Time-periodic solutions of wave equation via controllability and fictitious domain methods. (English) Zbl 1049.65056
Cohen, Gary C. (ed.) et al., Mathematical and numerical aspects of wave propagation, WAVES 2003. Proceedings of the sixth international conference on mathematical and numerical aspects of wave propagation, Jyväskylä, Finland, 30 June – 4 July 2003. Berlin: Springer (ISBN 3-540-40127-X/hbk). 805-810 (2003).
The authors combine the controllability and fictitious domain methods to compute time-periodic solution for the wave equation describing scattering by an obstacle \(\varphi_{tt}- \Delta\varphi= 0\) in \((\Pi\setminus\overline\Omega)\times (0,T)\); \(\varphi= g\) on \(\partial\Pi\times(0,T)\); \(\varphi_n+ \varphi_t= 0\) on \(\partial\Pi\times (0,T)\) in a rectangular domain \(\Pi\). The fictitious domain method uses distributed Lagrange multipliers to satisfy the Dirichlet boundary condition on the scatterer \(\Omega\). The controllability technique leads to an optimization problem which is solved by preconditioned conjugate gradient method. The results of numerical experiments are given for the cases when a disc and semi-open cavity are scatterers.
For the entire collection see [Zbl 1029.00072].
For the entire collection see [Zbl 1029.00072].
Reviewer: Boris V. Loginov (Ul’yanovsk)
MSC:
| 65K10 | Numerical optimization and variational techniques |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 35L05 | Wave equation |
| 93B05 | Controllability |
