Abstract
ABSTRACTOptimal control problems for PDEs arise in many important applications. A main step in the solution process is the solution of the arising linear system, where the crucial point is usually finding a proper preconditioner. We propose both proper block diagonal and more involved preconditioners, and derive mesh independent superlinear convergence of the preconditioned GMRES iterations based on a compact perturbation property of the underlying operators.
Highlights
Optimal control problems for partial di erential equations (PDEs), where we want to steer the solution of the modeled process close to some desired target solution by use of a control function, arise in many important applications
A main step in the solution process is the solution of the arising linear system, where the crucial point is usually nding a proper preconditioner
We propose both proper block diagonal and more involved preconditioners
Summary
Optimal control problems for partial di erential equations (PDEs), where we want to steer the solution of the modeled process close to some desired target solution by use of a control function, arise in many important applications. Such problems have been dealt with in several publications, such as [2, 3, 10, 16, 21], see the references therein. Earlier publications have mostly dealt with problems when the control and observation domains coincide, in recent papers they may be allowed to be di erent. KARÁTSON new results are presented in detail for a time-independent distributed control problem, nally some related problems are mentioned in the last section
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
