Improving derivative performance for CFD by using simplified recurrences

Many scientific programs generate solutions to partial differential equations by using an iterative process to reduce a residual quantity. Straightforward differentiation of these programs yields an iterative recurrence that involves both the derivative of the residual, and the derivative of the original process. For a certain class of these problems, the derivative recurrence can be simplified to avoid computing the derivative of the original process. A program implementing a simplified recurrence should run faster than its fully differentiated counterpart, since it avoids the redundant computation. In this paper we demonstrate a method for using automatic differentiation tools to facilitate the production of simplified derivative recurrence programs. We illustrate our technique by constructing and validating a simplified derivative version of the OVERFLOW computational fluid dynamics program using the ADIFOR automatic differentiation tool.