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A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains. (English) Zbl 0860.65121
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.

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
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