Multigrid Computation of Axisymmetric Electromagnetic Fields

摘要: The focus of this paper is on boundary value problems for Maxwell's equations that feature cylindrical symmetry both the domain Ω⊂R 3 and data. Thus, by resorting to coordinates, a reduction two dimensions possible. However, coordinates introduce potentially malicious singularity at axis rendering variational degenerate. As consequence, analysis multigrid solvers along lines theory confronts severe difficulties. Line relaxation in radial direction semicoarsening can successfully reign degeneracy. In addition, lack H 1-ellipticity double-curl operator entails using special hybrid smoothing procedures. All these techniques combined yield fast solver. theoretical investigation method relies blending generalized Fourier modern theory. We first determine invariant subspaces iteration analyze smoothers therein. Under certain assumptions material parameters we manage show uniform convergence symmetric V-cycle.