In this paper new space-time finite element methods, based on a time-discontinuous variational formulation for fluid-structure interaction, are developed for the solution of coupled structural acoustics in unbounded domains. The formulation employs a finite computational fluid domain surrounding the structure and incorporates high-order accurate radiation boundary conditions on the fluid truncation boundary. A new sequence of time-dependent radiation boundary conditions for the wave equation are developed, which are exact for the first N spherical wave harmonics on the truncation boundary. These boundary conditions are developed from the exact localization of the nonlocal Dirichlet-to-Neumann (DtN) map in the frequency domain. Time-dependent boundary conditions which are local in both space and time are obtained through an inverse Fourier transform. In addition, we show that an inverse Fourier transform exists for the full DtN map, allowing for exact boundary conditions that are local in time but nonlocal in space. An important ingredient for the success of the proposed space-time finite element methods is the incorporation of time-discontinuous jump operators that weakly enforce continuity of the solution between space-time slabs. The specific form of these temporal jump operators are designed such that unconditional stability can be proved for general unstructured discretizations in both space and time. In order to add additional stability, and to prove convergence for higher-order element interpolations, least-squares operators based on local residuals of the Euler-Lagrange equations for the coupled system, including the non-reflecting boundary conditions, are incorporated into the space-time formulation.

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