Multigrid computation of axisymmetric electromagnetic fields
type: Item
instance of: scholarly article
title: Multigrid computation of axisymmetric electromagnetic fields
zbMATH Open document ID: 0998.65124
DOI: 10.1023/A:1014533409747
published in: Advances in Computational Mathematics
publication date: 2002-06-09T00:00:00Z
review text: 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.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 1752550
zbMATH Keywords: computational electromagnetism
zbMATH Keywords: multigrid method
zbMATH Keywords: edge elements
zbMATH Keywords: semi-coarsening
zbMATH Keywords: degenerate problems
zbMATH Keywords: Maxwell equations
zbMATH Keywords: convergence
author: Steffen Börm
author: Ralf Hiptmair
MaRDI profile type: Publication
full work available at URL: a:1014533409747
OpenAlex ID: W125900770
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description: scientific article; zbMATH DE number 1752550