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This report documents the results obtained during a one-year Laboratory Directed Research and Development (LDRD) initiative aimed at investigating coupled structural acoustic interactions by means of algorithm development and experiment. Finite element acoustic formulations have been developed based on fluid velocity potential and fluid displacement. Domain decomposition and diagonal scaling preconditioners were investigated for parallel implementation. A formulation that includes fluid viscosity and that can simulate both pressure and shear waves in fluid was developed. An acoustic wave tube was built, tested, and shown to be an effective means of testing acoustic loading on simple test structures. The tube is capable of creating a semi-infinite acoustic field due to nonreflecting acoustic termination at one end. In addition, a micro-torsional disk was created and tested for the purposes of investigating acoustic shear wave damping in microstructures, and the slip boundary conditions that occur along the wet interface when the Knudsen number becomes sufficiently large.

We discuss application of the FETI-DP linear solver within the Salinas finite element application. An overview of Salinas and of the FETI-DP solver is presented. We discuss scalability of the software on ASCI-red, Cplant and ASCI-white. Options for solution of the coarse grid problem that results from the FETI problem are evaluated. The finite element software and solver are seen to be numerically and cpu scalable on each of these platforms. In addition, the software is very robust and can be used on a large variety of finite element models.

The FETI algorithms are numerically scalable iterative domain decomposition methods. These methods are well documented for solving equations arising from the Finite Element discretization of second or fourth order elasticity problems. The one level FETI method equipped with the Dirichlet preconditioned was shown to be numerically scalable for second order elasticity problems while the two level FETI method was designed to be numerically scalable for fourth order elasticity problems. The second level coarse grid is an enriched version of the original one level FETI method with coarse grid. The coarse problem is enriched by enforcing transverse displacements to be continuous at the corner points. This coarse problem grows linearly with the number of subdomains. Current implementations use a direct solution method to solve this coarse problem. However, the current implementation gives rise to a full matrix system. This full matrix can lead to increased storage requirements especially if working within a distributed memory environment. Also, the factorization and subsequent forward/backward substitutions of the second level coarse problem becomes the dominant factor in solving the global problem as the number of subdomains becomes large (N{sub s} > 1,000). The authors introduce an alternative formulation of the two level coarse problem that leads to a sparse system better suited for a direct method. Then they show extensions to the alternate formulation that allow optional admissible constraints to be added to improve convergence. Lastly, they report on the numerical performance, parallel efficiency, memory requirements, and overall CPU time as compared to the classical two level FETI on some large scale fourth order elasticity problems.