonM. Sc. Jiping Xinaus G¨oteborg, SwedenTag der mundlic¨ hen prufung:¨ 13.07.2011Referent: Prof. Dr. Christian WienersKorreferent: Prof. Dr. Willy D¨orflerContentsAbstract iiiList of Figures vList of Tables v1 Boundary Element Methods for Boundary Value Problems 11.1 Classical electrodynamics.......................... 31.2 The Helmholtz case ............................. 61.2.1 Representation formula....................... 71.2.2 Function spaces........................... 71.2.3 Boundary integral equations .................... 91.2.4 Variational formulations ...................... 121.2.5 Galerkin-BEMs 131.2.6 Numerical tests 171.3 The Maxwell case.............................. 191.3.1 Representation formula 191.3.2 Function spaces 211.3.3 Boundary integral equations .................... 231.3.4 Variational formulations ...................... 271.3.5 Galerkin-BEMs........................... 291.3.6 Numerical tests 322 Domain Decomposition Methods 342.1 The Helmholtz case ............................. 342.1.1 Interface problem.......................... 342.1.2 Domain decomposition method .................. 352.1.3 Variational formulation ....................... 362.1.4 Galerkin-BEM 372.1.5 Numerical tests ....