Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems

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dc.contributor.authorHeinkenschloss, Matthiasen_US
dc.contributor.authorNguyen, Hoangen_US
dc.date.accessioned2018-06-18T17:51:08Zen_US
dc.date.available2018-06-18T17:51:08Zen_US
dc.date.issued2003-12en_US
dc.date.noteDecember 2003en_US
dc.description.abstractWe present Neumann-Neumann domain decomposition (DD) preconditioners for the solution of elliptic linear quadratic optimal control problems. The preconditioner is applied to the optimality system. A Schur complement formulation is derived that reformulates the original optimality system as a system in the state and adjoint variables restricted to the subdomain boundaries. The application of the Schur complement matrix requires the solution of subdomain optimal control problems with Dirichlet boundary conditions on the subdomain interfaces. The application of the inverses of the subdomain Schur complement matrices require the solution of subdomain optimal control problems with Neumann boundary conditions on the subdomain interfaces. Numerical tests show that the dependence of this preconditioner on mesh size and subdomain size is comparable to its counterpart applied to elliptic equations only.en_US
dc.format.extent8 ppen_US
dc.identifier.citationHeinkenschloss, Matthias and Nguyen, Hoang. "Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems." (2003) <a href="https://hdl.handle.net/1911/102013">https://hdl.handle.net/1911/102013</a>.en_US
dc.identifier.digitalTR03-17en_US
dc.identifier.urihttps://hdl.handle.net/1911/102013en_US
dc.language.isoengen_US
dc.relation.HasVersionProceedings of the 15th International Conference on Domain Decomposition, R. Kornhuber, R. H. W. Hoppe, J. Periaux, O. Pironneau, O. B. Widlund, and J. Xu (eds.), Lecture Notes in Computational Science and Engineering, Springer-Verlag, Heidelberg, 2004, pp. 589-596.en_US
dc.titleBalancing Neumann-Neumann Methods for Elliptic Optimal Control Problemsen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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