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Wavelet filtering for exact controllability of the wave equation. (English) Zbl 1131.65056

The authors propose a wavelet-based numerical method for exact controllability of the one-dimensional wave equation, concentrating on the particular case of Dirichlet controls. Combining a multilevel finite element discretization and a two-grid filtering technique in the spline wave basis achieves quite effective numerical methods for approximating the boundary control.

MSC:

65K10 Numerical optimization and variational techniques
35L05 Wave equation
93B05 Controllability
93B07 Observability
93C20 Control/observation systems governed by partial differential equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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