Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model
Numerical Analysis
2013-08-05 v2 Optimization and Control
Abstract
We consider the development of implicit-explicit time integration schemes for optimal control problems governed by the Goldstein-Taylor model. In the diffusive scaling this model is a hyperbolic approximation to the heat equation. We investigate the relation of time integration schemes and the formal Chapman-Enskog type limiting procedure. For the class of stiffly accurate implicit-explicit Runge-Kutta methods (IMEX) the discrete optimality system also provides a stable numerical method for optimal control problems governed by the heat equation. Numerical examples illustrate the expected behavior.
Keywords
Cite
@article{arxiv.1307.8303,
title = {Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model},
author = {Giacomo Albi and Michael Herty and Christian Jörres and Lorenzo Pareschi},
journal= {arXiv preprint arXiv:1307.8303},
year = {2013}
}