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.

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

ALBI, Giacomo;PARESCHI, Lorenzo
2014

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.
2014
Albi, Giacomo; Michael, Herty; Christian, Jörres; Pareschi, Lorenzo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2187013
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