Abstract
A parallel domain decomposition algorithm for solving an optimal control problem governed by a parabolic partial differential equation is proposed. This algorithm is based upon non-overlapping domain decomposition. In every iteration, the global problem is reduced to solve simultaneously some implicit subproblems on many sub-domains by using explicit flux approximations near inner-boundaries at each time-step. Both a priori error bounds of optimal orders and optimal rates of convergence for the iterative schemes are presented. Numerical experiments are also performed to verified the theoretical analysis.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 13dz2260400
Funding statement: This work was supported in part by the National Natural Science Foundation of China under grants 11571115, 11171113 and Science and Technology Commission of Shanghai Municipality, grant No. 13dz2260400.
Acknowledgment
The authors would like to express their sincere thanks to the editor and referees for their very helpful comments and suggestions, which greatly improved the quality of this paper.
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