Solution of a parabolic optimal control problem using fictitious domain method

  • Lapin A.
  • Laitinen E.
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Publication date
March 2020
Journal
issn:2190-3018

Abstract

© 2019, Springer Nature Switzerland AG. A linear-quadratic parabolic optimal control problem in a cylinder with spatial curvilinear domain is solved numerically by means of embedding fictitious domain method and finite difference approximation on a regular orthogonal mesh. A regularized mesh problem in a parallelepiped containing initial space-time domain is constructed. This problem is loaded by additional constraints for control and state functions in the fictitious subdomain. The restriction of its solution to the initial domain tends to the solution of the initial problem as regularization parameter tends to zero. Efficiently implementable finite difference methods can be used for the state and co-state problems of the new optimal contr...

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