A SPACE-TIME FINITE-ELEMENT METHOD FOR THE EXTERIOR STRUCTURAL ACOUSTICS PROBLEM - TIME-DEPENDENT RADIATION BOUNDARY-CONDITIONS IN 2 SPACE DIMENSIONS

A time-discontinuous Galerkin space-time finite element method is form ulated for the exterior structural acoustics problem in two space-dime nsions. The problem is posed over a bounded computational domain with local time-dependent radiation (absorbing) boundary conditions applied to the fluid truncation boundary. Absorbing boundary conditions are i ncorporated as 'natural' boundary conditions in the space-time variati onal equation, i.e. they are enforced weakly in both space and lithe: Following Bayliss and Turkel, time-dependent radiation boundary condit ions for the two-dimensional wave equation are developed from an asymp totic approximation to the exact solution in the frequency domain expr essed in negative powers of a non-dimensional wavenumber. In this pape r, we undertake a brief development of the time-dependent radiation bo undary conditions, establishing their relationship to the exact impeda nce (Dirichlet-to-Neumann map) for the acoustic fluid, and characteriz e their accuracy when implemented in our space-time finite element for mulation for transient structural acoustics. Stability estimates are r eported together with an analysis of the positive form of the matrix p roblem emanating from the space-time variational equations for the cou pled fluid-structure system, Several numerical simulations of transien t radiation and scattering in two space dimensions are presented to de monstrate the effectiveness of the space-time method.