Finite element methods for the interaction of acoustic fluids with elastic solids

Computation is essential to the solution of many problems of stnictural acoustics, particularly when wavelengths are of the same order as characteristic length scales. The development of finite element methods for large-scale computation of solutions to these problems should be preceded by a thorough analytical understanding of their performance in simplified settings in order to validate application to general configurations. Coupling such an analysis with the design of numerical methods that is based on understanding the underljdng mathematical framework leads to the development of robust methods in which stability properties are enhanced while maintaining higher-order accuracy. In this work we develop finite element methods for exterior problems of time-harmonic acoustic-structure interaction. Exterior boundary conditions are derived from an exact relation between the solution and its derivatives on an artificial boundary by the DtN method, yielding an equivalent problem in a bounded region that is suitable for domain-based computation. Solutions to the equivalent problem are unique, precluding singular behavior in finite element models. Galerkin/least-squares technology is specialized to these problems in order to counter the numerical difficulties that result from employing traditional Galerkin methods. This is achieved by appending terms in least-squares form containing residuals of the Euler-Lagrange equations to the, standard Galerkin formulation. The Galerkin/least-squares method is designed to yield dispersion-free finite element solutions to model problems, leading to superior performance on general, multi-dimensional configurations. Two one-dimensional model problems are investigated over a wide range of combinations of material properties of both media. In the first an exterior acoustic problem with impedance boundary conditions is analyzed, in order to study the influence of the elastic body on the acoustic medium. In the second, an elastic rod with an exterior acoustic medium is investigated in order to examine propagation from the solid to the fluid. The resulting method exhibits superior performance for fluid-solid interaction in multi-dimensional configurations. One version of the method offers particularly good representation of interface values.