Controllability methods for the computation of time-periodic solutions; application to scattering
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Journal of Computational Physics
Controllability method for acoustic scattering with spectral elements
Journal of Computational and Applied Mathematics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
Time-harmonic elasticity with controllability and higher-order discretization methods
Journal of Computational Physics
Journal of Computational Physics
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The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral elements and in time domain with central finite differences. After discretization, exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method.