000K utf8 1100 $c2006 1500 eng 2050 urn:nbn:de:gbv:8-diss-16644 3000 Gheorghe, Simona 4000 On multigrid methods for solving electromagnetic scattering problems$hChristian-Albrechts-Universität zu Kiel [Gheorghe, Simona] 4030 Kiel$nChristian-Albrechts-Universität zu Kiel 4209 This thesis researches the suitability and performance of some classical numerical algorithms, especially multigrid methods, applied to two-dimensional electromagnetic problems in the low frequency domain, among which the scattering of time-harmonic electromagnetic waves and their propagation in waveguides with discontinuities. For the discretization of the governing Helmholtz equation we have used the Finite Element method, coupled with absorbing-boundary conditions, like the Bayliss-Turkel boundary conditions, Dirichlet-to-Neumann mapping, eigenfunctions expansion and boundary element method. Based on numerical studies we recommended the use of full-multigrid with at most three multigrid cycles per level for the model problems with a low wavenumber. For problems with a medium wavenumber, while standard multigrid as well as full multigrid with linear prolongation failed to converge, the multigrid-preconditioned BICGSTAB proved to be the most reliable and the fastest from the tested algorithms, for both model problems and any type of boundary conditions. 4950 https://nbn-resolving.org/urn:nbn:de:gbv:8-diss-16644$xR$3Volltext$534 4961 https://macau.uni-kiel.de/receive/diss_mods_00001664 5051 530 5550 absorbing-boundary conditions 5550 electromagnetic scattering 5550 Elektromagnetische Streuung 5550 FEM 5550 iterative methods 5550 Mehrgitterverfahren 5550 multigrid