Advances in Space-Time Finite Element Methods for Structural Acoustics and Fluid-Solid Interaction

Traditional computational approaches toward simulation of radiation and scattering from elastic bodies submerged in an acoustic uid have been primarily based on frequency domain formulations. Classical time-harmonic approaches (including boundary element, nite element, and nite diierence methods) have been eeective for problems involving a limited number of frequencies (narrow band response) and scales (wavelengths) that are large compared to the characteristic dimensions of the elastic structure. Attempts at solving large-scale structural acoustic systems with dimensions that are much larger than the operating wavelengths and which are complex, consisting of many diierent components with diierent scales and broadband frequencies, has revealed limitations of many of the classical methods. As a result, in recent times there has been renewed interest in new and alternative approaches, including time-domain approaches. This paper describes recent advances in the development of a new class of high-order accurate and unconditionally stable space-time methods which employ nite element discretization of the time domain as well as the usual discretization of the spatial domain. The formulation is based on a space-time variational equation for both the acoustic uid and elastic solid together with their interaction. This novel approach to the modeling of the temporal variables allows for the consistent use of high-order adaptive solution strategies for unstructured grids in both time and space; a technology that is vital for the eeciency of the resulting computational algorithm. Another important feature is the incorporation of temporal jump operators which allow for discretizations that are discontinuous in time. The speciic form of these jump operators are designed to capture multiple scales in the response of large-scale structural acoustic systems. For additional stability, least-squares operators based on local residuals of the Euler-Lagrange equations including non-reeecting boundary conditions are incorporated. Topics to be discussed include the development and implementation of new higher-order accurate non-reeecting boundary conditions based on the exact impedance relation through the Dirichlet-to-Neumann (DtN) map, multi-eld representations based on acoustic pressure and velocity potential variables, error estimation and stability.