On multigrid methods for solving electromagnetic scattering problems
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.