SUMMARYProblems of the form Z( )u( ) = f( ), where Z is a given matrix, f is a given vector, and is a circular frequency or circular frequency-related parameter arise in many applications including computational structural and fluid dynamics, and computational acoustics and electromagnetics. The straightforward solution of such problems for fine increments of is computationally prohibitive, particularly when Z is a large-scale matrix. This paper discusses an alternative solution approach based on the efficient computation of u and its successive derivatives with respect to at a few sample values of this parameter, and the reconstruction of the solution u( ) in the frequency band of interest using multi-point Padé approximants. This computational methodology is illustrated with applications from structural dynamics and underwater acoustic scattering. In each case, it is shown to reduce the CPU time required by the straightforward approach to frequency sweep computations by two orders of magnitude.

We present Salinas, a scalable implicit software application for the finite element static and dynamic analysis of complex structural real-world systems. This relatively complete engineering software with more than 100,000 lines of ¤ ¥ ¥ code and a long list of users sustains 292.5 Gflop/s on 2,940 ASCI Red processors, and 1.16 Tflop/s on 3,375 ASCI White processors.

An a posteriori error estimator is developed for the eigenvalue analysis of three-dimensional heterogeneous elastic structures. It constitutes an extension of a well-known explicit estimator to heterogeneous structures. We prove that our estimates are independent of the variations in material properties and independent of the polynomial degree of finite elements. Finally, we study numerically the effectivity of this estimator on several model problems.

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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.