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, however, it is practical neither for design applications nor for comprehensive analysis models that lead to large systems (M > 100); the run time on a sequential computer is simply prohibitive. Accordingly, a massively parallel Floquet analysis is developed with emphasis on large systems, and it is implemented on two SIMD or single-instruction, multiple-data computers with 4096 and 8192 processors. The focus of this development is a parallel shooting method with damped Newton iteration to generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct. The eigenvalues and eigenvectors of the FTM are computed by a parallel QR method, and thereby stability results are generated. For illustration, nap and flap-lag stability of isolated rotors are treated by the parallel analysis and by a corresponding sequential analysis with the conventional shooting and QR methods; linear quasisteady airfoil aerodynamics and a finite-stale three-dimensional wake model are used. Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition numbers of the eigenvalues and the residual errors of the eigenpairs, and reliability figures are comparable in both the parallel and sequential analyses. Compared to the sequential analysis, the parallel analysis reduces the run time of large systems dramatically, and the reduction increases with increasing system order; this finding offers considerable promise for design and comprehensive-analysis applications.