Automatic differentiation using almost any language

Jerrell, Max E.

doi:10.1145/1057967.1057968

Cited by 12 publications

(4 citation statements)

References 3 publications

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“…This language allows to overload classical operators in a simple way [39]. Notice that AD by operator overloading has already been implemented since a long time in other classical languages [40]. Interested readers can refer to [41] for a good review of AD techniques.…”

Section: Ad With Operator Overloading Techniquementioning

confidence: 99%

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Lejeune

Boudaoud

Potier‐Ferry

et al. 2013

Numerical Meth Engineering

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In general, nonlinear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two nonlinear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, while the second one is a nonlinear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex nonlinear problems, a computation technique based on Automatic Differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher-order derivatives of these constitutive laws and thereafter to define Taylor series that are the basis of the continuation technique called Asymptotic Numerical Method. The algorithm is about the same with an explicit or an implicit constitutive relation. In the modeling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code: the user is only required to define the tool geometry and the computer is able to get the higher-order derivatives.

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Section: Ad With Operator Overloading Techniquementioning

confidence: 99%

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Lejeune

Boudaoud

Potier‐Ferry

et al. 2013

Numerical Meth Engineering

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“…This language enables to overload classical operators in a simple way [54]. Notice that AD by operator overloading has already been implemented for a long time in other classical languages [55].…”

Section: Automatic Differentiation (Ad)mentioning

confidence: 99%

Object-oriented design to automate a high order non-linear solver based on asymptotic numerical method

Lejeune

Béchet²,

Boudaoud³

et al. 2012

Advances in Engineering Software

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The Manitoo library is devoted to the resolution of analytical non-linear problems using a high order method called asymptotic numerical method. We describe here the Object Oriented design of this library and especially the choices made to obtain a quite generic and flexible numerical solver.Through classical examples, we present a comparison with some existing tools implemented in Matlab and Fortran 77.

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“…Fortunately, there is a numerical tool called "automatic differentiation" or "differentiation arithmetic" which employs recursion to give successively higher order derivatives at a point c. Detailed descriptions of automatic differentiation can be found In , , , Jerrell (1989), and .…”

Section: Discussionmentioning

confidence: 99%

“…-[Va"(X^),Ab"(X^)] be the interval hull of U X"(y-), where V and A denote directed downward and upward roundings, respectively. Using the argument which gave us that the interval extension of (u^(c^))j is inclusion , , , , and Jerrell (1989)…”

Section: \(Yi Wmentioning

confidence: 99%

Numerical methods for self-validating computations of probabilities and percentiles in selected distributions using interval analysis

Wang

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Comparison of algorithms for computing probabilities and percentiles is often carried out In an effort to Identify the best algorithm for various applications. One requirement when conducting comparative studies is some useable source of "satisfactory approximations to correct answers" to use as a basis when making accuracy comparisons. This paper reports success in applying elements of interval analysis to obtain a self-validating computational method for Blvariate Normal Probabilities. Results from applying this method can be used to provide a basis for accuracy studies of algorithms for Blvariate Normal probabilities. A study to compare several methods for computing probabilities over rectangles for this probability distribution, using the self-validated base values, was carried out. The paper reports a choice of best method.

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Automatic differentiation using almost any language

Cited by 12 publications

References 3 publications

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Object-oriented design to automate a high order non-linear solver based on asymptotic numerical method

Numerical methods for self-validating computations of probabilities and percentiles in selected distributions using interval analysis

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