On the Use of a Differentiated Finite Element Package for Sensitivity Analysis.

Abstract

Derivatives are ubiquitous in various areas of computational science including sensitivity analysis and parameter optimization of computer models. Among the various methods for obtaining derivatives, automatic differentiation (AD) combines freedom from approximation errors, high performance, and the ability to handle arbitrarily complex codes arising from large-scale scientific investigations. In this note, we show how AD technology can aid in the sensitivity analysis of a computer model by considering a classic fluid flow experiment as an example. To this end, the software tool ADIFOR implementing the AD technology for functions written in Fortran 77 was applied to the large finite element package SEPRAN.@ Differentiated versions of SEPRAN enable sensitivity analysis for a wide range of applications, not only from computational fluid dynamics.