Solving a fluid-plate interaction problem using finite element methods with domain decomposition strategies

This thesis studies numerically a fluid-plate interaction problem which models the coupled vibration between an acoustic field and an elastic thin plate. Since the thickness of the plate is negligible, the plate serves a dual role in the model. It is the solid medium and at the same time it is the interface between the acoustic field and the solid. Mathematically, the interaction problem is described by the acoustic wave equation in the fluid and the fourth order plate vibration equation on the plate. The pressure in the fluid and the vertical displacement of the plate are the primary variables to be solved numerically. The objectives of the thesis are to propose and to implement on computers a numerical scheme for computing the solution of the interaction problem. In the scheme, the finite element method is used for the spatial discretization, and the finite difference method is employed for the temporal discretization. The fully discrete finite element equations are then solved by using a parallelizable domain decomposition algorithm. A computer code is developed, and its efficiency and accuracy are tested on the specific examples.