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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 ..."
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. 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...
Automatic Differentiation and NavierStokes Computations
"... this paper, we discuss how AD can be used to enhance a compressible NavierStokes solver. Section 2 describes the twodimensional NavierStokes model and solver used in our studies. Section 3 gives a brief introduction to source transformation tools for automatic differentiation. Section 4 discusses ..."
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this paper, we discuss how AD can be used to enhance a compressible NavierStokes solver. Section 2 describes the twodimensional NavierStokes model and solver used in our studies. Section 3 gives a brief introduction to source transformation tools for automatic differentiation. Section 4 discusses how derivatives computed using AD can be used for shape optimization. Section 5 explains how an explicit solver can be transformed into an implicit solver using a Jacobian computed using AD. Section 6 briefly describes how AD might be used in optimal control. We conclude with a summary of our results and a discussion of how insight into the highlevel mathematics of a computation can greatly reduce the cost of derivative computations using AD.
Application of the automatic differentiation tool  Odyssee to a system of thermohydraulic equations
"... The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat exchangers is examined. More specifically, the challenge is to differentiate Thyc1D, a 1D mockup of the 3D code Thyc implementing these equations, by means of the ..."
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The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat exchangers is examined. More specifically, the challenge is to differentiate Thyc1D, a 1D mockup of the 3D code Thyc implementing these equations, by means of the automatic differentiator Odyssee with as few manual interventions as possible. The program to differentiate contains 23 subroutines, including linear solvers and blackbox functions, whose code is not available. 1
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"... Application of the automatic differentiation tool Odyssée to a system of thermohydraulic equations1 C. Duval2and P. Erhard2and Ch. Faure3and J.Ch. Gilbert4 Abstract. The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat ..."
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Application of the automatic differentiation tool Odyssée to a system of thermohydraulic equations1 C. Duval2and P. Erhard2and Ch. Faure3and J.Ch. Gilbert4 Abstract. The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat exchangers is examined. More specifically, the challenge is to differentiate Thyc1D, a 1D mockup of the 3D code Thyc implementing these equations, by means of the automatic differentiator Odyssée with as few manual interventions as possible. The program to differentiate contains23subroutines, including linear solvers and blackbox functions, whose code is not available. 1
Optimization of aerodynamic and acoustic
"... performance of supersonic civil transports ..."
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Automatic differentiation: an implementation in Maple
, 1998
"... In this report we present our implementation of automatic differentiation (ie. differentiation of functions represented by programs) in Maple: it fully supports the reverse mode and extends differentiation to cope with common linearalgebra operators. It also makes use of standard features of CAS to ..."
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In this report we present our implementation of automatic differentiation (ie. differentiation of functions represented by programs) in Maple: it fully supports the reverse mode and extends differentiation to cope with common linearalgebra operators. It also makes use of standard features of CAS to determine conflicts, optimize computation sequences and memory allocation. Keywords: automatic differentiation, source transformation, optimization, linear algebra operators, computer algebra system. Introduction Automatic Differentiation (AD) has gained an increasing interest over the last decade [13, 9, 4, 8, 16, 15, 1] because computation of derivatives is involved in almost all numerical problems (optimization, adaptative stepsize integration, . . . ) and because divided differences are not accurate nor numerically stable. Most automatic differentiators are designed to deal with numerical codes written in fortran77 (Odyss'ee [16], Adifor [4]) or C (AdiC). It may seem weird to differ...