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DOI 10.5286/raltr.2008018
Persistent URL http://purl.org/net/epubs/work/43760
Record Status Checked
Record Id 43760
Title Optimal solvers for PDE-constrained optimization
Abstract Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The solution of such PDE-constrained optimization problems is usually a major computational task. Here we consider simple problems of type: distrubuted control problems in which the 2- and 3-dimensional Poisson problem is the PDE. The large dimensional linear systems which result from discretization and which need to be solved are of saddle-point type. We introduce two optimal preconditioners for these systems which lead to convergence of symmetric Krylov subspace iterative methods in a number of iterations which does not increase with the dimension of the discrete problem. These preconditioners are block structured and involve standard multigrid cycles. The optimality of the preconditioned iterative solver is proved theoretically and verified computationally in several test cases/ The theoretical proof indicates that these approaches may have much broader applicability for other partial differential equations.
Organisation CSE , CSE-NAG , STFC
Keywords PDE-constrained optimization , optimal control , linear systems , preconditioning , saddle-point problems , all-at-once methods
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2008-018. STFC, 2008. rdwRAL2008018.pdf 2008