Parallel Eigenvalue Algorithms for Large-Scale Control-Optimization Problems

Abstract

In a recent article, the authors presented the formulation and outline of parallel algorithms for the integrated structural/control optimization problem. The solutions of the Riccati equation, open-loop system of equations, and closed loop system of equations encountered in this problem require repeated solution of the complex eigenvalue problem of a general unsymmetric matrix. This is the bottleneck for simultaneous optimization of structural and control systems and its application to design of large adaptive/smart structures. In this paper, robust parallel-vector algorithms are presented for the solution of the eigenvalue problem of a general unsymmetric real matrix employing the architecture of shared memory supercomputers such as Cray YMP 8/8128. Judicious combination of vectorization, microtasking, and macrotasking is explored in order to achieve maximum efficiency. The algorithms are applied to large matrices including one resulting from a 21-story space truss structure. It is shown that the speedup due to both vectorization and parallel processing increases with the size of the problem, thus making the algorithms particularly attractive for integrated structural/control optimization of large adaptive structures.