Multigrid computation of vector potentials
type: Item
instance of: scholarly article
title: Multigrid computation of vector potentials
zbMATH Open document ID: 0860.65125
DOI: 10.1016/0377-0427(94)00106-8
author: Shangyou Zhang
author: Peter Monk
published in: Journal of Computational and Applied Mathematics
publication date: 1997-04-14T00:00:00Z
review text: The authors analyze the use of edge finite elements and the multigrid method to approximate the problem of computing a static magnetic field in a cavity. Using a discrete analogue of the second kind Friedrichs' inequality, it is shown that the mixed finite element discrete problem may be reformulated as a symmetric positive definite system. It is shown how the multigrid method may be applied to compute the magnetic vector potential. The difficulty here is that the bilinear forms on different meshes are not related in the standard way. Two different intergrid transfer operators are defined in the paper for the multigrid method. The convergence theory and the numerical tests include both algorithms.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 903480
zbMATH Keywords: numerical examples
zbMATH Keywords: finite elements
zbMATH Keywords: multigrid method
zbMATH Keywords: static magnetic field
zbMATH Keywords: Friedrichs' inequality
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)00106-8
OpenAlex ID: W2033822578
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description: scientific article; zbMATH DE number 903480