Domain decomposition methods for linear-quadratic elliptic optimal control problems

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dc.contributor.advisorHeinkenschloss, Matthias
dc.creatorNguyen, Hoang Q.
dc.date.accessioned2009-06-04T08:10:50Z
dc.date.available2009-06-04T08:10:50Z
dc.date.issued2005
dc.description.abstractThis thesis is concerned with the development of domain decomposition (DD) based preconditioners for linear-quadratic elliptic optimal control problems (LQ-EOCPs), their analysis, and numerical studies of their performance on model problems. The solution of LQ-EOCPs arises in many applications, either directly or as subproblems in Newton or Sequential Quadratic Programming methods for the solution of nonlinear elliptic optimal control problems. After a finite element discretization, convex LQ-EOCPs lead to large scale symmetric indefinite linear systems. The solution of these large systems is a very time consuming step and must be done iteratively, typically with a preconditioned Krylov subspace method. Developing good preconditioners for these linear systems is an important part of improving the overall performance of the solution method. The DD preconditioners for LQ-EOCPs studied in this thesis are extensions of overlapping and nonoverlapping Neumann-Neumann DD preconditioners applied to single elliptic partial differential equations (PDEs). In our case, DD is applied on the optimization level. In particular, the proposed preconditioners require the parallel solution of subdomain optimal control problems that are related to restrictions of the original LQ-EOCP to a subdomain. Numerical results on several test problems have shown that the new preconditioners are effective. Their performance relative to decreases in finite element mesh size or increase in number of subdomains seem to be numerically comparable to that of overlapping and Neumann-Neumann preconditioners for single PDEs. Remarkably, the proposed preconditioners seem to be rather insensitive to control regularization parameters. For overlapping methods, theoretical results are provided to support the numerical observations.
dc.format.extent134 p.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS MATH. SCI. 2005 NGUYEN
dc.identifier.citationNguyen, Hoang Q.. "Domain decomposition methods for linear-quadratic elliptic optimal control problems." (2005) Diss., Rice University. <a href="https://hdl.handle.net/1911/18848">https://hdl.handle.net/1911/18848</a>.
dc.identifier.urihttps://hdl.handle.net/1911/18848
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectMathematics
dc.titleDomain decomposition methods for linear-quadratic elliptic optimal control problems
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematical Sciences
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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