[1] 
Christian H. Bischof, H. Martin Bücker, Arno Rasch, Emil Slusanschi, and
Bruno Lang.
Automatic differentiation of the generalpurpose computational fluid
dynamics package FLUENT.
ASME J. Fluids Engrg., 129(5):652658, May 2007.
Derivatives are a crucial ingredient to a broad variety of computational techniques in science and engineering. While numerical approaches for evaluating derivatives suffer from truncation error, automatic differentiation is accurate up to machine precision. The term automatic differentiation comprises a set of techniques for mechanically transforming a given computer program to another one capable of evaluating derivatives. A common misconception about automatic differentiation is that this technique only works on local pieces of fairly simple code. Here, it is shown that automatic differentiation is not only applicable to small academic codes, but scales to advanced industrial software packages. In particular, the generalpurpose computational fluid dynamics software package FLUENT is transformed by automatic differentiation.

[2] 
C. H. Bischof, H. M. Bücker, B. Lang, A. Rasch, and J. W. Risch.
Extending the functionality of the generalpurpose finite element
package SEPRAN by automatic differentiation.
Int. J. Numer. Meth. Engng., 58(14):22252238, December
2003.
From an abstract point of view, a numerical simulation implements a mathematical function that produces some output from some given input. Derivatives (or sensitivities) of the function's output with respect to its input can be obtainedfree from truncation errorby using a technique called automatic differentiation. Given a computer code in a highlevel programming language like Fortran, C, or, C++, automatic differentiation generates another code capable of computing not only the original function but also its derivatives. Thus, the application of automatic differentiation significantly extends the functionality of a simulation package. For instance, automatic differentiation enables, in a completely mechanical fashion, the usage of derivativebased optimization algorithms where the evaluation of the objective function comprises some given largescale engineering simulation. In this note, the automatic differentiation tool Adifor is used to transform the general purpose finite element package SEPRAN.In doing so, we automatically translate the given 400,000 lines of Fortran 77 into a new program consisting of 600,000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical differentiation and quantify its advantages in terms of accuracy and computational efficiency for a standard fluid flow problem.

[3] 
Christian H. Bischof, H. Martin Bücker, Bruno Lang, and Arno Rasch.
Solving largescale optimization problems with EFCOSS.
Advances Engrg. Software, 34(10):633639, October 2003.
Derivatives play a prominent role in many areas of scientific computing. Traditionally, divided differences are employed to approximate derivatives, leading to results of dubious quality at often great computational expense. Automatic differentiation (AD), by contrast, is a powerful technique for accurately evaluating derivatives of functions described in a highlevel programming language. AD requires little human effort and produces derivatives without truncation error. Although there is no conceptual difference between small and large codes, applying AD to programs with hundreds of thousands lines of code is still a challenging task and requires a robust AD tool. We report on recent accomplishments of AD applied to the general purpose finite element package SEPRAN consisting of approximately 400,000 lines of Fortran77 and its integration into a prototype problem solving environment called EFCOSS supporting interoperability of simulation codes with optimization software using AD technology.

[4] 
Christian H. Bischof, H. Martin Bücker, Bruno Lang, and Arno Rasch.
An interactive environment for supporting the paradigm shift from
simulation to optimization.
Scientific Prog., 11(4):263272, 2003.
Numerical simulation is a powerful tool in science and engineering, and it is also used for optimizing the design of products and experiments rather than only for reproducing the behavior of scientific and engineering systems. In order to reduce the number of simulation runs, the traditional “trial and error” approach for finding neartooptimum design parameters is more and more replaced with efficient numerical optimization algorithms. Done by hand, the coupling of simulation and optimization software is tedious and errorprone. In this note we introduce a software environment called EFCOSS (Environment For Combining Optimization and Simulation Software) that facilitates and speeds up this task by doing much of the required work automatically. Our framework includes support for automatic differentiation providing the derivatives required by many optimization algorithms. We describe the process of integrating the widely used computational fluid dynamics package FLUENT and a MINPACK1 least squares optimizer into EFCOSS and follow a sample session solving a data assimilation problem.

