Publication: Improving Derivative Performance for CFD by Using Simplified Recurrences
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Improving Derivative Performance for CFD by Using Simplified Recurrences

- incollection -
 

Area
Computational Fluid Dynamics

Author(s)
Alan Carle , Mike Fagan

Published in
Computational Differentiation: Techniques, Applications, and Tools

Editor(s)
Martin Berz, Christian Bischof, George Corliss, Andreas Griewank

Year
1996

Publisher
SIAM

Abstract
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.

Cross-References
Berz1996CDT

AD Tools
ADIFOR

AD Theory and Techniques
Fixpoint

BibTeX
@INCOLLECTION{
         Carle1996IDP,
       author = "Alan Carle and Mike Fagan",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "Improving Derivative Performance for {CFD} by Using Simplified Recurrences",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "343--351",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Carle1996IDP",
       crossref = "Berz1996CDT",
       abstract = "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 {\em 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.",
       keywords = "Simplified recurrence, incremental iterative, CFD, OVERFLOW, ADIFOR.",
       ad_area = "Computational Fluid Dynamics",
       ad_tools = "ADIFOR",
       ad_theotech = "Fixpoint",
       year = "1996"
}


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