## Domain decomposition preconditioners for linear–quadratic elliptic optimal control problems (2004)

Citations: | 16 - 4 self |

### BibTeX

@TECHREPORT{Heinkenschloss04domaindecomposition,

author = {Matthias Heinkenschloss and Hoang Nguyen},

title = {Domain decomposition preconditioners for linear–quadratic elliptic optimal control problems},

institution = {},

year = {2004}

}

### OpenURL

### Abstract

ABSTRACT. We develop and analyze a class of overlapping domain decomposition (DD) preconditioners for linear-quadratic elliptic optimal control problems. Our preconditioners utilize the structure of the optimal control problems. Their execution requires the parallel solution of subdomain linear-quadratic elliptic optimal control problems, which are essentially smaller subdomain copies of the original problem. This work extends to optimal control problems the application and analysis of overlapping DD preconditioners, which have been used successfully for the solution of single PDEs. We prove that for a class of problems the performance of the two-level versions of our preconditioners is independent of the mesh size and of the subdomain size. 1.

### Citations

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Citation Context ...∗ − w) = 0, so w is a solution to (2.4). □ The transformed problem (2.24) may be solved by using a linear iterative method. The operator T is nonsymmetric, in general, and we solve (2.24) using GMRES =-=[46]-=-, QMR [26] or any other method for nonsymmetric systems [45]. In Section 3.3, we show that the operator T has structure that allows the application of the symmetric QMR (sQMR) method [27, 28]. Let A(·... |

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decomposition algorithms with small overlap
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Citation Context ...assumption one can show that the constant C0a in Lemma 3.5 satisfies (3.34) C 2 0a ≤ ˜ C 2 0a(1 + H/δ), where ˜ C0a is independent of H, h (and α) and δ is the amount of overlap defined in (3.7) (see =-=[23]-=-, [48, Thm. 2].) □16 MATTHIAS HEINKENSCHLOSS AND HOANG NGUYEN Lemma 3.6. There exists a constant C0q > 0 (independent of H, h, and α) such that for , with all u h ∈ U h , there exists a two-level dec... |

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