A comprehensive study of adjoint-based optimization of non-linear systems with application to Burgers’ equation

Alexandru Fikl; Vincent Le Chenadec; Taraneh Sayadi; Peter J. Schmid

doi:10.2514/6.2016-3805

A comprehensive study of adjoint-based optimization of non-linear systems with application to Burgers’ equation

Alexandru Fikl, Vincent Le Chenadec, Taraneh Sayadi, Peter J. Schmid

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Scopus citations

Abstract

In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers” equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.

Original language	English (US)
Title of host publication	46th AIAA Fluid Dynamics Conference
Publisher	American Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)	9781624104367
DOIs	https://doi.org/10.2514/6.2016-3805
State	Published - Jan 1 2016
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2022-09-13

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@inproceedings{0f2fefaf1d3a48baa2999bbac97c133e,

title = "A comprehensive study of adjoint-based optimization of non-linear systems with application to Burgers{\textquoteright} equation",

abstract = "In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers” equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.",

author = "Alexandru Fikl and {Le Chenadec}, Vincent and Taraneh Sayadi and Schmid, {Peter J.}",

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month = jan,

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doi = "10.2514/6.2016-3805",

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A comprehensive study of adjoint-based optimization of non-linear systems with application to Burgers’ equation. / Fikl, Alexandru; Le Chenadec, Vincent; Sayadi, Taraneh et al.
46th AIAA Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics Inc, AIAA, 2016.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Fikl, Alexandru

AU - Le Chenadec, Vincent

AU - Sayadi, Taraneh

AU - Schmid, Peter J.

N1 - Generated from Scopus record by KAUST IRTS on 2022-09-13

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers” equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.

AB - In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers” equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.

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DO - 10.2514/6.2016-3805

M3 - Conference contribution

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BT - 46th AIAA Fluid Dynamics Conference

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

ER -

A comprehensive study of adjoint-based optimization of non-linear systems with application to Burgers’ equation

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