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A wavelet approach to robust multilevel solvers for anisotropic elliptic problems. (English) Zbl 0864.65073
Summary: A wavelet variation of the frequency decomposition multigrid method (FDMGM) of W. Hackbusch [Numer. Math. 56, No. 2/3, 229-245 (1989; Zbl 0673.65062)] is presented. The perfect reconstruction property and the multiresolution structure of wavelets yield the robustness of the additive as well as of the multiplicative version of a two-level method corresponding to any intermediate level in the FDMGM. Aspects of the robustness of the multilevel scheme are discussed. Numerical experiments confirm the theoretical results. The wavelet version of the FDMGM presented here involves wavelet packets which have been used before this primarily in signal processing.

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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