Preconditioning methods for eddy current optimally controlled time-harmonic electromagnetic problems

0495498 - ÚGN 2020 RIV DE eng J - Journal Article
Axelsson, Owe - Lukáš, D.
Preconditioning methods for eddy current optimally controlled time-harmonic electromagnetic problems.
Journal of Numerical Mathematics. Roč. 27, č. 1 (2019), s. 1-21. ISSN 1570-2820. E-ISSN 1569-3953
R&D Projects: GA MŠMT LQ1602
Grant - others:Ga MŠk(CZ) LM2015070
Institutional support: RVO:68145535
Keywords : Boundary element method * Integral equations * multipole boundary
OECD category: Applied mathematics
Impact factor: 3.240, year: 2019
Method of publishing: Limited access
https://www.degruyter.com/view/j/jnma.2019.27.issue-1/jnma-2017-0064/jnma-2017-0064.xml?format=INT

Time-harmonic problems arise in many important applications, such as eddy current optimally controlled electromagnetic problems. Eddy cur-
rent modelling can also be used in non-destructive testings of conducting materials. Using a truncated Fourier series to approximate the solution, for linear problems the equation for different frequencies separate, so it suffices to study solution methods for the problem for a single frequency. The arising discretized system takes a two-by-two or four-by-four block matrix form. Since the problems are in general three-dimensional in space and hence of very large scale, one must use an iterative solution method. It is then crucial to construct efficient preconditioners. It is shown that an earlier used preconditioner for optimal control problems is applicable here also and leads to very tight eigenvalue bounds and hence very fast convergence such as for a Krylov subspace iterative solution method. A comparison is done with an earlier used block diagonal preconditioner.
Permanent Link: http://hdl.handle.net/11104/0288467