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arXiv · 1307.8303

Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model

Giacomo Albi·Michael Herty·Christian Jörres·Lorenzo Pareschi
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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.

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Giacomo Albi, Michael Herty, Christian Jörres, Lorenzo Pareschi. 2013-07-31. Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model. https://arxiv.org/abs/1307.8303

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