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Erschienen in: Numerical Algorithms 3/2020

16.01.2020 | Original Paper

Fast solver of optimal control problems constrained by Ohta-Kawasaki equations

verfasst von: Rui-Xia Li, Guo-Feng Zhang, Zhao-Zheng Liang

Erschienen in: Numerical Algorithms | Ausgabe 3/2020

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Abstract

This paper is concerned with fast solver of distributed optimal control problems constrained by a nonlocal Cahn-Hilliard equation. By eliminating the control variable, a linear system on four-by-four block matrix form is obtained after discretization. Deforming the corresponding coefficient matrix into a form with special structure, an efficient preconditioner that can be utilized in an inner-outer way is designed, which leads to a fast Krylov subspace solver, that is robust with respect to mesh sizes, model parameters, and regularization parameters. Moreover, we prove that the eigenvalues of the corresponding preconditioned system are all real. Numerical experiments are presented to illustrate the robustness of the proposed solution methods.

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Metadaten
Titel
Fast solver of optimal control problems constrained by Ohta-Kawasaki equations
verfasst von
Rui-Xia Li
Guo-Feng Zhang
Zhao-Zheng Liang
Publikationsdatum
16.01.2020
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 3/2020
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00837-0

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