Leapfrog multigrid methods for parabolic optimal control problems

Buyang Li, Jun Liu, Mingqing Xiao

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review


A second-order leapfrog finite difference scheme in time is proposed to solve the first-order necessary optimality systems arising from parabolic optimal control problems. Different from classical approximation, the proposed leapfrog scheme appears to be unconditionally stable. More importantly, the developed leapfrog scheme provides a well-structured discrete algebraic system and allows us to establish a fast linear solver under the multigrid framework. The unconditional stability of the scheme is proved under the L2 norm. Numerical results show that our presented scheme significantly outperforms the widely used Crank-Nicolson scheme and the resultant fast solver demonstrates a mesh-independent convergence rate as well as a desirable feature of linear time complexity.
Original languageEnglish
Title of host publicationProceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015
Number of pages7
ISBN (Electronic)9781479970179
Publication statusPublished - 1 Jan 2015
Externally publishedYes
Event27th Chinese Control and Decision Conference, CCDC 2015 - Qingdao Haiqing Hotel, Qingdao, China
Duration: 23 May 201525 May 2015


Conference27th Chinese Control and Decision Conference, CCDC 2015


  • Finite difference
  • Leapfrog scheme
  • Multigrid method
  • Parabolic optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Management Science and Operations Research


Dive into the research topics of 'Leapfrog multigrid methods for parabolic optimal control problems'. Together they form a unique fingerprint.

Cite this