A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation
Computational Physics
2022-09-08 v1
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.
Keywords
Cite
@article{arxiv.2209.03270,
title = {A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation},
author = {Alexandru Fikl and Vincent Le Chenadec and Taraneh Sayadi and Peter J. Schmid},
journal= {arXiv preprint arXiv:2209.03270},
year = {2022}
}
Comments
28 pages, 6 figures, published 10 Jun 2016