H. M. Bücker

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.

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

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.

Parallel programming in computational science: an introductory practical training course for computer science undergraduates at Aachen University

Parallel programming of high-performance computers has emerged as a key technology for the numerical solution of large-scale problems arising in computational science and engineering (CSE). The authors believe that principles and techniques of parallel programming are among the essential ingredients of any CSE as well as computer science curriculum. Today, opinions on the role and importance of parallel programming are diverse. Rather than seeing it as a marginal beneficial skill optionally taught at the graduate level, we understand parallel programming as crucial basic skill that should be taught as an integral part of the undergraduate computer science curriculum. A practical training course developed for computer science undergraduates at Aachen University is described. Its goal is to introduce young computer science students to different parallel programming paradigms for shared and distributed memory computers as well as to give a first exposition to the field of computational science by simple, yet carefully chosen sample problems.