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Erschienen in:
1989 | OriginalPaper | Buchkapitel
Effective Preconditioning for Spectral Multigrid Methods
verfasst von : Wilhelm Heinrichs
Erschienen in: Robust Multi-Grid Methods
Verlag: Vieweg+Teubner Verlag
Enthalten in: Professional Book Archive
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Spectral methods employ global polynomials for the approximation of elliptic problems. They give very accurate approximations for smooth Solutions with relatively few degrees of freedom. On the other hand, the matrices involed are full and yield high condition numbers, growing as O(N4) (for polynomials of degree ≤N in each variable). Never-theless the spectral Systems can be efficiently solved using spectral multigrid (SMG) methods. Utilizing FFTs only 0(N2lnN) Operations are necessary for the evaluation of the spectral residual. We investigate effective preconditioners for SMG based on line relaxation techniques and show the robustness of minimal residual relaxation. We also present numerical results for L-shaped regions where the Schwarz alternating procedure has been used.