Results 1  10
of
105
Latin Hypercube Sampling and the propagation of uncertainty in analyses of complex systems,” Reliability Engineering and System Safety
, 2003
"... ..."
ADIC: An Extensible Automatic Differentiation Tool for ANSIC
, 1997
"... . In scientific computing, we often require the derivatives @f=@x of a function f expressed as a program with respect to some input parameter(s) x, say. Automatic differentiation (AD) techniques augment the program with derivative computation by applying the chain rule of calculus to elementary oper ..."
Abstract

Cited by 95 (13 self)
 Add to MetaCart
(Show Context)
. In scientific computing, we often require the derivatives @f=@x of a function f expressed as a program with respect to some input parameter(s) x, say. Automatic differentiation (AD) techniques augment the program with derivative computation by applying the chain rule of calculus to elementary operations in an automated fashion. This article introduces ADIC (Automatic Differentiation of C), a new AD tool for ANSIC programs. ADIC is currently the only tool for ANSIC that employs a sourcetosource program transformation approach; that is, it takes a C code and produces a new C code that computes the original results as well as the derivatives. We first present ADIC "by example" to illustrate the functionality and ease of use of ADIC and then describe in detail the architecture of ADIC. ADIC incorporates a modular design that provides a foundation for both rapid prototyping of better AD algorithms and their sharing across AD tools for different languages. A component architecture call...
What color is your Jacobian? Graph coloring for computing derivatives
 SIAM REV
, 2005
"... Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian and Hessian matrices using either finite differences or automatic differentiation. Several coloring problems occur in this context, depending on whether the matrix is a Jacobian or a Hessian, and on the specific ..."
Abstract

Cited by 59 (11 self)
 Add to MetaCart
(Show Context)
Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian and Hessian matrices using either finite differences or automatic differentiation. Several coloring problems occur in this context, depending on whether the matrix is a Jacobian or a Hessian, and on the specifics of the computational techniques employed. We consider eight variant vertexcoloring problems here. This article begins with a gentle introduction to the problem of computing a sparse Jacobian, followed by an overview of the historical development of the research area. Then we present a unifying framework for the graph models of the variant matrixestimation problems. The framework is based upon the viewpoint that a partition of a matrixinto structurally orthogonal groups of columns corresponds to distance2 coloring an appropriate graph representation. The unified framework helps integrate earlier work and leads to fresh insights; enables the design of more efficient algorithms for many problems; leads to new algorithms for others; and eases the task of building graph models for new problems. We report computational results on two of the coloring problems to support our claims. Most of the methods for these problems treat a column or a row of a matrixas an atomic entity, and partition the columns or rows (or both). A brief review of methods that do not fit these criteria is provided. We also discuss results in discrete mathematics and theoretical computer science that intersect with the topics considered here.
Multidisciplinary Design Optimization Techniques: Implications and Opportunities for Fluid Dynamics Research
 JAROSLAW SOBIESZCZANSKISOBIESKI AND RAPHAEL T. HAFTKA ”MULTIDISCIPLINARY AEROSPACE DESIGN OPTIMIZATION: SURVEY OF RECENT DEVELOPMENTS,” 34TH AIAA AEROSPACE SCIENCES MEETING AND EXHIBIT
, 1999
"... A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the de ..."
Abstract

Cited by 24 (0 self)
 Add to MetaCart
A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASA/ISSMO Symposia on Multidisciplinary Analysis and Optimization, the MDO technical community focuses on vehicle and system design issues. This paper provides an overview of the MDO technology field from a fluid dynamics perspective, giving emphasis to suggestions of specific applications of recent MDO technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.
On the Future of Problem Solving Environments

, 2000
"... In this paper we review the current state of the problem solving environment (PSE) field and make projections for the future. First we describe the computing context, the definition of a PSE and the goals of a PSE. The stateoftheart is summarized along with sources (books, bibliographics, web sit ..."
Abstract

Cited by 23 (2 self)
 Add to MetaCart
In this paper we review the current state of the problem solving environment (PSE) field and make projections for the future. First we describe the computing context, the definition of a PSE and the goals of a PSE. The stateoftheart is summarized along with sources (books, bibliographics, web sites) of more detailed information. The principal components and paradigms for building PSEs are presented. The discussion of the future is given in three parts: future trends, scenarios for 2010/2025, and research
Preliminary results from the application of automated code generation to CFL3D
 Proceedings, 12th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and
, 1998
"... This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widelyused computational fluid dynamics flow solver to compute derivatives. These preliminary results with this augmented code suggest that, even in its infancy, the automated adjoi ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widelyused computational fluid dynamics flow solver to compute derivatives. These preliminary results with this augmented code suggest that, even in its infancy, the automated adjoint code generator can accurately and efficiently deliver derivatives for use in transonic Eulerbased aerodynamic shape optimization problems with hundreds to thousands of independent design variables.
A user’s guide to solving dynamic stochastic games using the homotopy method
, 2008
"... This paper provides a stepbystep guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homot ..."
Abstract

Cited by 19 (9 self)
 Add to MetaCart
This paper provides a stepbystep guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method.
On the implementation of automatic differentiation tools
 HigherOrder and Symbolic Computation
, 2004
"... Abstract. Automatic differentiation is a semantic transformation that applies the rules of differential calculus to source code. It thus transforms a computer program that computes a mathematical function into a program that computes the function and its derivatives. Derivatives play an important ro ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Automatic differentiation is a semantic transformation that applies the rules of differential calculus to source code. It thus transforms a computer program that computes a mathematical function into a program that computes the function and its derivatives. Derivatives play an important role in a wide variety of scientific computing applications, including numerical optimization, solution of nonlinear equations, sensitivity analysis, and nonlinear inverse problems. We describe the forward and reverse modes of automatic differentiation and provide a survey of implementation strategies. We describe some of the challenges in the implementation of automatic differentiation tools, with a focus on tools based on source transformation. We conclude with an overview of current research and future opportunities.
Algorithms and Design for a SecondOrder Automatic Differentation Module
, 1997
"... This paper describes approaches to computing secondorder derivatives with automatic differentiation (AD) based on the forward mode and the propagation of univariate Taylor series. Performance results are given which show the speedup possible with these techniques. We also describe a new source tran ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
This paper describes approaches to computing secondorder derivatives with automatic differentiation (AD) based on the forward mode and the propagation of univariate Taylor series. Performance results are given which show the speedup possible with these techniques. We also describe a new source transformation AD module for computing secondorder derivatives of C and Fortran codes and the underlying infrastructure used to create a languageindependent translation tool.