Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems
type: Item
instance of: scholarly article
title: Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems
zbMATH Open document ID: 1428.65040
author: Owe Axelsson
author: Dalibor Lukáš
published in: Journal of Numerical Mathematics
publication date: 2019-05-27T00:00:00Z
review text: At first, the Maxwell's equations for finding a time-dependent magnetic vector potential in a bounded three-dimensional domain are given. It is described that the finite element discretization of the considered problem leads to a system of linear equations, where the matrix \(\mathcal{A}\) has a two-by-two block structure. Then, a preconditioner \(\mathcal{C}\) for such systems of equations is presented and estimates of the eigenvalues of the matrix \(\mathcal{C}^{-1}\mathcal{A}\) are derived. As an application of the proposed preconditioner, an optimal control problem of parabolic type with a time-harmonic target state is discussed. Furthermore, an eddy current electromagnetic problem is considered. Its discretization leads to a matrix with a double two-by-two block structure. The construction of a preconditioner is described for two cases, namely, the situation where the control and observation functions are defined on the whole space and the situation where these functions are prescribed only on a subset of the whole domain. Numerous numerical tests are presented, which show the robustness and performance of the iterative solver with the new preconditioners.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 7059684
zbMATH Keywords: preconditioning
zbMATH Keywords: iterative solution method
zbMATH Keywords: optimal control
zbMATH Keywords: eddy current problems
reviewed by: Michael Jung
describes a project that uses: MinRes
MaRDI profile type: Publication
full work available at URL: jnma-2017-0064
OpenAlex ID: W2789728292
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DOI: 10.1515/JNMA-2017-0064
description: scientific article