Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations

0495401 - ÚGN 2019 RIV NL eng J - Článek v odborném periodiku
Axelsson, Owe - Karátson, J. - Magoulès, F.
Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations.
Journal of Computational and Applied Mathematics. Roč. 340, October 2018 (2018), s. 424-431. ISSN 0377-0427. E-ISSN 1879-1778
Grant CEP: GA MŠMT LQ1602
Institucionální podpora: RVO:68145535
Klíčová slova: Helmholtz equations * iterative solution * preconditioning * mesh-independent superlinear convergence
Obor OECD: Applied mathematics
Impakt faktor: 1.883, rok: 2018
https://www.sciencedirect.com/science/article/pii/S037704271830058X

Complex-valued Helmholtz equations arise in the modelling of various applied problems, for instance, when air is
periodically compressed into some closed compartment, e.g., in a car. For the iterative solution of their discretization,
standard preconditioning methods such as incomplete factorization or (algebraic) multigrid methods are not efficient,
mainlyduetotheeffectofhighindefinitenessandlargewave-numbers(1,2),thereforemoreefficientiterativesolversare
stillofgreatinterest.Alotofrecentresearchhasbeendevotedtopreconditionersarisingasthediscretizationoftheso-called
‘‘complexshiftedLaplace’’problems,see,e.g.,(1,3–6).Thesepreconditionersrequire,however,useofcomplexarithmetics
andsolutionofastillsomewhatinvolvedpreconditioner.Inthisnotewemodifythepreconditionersothatitcanbesolved
directlyinrealarithmeticsandstillpreservethefavourablepropertiesofconvergence.Eachapplicationoftheactionofthe
preconditionerinvolvesessentiallythesolutionofonlytwostandardellipticproblems.
Trvalý link: http://hdl.handle.net/11104/0288391