Asymptotic Preserving Time-Discretization of Optimal Control Problems for the Goldstein-Taylor Model

作者：Albi Giacomo; Herty Michael; Joerres Christian; Pareschi Lorenzo

来源：Numerical Methods for Partial Differential Equations, 2014, 30(6): 1770-1784.

DOI：10.1002/num.21877

• asymptotic-preserving schemes
• hyperbolic conservation laws
• implicit-explicit Runge-Kutta methods
• kinetic equations
• optimal boundary control

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, 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.

• 出版日期2014-11