Parallel Sensitivity Analysis of Rotor Blade Cross-sections

Designing mechanical systems in a robust way requires computational tools that not only conduct the direct analysis (aerodynamic, structural, etc.), but can also carry out a robust sensitivity analysis of the outputs with respect to the design parameters. This is especially the case for highly nonlinear, multidisciplinary systems such as helicopter rotors. The structural analysis aspect of rotor blade design has been comprehensively studied in the literature, as shown by the multiple software packages available. On the other hand, very few instances of general-purpose sensitivity analysis tools exist. This is not the case in the aerodynamics area, where most software packages already provide design sensitivities. Building upon a recently developed tool for the adjoint sensitivity analysis of beam cross-sections with respect to material properties, this paper presents a systematic evaluation of its parallel efficiency. Both OpenMP and MPI libraries are used to run the code in parallel on examples of varying size, and the results are compared with those obtained through parallel numerical differentiation (real and complex). The results show that the adjoint method is more efficient than both complex- and real-step differentiation methods, and almost as accurate as complex-step differentiation.