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Preprint-No.: <   371   >   Published in: July 2013   PDF-File: IGPM371_k.pdf
Title:Asymptotic Preserving Time–Discretization of Optimal Control Problems for the Goldstein–Taylor Model
Authors:Giacomo Albi, Michael Herty, Christian Jörres, Lorenzo Pareschi
Abstract:
We consider the development of implicit-explicit time integration schemes for opti- mal 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 rela- tion of time integration schemes and the formal Chapman-Enskog type limiting proce- dure. 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:IMEX Runge–Kutta methods, optimal boundary control, hyperbolic conservation laws, asymptotic analysis
DOI: 10.1002/num.21877
Publication:Numerical methods for partial differential equations
30(6), 1770-1784 (2014)