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

0495498 - ÚGN 2020 RIV DE eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT LQ1602
Grant ostatní: Ga MŠk(CZ) LM2015070
Institucionální podpora: RVO:68145535
Klíčová slova: Boundary element method * Integral equations * multipole boundary
Obor OECD: Applied mathematics
Impakt faktor: 3.240, rok: 2019
Způsob publikování: Omezený přístup
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.
Trvalý link: http://hdl.handle.net/11104/0288467