Solution of a Parabolic Optimal Control Problem Using Fictitious Domain Method
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 control problem. The optimal control problem is solved by an iterative method, the rate of its convergence is proved. Numerical tests demonstrate the efficiency of the proposed approach for solving formulated problem.
KeywordsParabolic optimal control Fictitious domain method Finite-difference approximation
The work of the first author was supported by Russian Foundation of Basic Researches, project 16-01-00408, and by Academy of Finland, project 318175. The work of the second author was supported by Academy of Finland, project 318303.
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