Citation

Subramanian S, Venkataratnam S, Gaonkar GH. Math. Comput. Model. 2001; 33(10-11): 1155-1176.

Copyright

(Copyright © 2001, Elsevier Publishing)

DOI

10.1016/S0895-7177(00)00305-8

PMID

unavailable

Abstract

A parallel shooting method based on the fast-Floquet theory and damped Newton iteration is developed to predict helicopter trim (control settings and periodic responses) and the equivalent Floquet transition matrix; the parallel eigenanalysis of this matrix by a library subroutine leads to the damping levels and frequencies. The parallel fast-Floquet analysis comprises these shooting and eigenanalysis methods. It is compared with three other analyses: the parallel analysis based on Floquet theory and the serial analyses based on Floquet and fast-Floquet theories. The comparison is based on the growth of run time with the model order or number of states and on computational reliability figures such as eigenvalue condition numbers. The parallel fast-Floquet analysis is further investigated on the basis of performance measures such as speedup and efficiency, which, respectively, quantify how the parallel run time compares with the predicted uniprocessor run time and how effectively the processors are used. Isolated-rotor models with nearly 600 states are treated with dynamic stall and wake; both rigid flap-lag and elastic flap-lag-torsion motions are considered. Even with the fast-Floquet theory, the serial run time still is prohibitive for models with more than 100 states; indeed it grows between quadratically and cubically with the model order. By contrast, in the parallel fast-Floquet analysis, the run time and its growth with the order can be controlled by increasing the number of processors on the basis of speedup and efficiency.