Function minimization and automatic differentiation using C++

Jerrell, Max E.

doi:10.1145/74877.74895

Cited by 2 publications

(2 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A natural approach is to use the forward mode by applying operator overloading. This is notably well-suited to C++ language [38]. This language allows to overload classical operators in a simple way [39].…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…A natural approach is to use the forward mode by applying operator overloading. This is notably well-suited with C++ language [53]. This language enables to overload classical operators in a simple way [54].…”

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

View full text Add to dashboard Cite

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.

show abstract

Function minimization and automatic differentiation using C++

Cited by 2 publications

References 4 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

Contact Info

Product

Resources

About