17 research outputs found
09061 Abstracts Collection -- Combinatorial Scientific Computing
From 01.02.2009 to 06.02.2009, the Dagstuhl Seminar 09061 ``Combinatorial Scientific Computing \u27\u27 was held in Schloss Dagstuhl -- Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Short Tutorial: Getting Started With Ipopt in 90 Minutes
Ipopt is an open-source software package for large-scale nonlinear optimization. This tutorial gives a short introduction that should allow the reader to install and test the package on a UNIX-like system, and to run simple examples in a short period of time
Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE
In an effort to increase the versatility of finite element codes, we explore
the possibility of automatically creating the Jacobian matrix necessary for the
gradient-based solution of nonlinear systems of equations. Particularly, we aim
to assess the feasibility of employing the automatic differentiation tool
TAPENADE for this purpose on a large Fortran codebase that is the result of
many years of continuous development. As a starting point we will describe the
special structure of finite element codes and the implications that this code
design carries for an efficient calculation of the Jacobian matrix. We will
also propose a first approach towards improving the efficiency of such a
method. Finally, we will present a functioning method for the automatic
implementation of the Jacobian calculation in a finite element software, but
will also point out important shortcomings that will have to be addressed in
the future.Comment: 17 pages, 9 figure
Algorithmic differentiation applied to the optimal calibration of a shallow water model
International audienceThe information on sensitivity provided by derivatives is indispensable in many fields of science. In numerical analysis, computing the accurate value of the derivatives of a function can be a challenge. The classical Finite Differences (FD) method is a simple solution to implement when estimating the value of a derivative. However, it remains highly sensitive numerically and costly in calculation time. Conversely, the Algorithmic Differentiation Method (AD) is a powerful tool for calculating the derivatives of a function described by a computer program. Whatever the complexity of the algorithms implemented in the expression of a function, AD calculates its derivative accurately and reduces development efforts. This article presents the contribution of AD in comparison to FD in the problem of calibrating an industrial class 1D shallow water model. Model calibration is performed by a deterministic mathematical optimiser requiring accurate calculation of the sensitivity of the water surface profile in relation to the friction on a river bed. Two comparative real test cases are presented. They permit validating the better performance expected from AD as a tool used to obtain optimal calibration.Les informations de sensibilité fournies par les dérivées sont indispensables en science dans de nombreux domaines. En analyse numérique, calculer très précisément la valeur des dérivées d'une fonction d'un simulateur physique peut relever du défi. La méthode classique des Différences Finies (DF) est une solution simple à mettre en oeuvre pour estimer la valeur d'une dérivée. Cependant, elle reste très sensible numériquement et coûteuse en temps de calcul. A contrario la méthode de la Différentiation Algorithmique (DA) est une aide puissante pour le calcul des dérivées d'une fonction décrite au moyen d'un programme informatique. Quelle que soit la complexité des algorithmes mis en oeuvre dans l'expression d'une fonction, elle calcule précisément sa dérivée en minimisant les efforts de développement. Cet article montre l'apport de la DA en comparaison des DF sur le problème du calage d'un modèle hydraulique à surface libre 1D de classe industrielle. Le calage du modèle est réalisé par un optimiseur mathématique déterministe nécessitant le calcul précis de la sensibilité de la cote d'eau par rapport au frottement sur le fond de la rivière. Deux cas tests réels de comparaison sont présentés. Ils permettent de valider la supériorité attendue de la DA comme outil d'aide à l'obtention d'un calage optimal
Sparse Automatic Differentiation for Large-Scale Computations Using Abstract Elementary Algebra
Most numerical solvers and libraries nowadays are implemented to use
mathematical models created with language-specific built-in data types (e.g.
real in Fortran or double in C) and their respective elementary algebra
implementations. However, built-in elementary algebra typically has limited
functionality and often restricts flexibility of mathematical models and
analysis types that can be applied to those models. To overcome this
limitation, a number of domain-specific languages with more feature-rich
built-in data types have been proposed. In this paper, we argue that if
numerical libraries and solvers are designed to use abstract elementary algebra
rather than language-specific built-in algebra, modern mainstream languages can
be as effective as any domain-specific language. We illustrate our ideas using
the example of sparse Jacobian matrix computation. We implement an automatic
differentiation method that takes advantage of sparse system structures and is
straightforward to parallelize in MPI setting. Furthermore, we show that the
computational cost scales linearly with the size of the system.Comment: Submitted to ACM Transactions on Mathematical Softwar
Elimination Techniques for Algorithmic Differentiation Revisited
All known elimination techniques for (first-order) algorithmic
differentiation (AD) rely on Jacobians to be given for a set of relevant
elemental functions. Realistically, elemental tangents and adjoints are given
instead. They can be obtained by applying software tools for AD to the parts of
a given modular numerical simulation. The novel generalized face elimination
rule proposed in this article facilitates the rigorous exploitation of
associativity of the chain rule of differentiation at arbitrary levels of
granularity ranging from elemental scalar (state of the art) to multivariate
vector functions with given elemental tangents and adjoints. The implied
combinatorial Generalized Face Elimination problem asks for a face elimination
sequence of minimal computational cost. Simple branch and bound and greedy
heuristic methods are employed as a baseline for further research into more
powerful algorithms motivated by promising first test results. The latter can
be reproduced with the help of an open-source reference implementation
Some highlights on Source-to-Source Adjoint AD
International audienceAlgorithmic Differentiation (AD) provides the analytic derivatives of functions given as programs. Adjoint AD, which computes gradients, is similar to Back Propagation for Machine Learning. AD researchers study strategies to overcome the difficulties of adjoint AD, to get closer to its theoretical efficiency. To promote fruitful exchanges between Back Propagation and adjoint AD, we present three of these strategies and give our view of their interest and current status