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Glowinski, Roland; Rieder, Andreas; Wells, Raymond O. jun.; Zhou, Xiaodong
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains. (English) Zbl 0860.65121
RAIRO, Modélisation Math. Anal. Numér. 30, No. 6, 711-729 (1996).
A wavelet-based multigrid method for an elliptic model problem over a square with periodic boundary conditions is introduced. Further, the authors show how this multigrid iteration can be used as a preconditioner for a conjugate gradient method applied to a linear system originating from a wavelet-Galerkin discretization of a Dirichlet boundary value problem via a penalty/fictious domain formulation. Numerical experiments described in the paper confirm the efficiency of this new iterative solver.
Reviewer: P.Chocholatý (Bratislava)

Cited in 2 Documents
MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
65F10 Iterative numerical methods for linear systems
Keywords:
numerical examples; wavelet-based multigrid method; preconditioner; conjugate gradient method; wavelet-Galerkin discretization; penalty/fictious domain formulation
Software:
Wesseling
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\textit{R. Glowinski} et al., RAIRO, Modélisation Math. Anal. Numér. 30, No. 6, 711--729 (1996; Zbl 0860.65121)
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