@misc{Beck, author = {Beck, Rudolf}, title = {Algebraic Multigrid by Component Splitting for Edge Elements on Simplicial Triangulations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4290}, number = {SC-99-40}, abstract = {Our focus is on Maxwell's equations in the low frequency range; two specific applications we aim at are time-stepping schemes for eddy current computations and the stationary double-curl equation for time-harmonic fields. We assume that the computational domain is discretized by triangles or tetrahedrons; for the finite element approximation we choose N\'{e}d\'{e}lec's \$H(curl)\$-conforming edge elements of the lowest order. For the solution of the arising linear equation systems we devise an algebraic multigrid preconditioner based on a spatial component splitting of the field. Mesh coarsening takes place in an auxiliary subspace, which is constructed with the aid of a nodal vector basis. Within this subspace coarse grids are created by exploiting the matrix graphs. Additionally, we have to cope with the kernel of the \$curl\$-operator, which comprises a considerable part of the spectral modes on the grid. Fortunately, the kernel modes are accessible via a discrete Helmholtz decomposition of the fields; they are smoothed by additional algebraic multigrid cycles. Numerical experiments are included in order to assess the efficacy of the proposed algorithms.}, language = {en} } @misc{SeebassBeckGellermannetal., author = {Seebass, Martin and Beck, Rudolf and Gellermann, Johanna and Nadobny, Jacek and Wust, Peter}, title = {Electromagnetic phased arrays for regional hyperthermia -- optimal frequency and antenna arrangement}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5961}, number = {00-28}, abstract = {In this paper we investigate the effects of the three-dimensional arrangement of antennas and frequency on temperature distributions that can be achieved in regional hyperthermia using an electromagnetic phased array. We compare the results of power-based and temperature-based optimization. Thus we are able to explain the discrepancies between previous studies favouring more antenna rings on the one hand and more antennas per ring on the other hand. We analyze the sensitivity of the results with respect to changes in amplitudes and phases as well as patient position. This analysis can be used for different purposes. First, it provides additional criteria for selecting the optimal frequency. Second, it can be used for specifying the required phase and amplitude accuracy for a real phased array system. Furthermore, it may serve as a basis for technological developments in order to reduce both types of sensitivities described above.}, language = {en} }