A SPACE-TIME FINITE-ELEMENT METHOD FOR STRUCTURAL ACOUSTICS IN INFINITE DOMAINS .2. EXACT TIME-DEPENDENT NONREFLECTING BOUNDARY-CONDITIONS

In Part 1, a new space-time finite element method for transient struct ural acoustics in exterior domains was given. The formulation employs a finite computational fluid domain surrounding the structure and inco rporates local time-dependent non-reflecting boundary conditions on th e fluid truncation boundary. In this paper, new exact rime-dependent n on-reflecting boundary conditions are developed for solutions of the s calar wave equation in three space dimensions. These high-order accura te absorbing boundary conditions are based on the exact impedance rela tion for the acoustic fluid through the Dirichlet-to-Neumann (DtN) map in the frequency domain and are exact for solutions consisting of the first N spherical wave harmonics. Time dependent boundary conditions are obtained through an inverse Fourier transform procedure. Two alter native sequences of boundary conditions are derived; the first involve s both temporal and spatial derivatives (local in time and local in sp ace version), and the second involves temporal derivatives and a spati al integral (local in time and non-local in space version). These non- reflecting boundary conditions are incorporated as 'natural' boundary conditions in the space-time variational equation, i.e. they are enfor ced weakly in both space and time. Several numerical examples involvin g transient radiation are presented to illustrate the high-order accur acy and efficiency achieved by the new space-time finite element formu lation for transient structural acoustics with non-reflecting boundari es.