PARALLEL COMPUTING CONCEPTS AND METHODS FOR FLOQUET ANALYSIS OF HELICOPTER TRIM AND STABILITY (VOL 41, PG 370, 1996)

Floquet analysis is widely used for small-order systems (say, order M < 100) to find trim results of control inputs and periodic responses, and stability results of damping levels and frequencies. Presently, ho wever, it is practical neither for design applications nor for compreh ensive analysis models that lead to large systems (M > 100); the run t ime on a sequential computer is simply prohibitive. Accordingly, a mas sively parallel Floquet analysis is developed with emphasis on large s ystems, and it is implemented on two SIMD or single-instruction, multi ple-data computers with 4096 and 8192 processors. The focus of this de velopment is a parallel shooting method with damped Newton iteration t o generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct. The eigenvalues and eigenvectors of the FTM are compu ted by a parallel QR method, and thereby stability results are generat ed. For illustration, nap and flap-lag stability of isolated rotors ar e treated by the parallel analysis and by a corresponding sequential a nalysis with the conventional shooting and QR methods; linear quasiste ady airfoil aerodynamics and a finite-stale three-dimensional wake mod el are used. Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition nu mbers of the eigenvalues and the residual errors of the eigenpairs, an d reliability figures are comparable in both the parallel and sequenti al analyses. Compared to the sequential analysis, the parallel analysi s reduces the run time of large systems dramatically, and the reductio n increases with increasing system order; this finding offers consider able promise for design and comprehensive-analysis applications.