Return to the Table of ContentsObjective: Proposed flight vehicles such as the High-Speed Civil Transport (HSCT), require comprehensive structural analysis and design sensitivity analysis which can only be performed in sufficient detail on high-performance parallel supercomputers. Parallel methods to perform design sensitivity analysis on high-performance computers are required.
Approach: Until recently, design sensitivity analysis was performed by two methods: finite difference of two complete analyses at two different locations (one slightly perturbed from the other), or by arduously adding gradient statements throughout the code. Adding such statements to a large finite element code is complicated and subject to error . A preprocessor, called ADIFOR, written at Argonne National Laboratory, permits gradient calculations by a much more straight-forward process. This process involves defines defining the dependent and independent variables at the beginning of the program. ADIFOR then produces an augmented FORTRAN code with the gradient calculations embedded throughout it. For the Mach 2.4 it is desirable to calculate the change in displacement subject to changes in element skin thickness. ADIFOR was used and compared with the two standard methods to compute displacement gradients for the 7,000 elements in the Mach 2.4 HSCT model. To exploit the full potential of the high-performance computers, multiple processors were used on the Intel Delta at Caltech.
Accomplishment: The time to compute displacement gradients using the finite difference method was significant; from 3-6 times that taken by hand-coding as the number of processors increased from 16 to 128 processors (see figure). On 16 processor, ADIFOR took nearly double the hand-coded time, however as the number of processors was increased to 128, the time for
ADIFOR and hand-coded gradients was nearly the same. The time for both finite difference and hand-coded gradients does not reduce as the number of processors increased to 128. However, the time for ADIFOR to compute gradients continued to decrease.
Significance: The introduction of the new Automated differentiation code, ADIFOR, eliminates the need for expensive finite difference calculations to computer structural gradients. In addition, it also eliminates the time consuming and accuracy-prone technique of hand-coding gradient calculations, as no substantial time savings are realized by hand coding. The accuracy was maintained by both ADIFOR and hand-coding, but was not reliable by finite difference, which required many repetitions to assure accuracy.
Status/Plans: Although this evaluation was restricted to one design variable (thickness), ADIFOR can evaluate multiple design variables. For Mach 2.4 HSCT analyses, displacement derivatives with respect to other design variables (leading edge sweep, chord, material properties) need to be determined.
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