A new multigrid method for unconstrained parabolic optimal control problems

作者：

Highlights：

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• A new leapfrog scheme in time is proposed for solving distributed parabolic optimal control problems.

• The scheme is proved to have a second-order accuracy under suitable regularity assumptions.

• A fast multigrid iterative solver is implemented based on the structured system matrix.

• Several numerical experiments are performed to validate the theoretical analysis and proposed algorithms.

摘要

•A new leapfrog scheme in time is proposed for solving distributed parabolic optimal control problems.•The scheme is proved to have a second-order accuracy under suitable regularity assumptions.•A fast multigrid iterative solver is implemented based on the structured system matrix.•Several numerical experiments are performed to validate the theoretical analysis and proposed algorithms.

论文关键词：Parabolic optimal control,Leapfrog scheme,Finite difference,Multigrid method

论文评审过程：Received 6 August 2016, Revised 7 March 2017, Available online 13 June 2017, Version of Record 26 June 2017.

论文官网地址：https://doi.org/10.1016/j.cam.2017.06.008