Transient finite element/equivalent sources using direct coupling and treating the acoustic coupling matrix as sparse.

Abstract

Transient structural-acoustic problems can be solved using time stepping procedures with the structure and fluid modeled using finite elements and equivalent sources, respectively. Limitations on the time step size for stable solutions have led to the current popularity of iterative coupling to enforce the boundary conditions at the fluid-structure interface, which also helps to alleviate difficulties caused by the fully populated acoustic coupling matrix. The research presented here examines a monolithic approach using a stabilized equivalent source formulation where the acoustic coupling matrix is either fully diagonal or treated as sparse. In theory, the matrix should be sparse because it relates nodal velocities to nodal acoustic pressure forces during a single time step, and the pressure waves can only travel a distance equal to the sound speed multiplied by the time step. The numerical results demonstrate that for the chosen example problems accurate results are obtained for either diagonal coupling matrices or with a large percentage of the terms set to zero. It is also demonstrated that the formulation adapts well to parallel processing environments and that the times associated with the equivalent source computations are proportional to the number of processors.