This CAREER project develops an adaptive space-time finite element methodology that allows for accurate and efficient prediction of the dynamic response of complex structural acoustic systems over a broad range of scales and frequencies - including the mid-frequency range. The methods employ finite element discretization of the time domain as well as the usual discretization of the spatial domain. This novel approach to the modeling of the temporal variables allows for the consistent use of adaptive solution strategies for unstructured grids in both time and space: a technique which significantly improves the efficiency and reliability of the resulting computational algorithm over standard methods. By orchestrating the distribution of mesh sizes and spectral orders in space-time, a modeling technique is obtained which has significant flexibility and scope. The educational plan enhances the learning process for both undergraduate and graduate students through a comprehensive array of innovative teaching activities and industrial exchanges. Educational activities include development of a curriculum in finite element analysis, setting up experimental, computational, and multimedia laboratories for graduate and undergraduate teaching, use of symbolic computing systems for innovative teaching and learning, involving undergraduate students in collaborative research projects, educational collaborations with industry, and outreach activities including delivering short courses and workshops over the Internet via video conferencing and the World Wide Web.
