Discrete adjoint computations for relaxation Runge-Kutta methods
Abstract
Relaxation Runge-Kutta methods reproduce a fully discrete dissipation (or conservation) of entropy for entropy stable semi-discretizations of nonlinear conservation laws. In this paper, we derive the discrete adjoint of relaxation Runge-Kutta schemes, which are applicable to discretize-then-optimize approaches for optimal control problems. Furthermore, we prove that the derived discrete relaxation Runge-Kutta adjoint preserves time-symmetry when applied to linear skew-symmetric systems of ODEs. Numerical experiments verify these theoretical results while demonstrating the importance of appropriately treating the relaxation parameter when computing the discrete adjoint.
Cite
@article{arxiv.2107.11408,
title = {Discrete adjoint computations for relaxation Runge-Kutta methods},
author = {Mario J. Bencomo and Jesse Chan},
journal= {arXiv preprint arXiv:2107.11408},
year = {2021}
}
Comments
39 pages, 7 figures (not including subfigures). Submitted to the Journal of Computational Physics