An Effective Computational Scheme for the Optimal Control of Wave Equations * * This project was supported in part by NSFC 11301262 and NSF 1021203, 1419028 of the United States.

摘要

Abstract: We proposed and analyzed a new leapfrog finite difference scheme in time for solving the first-order necessary optimality systems arising in optimal control of wave equations. With a standard second-order central finite difference scheme in space, the full discretization is proved to be unconditionally convergent with a second-order accuracy. Moreover, based on its favorable structure, an efficient preconditioned iterative method is provided for solving the discretized unsymmetric sparse linear system. Numerical examples are presented to confirm our theoretical conclusions and demonstrate the promising performance of our proposed algorithms.