Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Stokes control
The authors investigate the optimal control of Navier-Stokes equations and concentrate on the arising linear system that can be compressed after eliminating the control function. They apply an efficient block matrix preconditioner and the condition number of the so precontioned matrix is bounded by 2 under certain contions. They show that their preconditioner has a better performance in terms of the number of iterations and execution time than other preconditioners on the same problem. This article is well written, structured and explained, it contains seven sections: Section 1 on Introduction, Section 2 formulates the control problems with a PDE contraint, Section 3 is about the precontioner and condition number bounds, in Section 4 a summary of some other preconditioning methods is presented, Section 5 covers a summary of computional complexity of the preconditioners, Section 6 contains the numerical results, Section 7 on Conclusion.
scientific article; zbMATH DE number 6674008
scientific article