## Recent Advances in Algorithmic DifferentiationShaun Forth, Paul Hovland, Eric Phipps, Jean Utke, Andrea Walther 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. |

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### Contents

1 | |

Sparse Jacobian Construction for Mapped Grid ViscoResistive Magnetohydrodynamics | 10 |

Combining Automatic Differentiation Methods for HighDimensional Nonlinear Models | 23 |

Application of Automatic Differentiation to an Incompressible URANS Solver | 34 |

Applying Automatic Differentiation to the Community Land Model | 47 |

Using Automatic Differentiation to Study the Sensitivity of a Crop Model | 58 |

Efficient Automatic Differentiation of Matrix Functions | 71 |

Native Handling of MessagePassing Communication in DataFlow Analysis | 82 |

Using Directed Edge Separators to Increase Efficiency in the Determination of Jacobian Matrices via Automatic Differentiation | 208 |

An Integer Programming Approach to Optimal DerivativeAccumulation | 221 |

The Relative Cost of Function and Derivative Evaluations in the CUTEr Test Set | 232 |

Java Automatic Differentiation Tool Using Virtual OperatorOverloading | 241 |

HighOrder Uncertainty Propagation Enabled by Computational Differentiation | 251 |

Generative Programming for Automatic Differentiation | 261 |

AD in Fortran Implementation via Prepreprocessor | 273 |

An ADEnabled Optimization ToolBox in LabVIEW | 285 |

Increasing Memory Locality by Executing Several Model Instances Simultaneously | 93 |

Adjoint Mode Computation of Subgradients for McCormickRelaxations | 103 |

Evaluating an Element of the Clarke Generalized Jacobian of a Piecewise Differentiable Function | 114 |

The Impact of Dynamic Data Reshaping on Adjoint Code Generation for WeaklyTyped Languages Such as Matlab | 127 |

On the Efficient Computation of Sparsity Patterns for Hessians | 139 |

Exploiting Sparsity in Automatic Differentiation on Multicore Architectures | 150 |

Automatic Differentiation Through the Use of HyperDual Numbers for Second Derivatives | 163 |

Connections Between Power Series Methods and Automatic Differentiation | 174 |

Hierarchical Algorithmic Differentiation A Case Study | 187 |

Storing Versus Recomputation on Multiple DAGs | 197 |

CasADi A Symbolic Package for Automatic Differentiation and Optimal Control | 296 |

Efficient Expression Templates for Operator OverloadingBased Automatic Differentiation | 309 |

Computing Derivatives in a Meshless Simulation Using Permutations in ADOLC | 320 |

Lazy KWay Linear Combination Kernels for Efficient Runtime Sparse Jacobian Matrix Evaluations in C++ | 333 |

Implementation of Partial Separability in a SourcetoSource Transformation AD Tool | 343 |

Editorial Policy | 354 |

Lecture Notesin Computational Science and Engineering
| 356 |

Monographs in Computational Science
and Engineering | 360 |

### Other editions - View all

Recent Advances in Algorithmic Differentiation Shaun Forth,Paul Hovland,Eric Phipps,Jean Utke,Andrea Walther No preview available - 2014 |

Recent Advances in Algorithmic Differentiation Shaun Forth,Paul Hovland,Eric Phipps,Jean Utke,Andrea Walther No preview available - 2012 |

### Common terms and phrases

adjoint mode ADOL-C Advances in Algorithmic Algorithmic Differentiation applied approach approximation arguments array automatic differentiation Berlin Heidelberg 2012 biclique Bischof calculation CasADi components computational graph Computational Science constraints data structure data-flow analysis defined derivative computation e-mail efficient elemental Engineering 87 equations example expression template expression tree flow graph Fortran forward mode function evaluation function f gradient graph coloring Griewank Hessian Hovland implementation input iterations Jacobian Jacobian matrix LabVIEW Lecture Notes Leibniz notation linear loop LVAD Mathematics Matlab matrix method multiple Naumann nodes nonlinear Notes in Computational OpenAD OpenMP operator overloading optimization output parallel parameters performance polynomial problem propagation reverse mode runtime scalar Science and Engineering Sect SIAM simulation Software solution solver source code source transformation sparse sparsity pattern SPLC subgradient subroutine tangent-linear TAPENADE techniques template metaprogramming tensor tool Utke values vector vertex elimination