Multigrid computation of axisymmetric electromagnetic fields
Boundary value problems for Maxwell equations that feature cylindrical symmetry both of the domain and the data in three dimensions are considered. 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. For multigrid solvers line relaxation in radial direction and semicoarsening can successfully reign in the degeneracy. In addition, the lack of \( H^1\)-ellipticity of the double curl-operator makes special hybrid smoothing procedures necessary. The theoretical analysis relies on blending generalized Fourier techniques and modern variational multigrid theory. Under certain assumptions on the material parameters uniform convergence of a symmetric \(V\)-cycle is shown.
scientific article; zbMATH DE number 1752550