H. Martin Bücker

Advances in Automatic Differentiation

This collection covers advances in automatic differentiation theory and practice. Computer scientists and mathematicians will learn about recent developments in automatic differentiation theory as well as mechanisms for the construction of robust and powerful automatic differentiation tools. Computational scientists and engineers will benefit from the discussion of various applications, which provide insight into effective strategies for using automatic differentiation for inverse problems and design optimization.

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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Automatic Differentiation for Computational Finance

model and the renormalization group (RNG) k-

Bringing together automatic differentiation and OpenMP

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A parallel strategy for a level set simulation of droplets moving in a liquid medium

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.

Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids

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.

Binding nested OpenMP programs on hierarchical memory architectures

Automatic differentiation (AD) is a powerful technique allowing to compute derivatives of a function given by a (potentially very large) piece of code. The basic principles of AD and some available tools implementing this technology are reviewed. AD is superior to divided differences because AD-generated derivative values are free of approximation errors, and superior to symbolic differentiation because code of very high complexity can be handled, in contrast to computer algebra systems whose applicability is limited to rather simple functions. In addition, the cost for computing gradients of scalar-valued functions with either divided differences or symbolic differentiation grows linearly with the number of variables, whereas the so-called reverse mode of AD can compute such gradients at constant cost.

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

Derivatives of almost arbitrary functions can be evaluated efficiently by automatic differentiation whenever the functions are given in the form of computer programs in a high-level programming language such as Fortran, C, or C++. Furthermore, in contrast to numerical differentiation where derivatives are approximated, automatic differentiation generates derivatives that are accurate up to machine precision. The so-called forward mode of automatic differentiation computes derivatives by carrying forward a gradient associated with each intermediate variable simultaneously with the evaluation of the function itself. It is shown how software tools implementing the technology of automatic differentiation can benefit from simple concepts of shared memory programming to parallelize the gradient operations. The feasibility of our approach is demonstrated by numerical experiments. They were performed with a code that was generated automatically by the Adifor system and augmented with OpenMP directives.

Parallel Minimum

The simulation of two-phase flow problems involving two time-dependent spatial regions with different physical properties is computationally hard. The numerical solution of such problems is complicated by the need to represent the movement of the interface. The level set approach is a front-capturing method representing the position of the interface implicitly by the root of a suitably defined function. We describe a parallel adaptive finite element simulation based on the level set approach. For freely sedimenting n-butanol droplets in water, we quantify the parallel performance on a Xeon-based cluster using up to 256 processes.