Arno Rasch

Combining source transformation and operator overloading techniques to compute derivatives for MATLAB programs

Derivatives of mathematical functions play a key role in various areas of numerical and technical computing. Many of these computations are done in MATLAB, a popular environment for technical computing providing engineers and scientists with capabilities for mathematical computing, analysis, visualization, and algorithmic development. For functions written in the MATLAB language, a novel software tool is proposed to automatically transform a given MATLAB program into another MATLAB program capable of computing not only the original function but also user-specified derivatives of that function. That is, a program transformation known as automatic differentiation is performed to change the semantics of the program in a fashion based on the chain rule of differential calculus. The crucial ingredient of the tool is a combination of source-to-source transformation and operator overloading. The overall design of the tool is described and numerical experiments are reported demonstrating the efficiency of the resulting code for a sample problem.

Sensitivity Analysis of Turbulence Models Using Automatic Differentiation

Turbulence models are examples of computer simulations that parameterize complicated phenomena and depend on artificial model parameters heuristically justified from empirical information and experimental data. To assess the confidence in the results of such a turbulence simulation, a derivative-based sensitivity analysis is carried out. The sensitivities of the flow over a backward-facing step w.r. t. parameters of the turbulence model are investigated. The standard k-

A class of OpenMP applications involving nested parallelism

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Efficient and accurate derivatives for a software process chain in airfoil shape optimization

model and the renormalization group (RNG) k-

Software supporting optimal experimental design: A case study of binary diffusion using EFCOSS

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Automatic Differentiation of the General-Purpose Computational Fluid Dynamics Package FLUENT

model are compared. Both turbulence models are implemented in the FLUENT code to which automatic differentiation is applied using the ADIFOR system. In our case studies, all turbulence models yield results that are rather sensitive to some of the modeling parameters.

Computation of Sensitivity Information for Aircraft Design by Automatic Differentiation

Today, OpenMP is the de facto standard for portable shared-memory programming supporting multiple levels of parallelism. Unfortunately, most of the current OpenMP implementations are not capable of fully exploiting more than one level of parallelism. With the increasing number of processors available in high-performance computing resources, the number of applications that would benefit from multilevel parallelism is also increasing. Applying automatic differentiation to OpenMP programs is introduced as a new class of OpenMP applications with nested parallelism.

On the Use of a Differentiated Finite Element Package for Sensitivity Analysis

When using a Newton-based numerical algorithm to optimize the shape of an airfoil with respect to certain design parameters, a crucial ingredient is the derivative of the objective function with respect to the design parameters. In large-scale aerodynamics, this objective function is an output of a computational fluid dynamics program written in a high-level programming language such as Fortran or C. Numerical differentiation is commonly used to approximate derivatives but is subject to truncation and subtractive cancellation errors. For a particular two-dimensional airfoil, we instead apply automatic differentiation to compute accurate derivatives of the lift and drag coefficients with respect to geometric shape parameters. In automatic differentiation, a given program is transformed into another program capable of computing the original function together with its derivatives. In the problem at hand, the objective function consists of a sequence of programs: a MATLAB program followed by two Fortran 77 programs. It is shown how automatic differentiation is applied to a sequence of programs while keeping the computational complexity within reasonable limits. The derivatives computed by automatic differentiation are compared with approximations based on divided differences.

EFCOSS: An interactive environment facilitating optimal experimental design

Methods for optimal experimental design aim at minimizing uncertainty in parameter estimation problems. Despite their long tradition in applied mathematics and importance in practical applications, they are currently not widely used in computational science and engineering. To make the techniques of optimal experimental design more accessible to a broader community, we introduce a novel software environment called EFCOSS and demonstrate its ease of use and versatility in two case studies of binary diffusion experiments. Through the use of a component-based software architecture, integration of automatic differentiation technology and facilitated interfacing to optimization algorithms, EFCOSS minimizes the computational overhead for the user who can thus focus on model development and analysis itself. The presented case studies focus on diffusion experiments in liquids since these experiments are typically very demanding. The use of optimal experimental design techniques allows to reduce experimental time and effort significantly.

Modeling the performance of interface contraction

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 general-purpose computational fluid dynamics software package FLUENT is transformed by automatic differentiation.