A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation

A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation

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 p...

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Veröffentlicht in:arXiv.org 2022-09
Hauptverfasser: Fikl, Alexandru, Vincent Le Chenadec, Sayadi, Taraneh, Schmid, Peter J
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Sprache:eng
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Algorithms
Burgers equation
Conservation laws
Exact solutions
Nonlinear systems
Optimization
Physics - Computational Physics
Riemann solver
Sensitivity analysis
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Vincent Le Chenadec
Sayadi, Taraneh
Schmid, Peter J
description 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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subjects Algorithms
Burgers equation
Conservation laws
Exact solutions
Nonlinear systems
Optimization
Physics - Computational Physics
Riemann solver
Sensitivity analysis
title A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation
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