A study of solution algorithms for shape design sensitivity analysis on a supermini computer with an attached array processor

This paper presents a study and comparison of shape design sensitivity analysis algorithms that are based on the continuum adjoint variable method, the continuum direct differentiation method, and the finite difference method, implemented on a supermini computer with an attached array processor. The basic algorithms and their differences in evaluating shape design sensitivity coefficients are outlined. A solution method for solving a system of equations, using a general sparse storage technique, is used for numerical implementation of shape design sensitivity analysis. It is found that computing shape design sensitivity coefficients using the direct differentiation method is significantly more efficient than using the adjoint variable method or the finite difference method. A detailed performance evaluation of the methods, using an attached array processor, is presented. The performance of the attached array processor, compared to a supermini computer is shown to depend strongly on the type of computations to be carried out. When only parts of a program are running on an attached array processor, the CPU time distribution among the different subroutines of the program can change significantly, compared to using the host processor only.