Preconditioning a class of fourth order problems by operator splitting. (English) Zbl 1241.65031
The authors develop preconditioners for systems arising from finite element discretizations of paraboblic problems of fourth order in space domain. They consider boundary conditions leading to a splitting of the discretized fourth order operator into two discrete second order operators. This property is used in assembling the preconditioners.
The authors propose left and left-right preconditioners. They analyse the spectral properties of preconditioners. The results are presented on numerical experiments with the preconditioned conjugate gradients method and with the generalized minimal residual method.
The authors propose left and left-right preconditioners. They analyse the spectral properties of preconditioners. The results are presented on numerical experiments with the preconditioned conjugate gradients method and with the generalized minimal residual method.
Reviewer: Martin Plešinger (Liberec)
MSC:
| 65F08 | Preconditioners for iterative methods |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35K46 | Initial value problems for higher-order parabolic systems |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
preconditioning; fourth order problem; finite element discretization; operator splitting; left preconditioner; left-right preconditioner; parabolic problems; numerical experiments; conjugate gradients method; generalized minimal residual methodReferences:
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