371 RWTH Publication No: 230470        2013        IGPM371.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 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 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)