Geodesic
On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 403-424
In Erlangga and Nabben [SIAM J. Sci. Comput., 30 (2008), pp. 1572-1595], a multilevel Krylov method is proposed to solve linear systems with symmetric and nonsymmetric matrices of coefficients. This multilevel method is based on an operator which shifts some small eigenvalues to the largest eigenvalue, leading to a spectrum which is favorable for convergence acceleration of a Krylov subspace method. This shift technique involves a subspace or coarse-grid solve. The multilevel Krylov method is obtained via a recursive application of the shift operator on the coarse-grid system. This method has been applied successfully to 2D convection-diffusion problems for which a standard multigrid method fails to converge.
Classification : 65F10, 65F50, 65N22, 65N55
Keywords: multilevel Krylov method, GMRES, multigrid, Helmholtz equation, shifted-Laplace preconditioner 
@article{ETNA_2008__31__a0,
     author = {Erlangga,  Yogi A. and Nabben,  Reinhard},
     title = {On a multilevel {Krylov} method for the {Helmholtz} equation preconditioned by shifted {Laplacian}},
     journal = {Electronic transactions on numerical analysis},
     pages = {403--424},
     year = {2008},
     volume = {31},
     zbl = {1190.65050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a0/}
}
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%J Electronic transactions on numerical analysis
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%F ETNA_2008__31__a0
Erlangga,  Yogi A.; Nabben,  Reinhard. On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 403-424. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a0/