Abstract
We develop a class of V‐cycle‐type multilevel restricted additive Schwarz (RAS) methods and study the numerical and parallel performance of the new fully coupled methods for solving large sparse Jacobian systems arising from the discretization of some optimization problems constrained by nonlinear partial differential equations. Straightforward extensions of the one‐level RAS to multilevel do not work due to the pollution effects of the coarse interpolation. We then introduce, in this paper, a pollution removing coarse‐to‐fine interpolation scheme for one of the components of the multicomponent linear system and show numerically that the combination of the new interpolation scheme with the RAS smoothed multigrid method provides an effective family of techniques for solving rather difficult PDE‐constrained optimization problems. Numerical examples involving the boundary control of incompressible Navier–Stokes flows are presented in detail.
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.
