Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements
Mönkölä, S. (2010). Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements. Journal of Computational and Applied Mathematics, 234, 1904-1911. doi:10.1016/j.cam.2009.08.040
Published inJournal of Computational and Applied Mathematics
© Elsevier. This is an author's final draft version of an article whose final and definitive form has been published by Elsevier.
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.