Abstract
AbstractIn CFD, Newton solvers have the attractive property of quadratic convergence but they require derivative information. An efficient way of computing derivatives is by algorithmic differentiation (AD) also known as automatic differentiation or computational differentiation. AD allows us to evaluate derivatives, usually at a cheap cost, without the truncation errors associated with finite‐differencing. Recently, efficient and reliable AD tools for evaluating derivatives have been published. In this paper, we use some of the best AD tools currently available to build up the system Jacobian involved in the solution of a finite‐volume parabolized Navier–Stokes (PNS) solver. Our aim is to direct scientists and engineers confronted with the calculation of derivatives to the use of AD and to highlight those AD tools that they should try. Moreover, we introduce an AD tool that produces Jacobian code that runs usually twice as fast as that from conventional AD tools. We further show that the use of AD increases the performance of a Newton‐like solver for the PNS equations. Copyright © 2005 John Wiley & Sons, Ltd.
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