[5] 
H. Martin Bücker, Bruno Lang, Arno Rasch, and Christian H. Bischof.
Computing sensitivities of the electrostatic potential by automatic
differentiation.
Comput. Phys. Comm., 147(12):720723, August 2002.
Given a computer model for the electrostatic potential in an Lshaped region with media of different dielectric permeabilities in two subregions, we are interested in the robustness of the simulation by identifying the rate of change of the potential with respect to a change in the permeabilities. Such sensitivity analyses, assessing the rate of change of certain model outputs implied by varying certain model inputs, can be carried out by computing the corresponding partial derivatives. In largescale computational physics, the underlying computer model is typically available as a complicated computer code in a highlevel programming language such as Fortran, C, or C++. To obtain accurate and efficient derivatives of functions given in this form, we use a technique called automatic or algorithmic differentiation. Unlike numerical differentiation based on divided differences, derivatives generated by automatic differentiation are free of truncation error. Here, the automatic differentiation tool Adifor is used to transform the given computer modelimplemented with the general purpose finite element package SEPRANinto a new computer code computing the derivatives of the electrostatic potential with respect to the dielectric permeabilities. In doing so, we automatically translate 400,000 lines of Fortran 77 into a new program consisting of 600,000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical differentiation and quantify its advantages in terms of accuracy and computational efficiency.

[6] 
Christian H. Bischof, H. Martin Bücker, Bruno Lang, Arno Rasch, and
Jakob W. Risch.
A CORBAbased environment for coupling largescale simulation and
optimization software.
In H. R. Arabnia, editor, Proceedings of the International
Conference on Parallel and Distributed Processing Techniques and
Applications, PDPTA'2001, Las Vegas, Nevada, June 2528, 2001, volume 1,
pages 6872. CSREA Press, 2001.
Simulation is an essential part in computational science and engineering. Since the underlying physical models become more and more complex, the adjustment of certain model parameters (“parameter identification”) is often a nontrivial task and should be addressed by means of efficient numerical optimization algorithms. We describe an environment for coupling simulation and optimization software. The modular architecture of the system supports easy modification of the problem configuration, including the exchange of software components. Therefore our tool is wellsuited for rapid prototyping of optimization problems.

[7] 
H. Martin Bücker, Bruno Lang, Arno Rasch, and Christian H. Bischof.
From analytic to automated derivatives: A case study of the
electrostatic potential.
In Algorithms and Software for Mobile Communications, Proc. 10th Aachen Symposium on Signal Theory, Aachen, Germany, September 2021,
2001, pages 255260, Berlin, 2001. VDE Verlag.
Given a largescale engineering simulation, one is often interested in the derivatives of certain program outputs with respect to certain input parameters, e.g., for sensitivity analysis. From an abstract point of view, the computer program defines a mathematical function whose derivatives are sought. In this note, two cases are investigated where the underlying functions are given by the solution of different twodimensional electrostatic potential problems. For a rectangular region, the function and its derivatives can be derived analytically. For a function based on an Lshaped region, the function is computed by a simulation code and its derivatives are obtained by automatic differentiation. In general, this powerful technique is applicable if a function is given in the form of a computer program in a highlevel programming language such as Fortran, C, or C++. In contrast to numerical differentiation providing approximations based on divided differences, the derivatives computed by automatic differentiation are accurate. Furthermore, automatic differentiation is also shown to be computationally efficient.

[8] 
Christian H. Bischof, H. Martin Bücker, Bruno Lang, Arno Rasch, and
Jakob W. Risch.
On the use of a differentiated finite element package for sensitivity
analysis.
In Vassil N. Alexandrov, Jack J. Dongarra, Benjoe A. Juliano,
René S. Renner, and C. J. Kenneth Tan, editors, Computational
Science  ICCS 2001 International Conference San Francisco, CA, May 2001,
Proceedings, Part I, volume 2073 of LNCS, pages 795801, Berlin,
2001. Springer.
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 largescale 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.
