Recent Advances in Algorithmic Differentiation

1. Front Matter

   Pages i-xvii

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2. A Leibniz Notation for Automatic Differentiation

   • Bruce Christianson

   Pages 1-9

3. Sparse Jacobian Construction for Mapped Grid Visco-Resistive Magnetohydrodynamics

   • Daniel R. Reynolds, Ravi Samtaney

   Pages 11-21

4. Combining Automatic Differentiation Methods for High-Dimensional Nonlinear Models

   • James A. Reed, Jean Utke, Hany S. Abdel-Khalik

   Pages 23-33

5. Application of Automatic Differentiation to an Incompressible URANS Solver

   • Emre Özkaya, Anil Nemili, Nicolas R. Gauger

   Pages 35-45

6. Applying Automatic Differentiation to the Community Land Model

   • Azamat Mametjanov, Boyana Norris, Xiaoyan Zeng, Beth Drewniak, Jean Utke, Mihai Anitescu et al.

   Pages 47-57

7. Using Automatic Differentiation to Study the Sensitivity of a Crop Model

   • Claire Lauvernet, Laurent Hascoët, François-Xavier Le Dimet, Frédéric Baret

   Pages 59-69

8. Efficient Automatic Differentiation of Matrix Functions

   • Peder A. Olsen, Steven J. Rennie, Vaibhava Goel

   Pages 71-81

9. Native Handling of Message-Passing Communication in Data-Flow Analysis

   • Valérie Pascual, Laurent Hascoët

   Pages 83-92

10. Increasing Memory Locality by Executing Several Model Instances Simultaneously

    • Ralf Giering, Michael Voßbeck

    Pages 93-101

11. Adjoint Mode Computation of Subgradients for McCormick Relaxations

    • Markus Beckers, Viktor Mosenkis, Uwe Naumann

    Pages 103-113

12. Evaluating an Element of the Clarke Generalized Jacobian of a Piecewise Differentiable Function

    • Kamil A. Khan, Paul I. Barton

    Pages 115-125

13. The Impact of Dynamic Data Reshaping on Adjoint Code Generation for Weakly-Typed Languages Such as Matlab

    • Johannes Willkomm, Christian H. Bischof, H. Martin Bücker

    Pages 127-138

14. On the Efficient Computation of Sparsity Patterns for Hessians

    • Andrea Walther

    Pages 139-149

15. Exploiting Sparsity in Automatic Differentiation on Multicore Architectures

    • Benjamin Letschert, Kshitij Kulshreshtha, Andrea Walther, Duc Nguyen, Assefaw Gebremedhin, Alex Pothen

    Pages 151-161

16. Automatic Differentiation Through the Use of Hyper-Dual Numbers for Second Derivatives

    • Jeffrey A. Fike, Juan J. Alonso

    Pages 163-173

17. Connections Between Power Series Methods and Automatic Differentiation

    • David C. Carothers, Stephen K. Lucas, G. Edgar Parker, Joseph D. Rudmin, James S. Sochacki, Roger J. Thelwell et al.

    Pages 175-185

18. Hierarchical Algorithmic Differentiation A Case Study

    • Johannes Lotz, Uwe Naumann, Jörn Ungermann

    Pages 187-196

19. Storing Versus Recomputation on Multiple DAGs

    • Heather Cole-Mullen, Andrew Lyons, Jean Utke

    Pages 197-207

20. Using Directed Edge Separators to Increase Efficiency in the Determination of Jacobian Matrices via Automatic Differentiation

    • Thomas F. Coleman, Xin Xiong, Wei Xu

    Pages 209-219

The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the efficiency of matrix-operation derivatives, detection and exploitation of sparsity, partial separability, the treatment of nonsmooth functions, and other high-level mathematical aspects of the numerical computations to be differentiated. Applications stem from the Earth sciences, nuclear engineering, fluid dynamics, and chemistry, to name just a few. In many cases the applications in a given area of science or engineering share characteristics that require specific approaches to enable AD capabilities or provide an opportunity for efficiency gains in the derivative computation. The description of these characteristics and of the techniques for successfully using AD should make the proceedings a valuable source of information for users of AD tools.

• adjoint computation
• algorithmic differentiation
• optimization
• sensitivity analysis
• uncertainty quantification

• Shrivenham Campus, Applied Mathematics & Scientific Computi, Cranfield University, Swindon, United Kingdom

  Shaun Forth

• Mathematics and Computer Science Div., Argonne National Laboratory, Argonne, USA

  Paul Hovland, Jean Utke

• Sandia National Laboratory, Albuquerque, USA

  Eric Phipps

• , Mathematics, University of Paderborn, Paderborn, Germany

  Andrea Walther

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