A space-time finite element method for structural acoustics in infinite domains. I: Formulation, stability and convergence. II: Exact time-dependent non-reflecting boundary conditions (Q1372777)

A space-time finite element method for solution of the exterior structural acoustics problem involving the interaction of vibrating elastic structures submerged in an infinite acoustic fluid is formulated. In particular, time-discontinuous Galerkin and Galerkin least-squares variational formulations for coupled structural acoustics in unbounded domains are developed and analyzed for stability and convergence. The formulation employs a finite computational fluid domain surrounding the structure and incorporates time-dependent non-reflecting boundary conditions on the fluid truncation boundary. Energy estimates are obtained which allow us to prove the unconditional stability of the method for the coupled fluid-structure problem with absorbing boundaries. The methods developed are especially useful for the application of adaptive solution strategies for transient acoustics in which unstructured space-time meshes are used to track waves propagating along space-time characteristics.