R.
Hiptmair
dimensions_id
pub.1045949792
research_article
2019-04-10T22:30
Multigrid Computation of Axisymmetric Electromagnetic Fields
2002-05-01
https://scigraph.springernature.com/explorer/license/
en
The focus of this paper is on boundary value problems for Maxwell's equations that feature cylindrical symmetry both of the domain Ω⊂R3 and the data. Thus, by resorting to cylindrical coordinates, a reduction to two dimensions is possible. However, cylindrical coordinates introduce a potentially malicious singularity at the axis rendering the variational problems degenerate. As a consequence, the analysis of multigrid solvers along the lines of variational multigrid theory confronts severe difficulties. Line relaxation in radial direction and semicoarsening can successfully reign in the degeneracy. In addition, the lack of H1-ellipticity of the double-curl operator entails using special hybrid smoothing procedures. All these techniques combined yield a fast multigrid solver. The theoretical investigation of the method relies on blending generalized Fourier techniques and modern variational multigrid theory. We first determine invariant subspaces of the multigrid iteration operator and analyze the smoothers therein. Under certain assumptions on the material parameters we manage to show uniform convergence of a symmetric V-cycle.
2002-05
false
articles
331-356
http://link.springer.com/10.1023/A:1014533409747
Mathematical Sciences
Pure Mathematics
10.1023/a:1014533409747
doi
Kiel University
Institut für Praktische Mathematik, Universität Kiel, Germany
dae0f10eb5aa84582d4ae5980a94eb15060c4045d099565dd3b34c93ee6c26c4
readcube_id
S.
Börm
Springer Nature - SN SciGraph project
4
16
Sonderforschungsbereich 382, Universität Tübingen, Germany
University of Tübingen
1019-7168
Advances in Computational Mathematics
1572-9044