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SIAMSC
2010

Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems

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Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems
In this paper, we describe block matrix algorithms for the iterative solution of large scale linear-quadratic optimal control problems arising from the optimal control of parabolic partial differential equations over a finite control horizon. We describe three iterative algorithms. The first algorithm employs a CG method for solving a symmetric positive definite reduced linear system involving only the unknown control variables. This system can be solved using the CG method, but requires double iteration. The second algorithm is designed to avoid double iteration by introducing an auxiliary variable. It yields a symmetric indefinite system and a positive definite block preconditioner. The third algorithm uses a symmetric positive definite block diagonal preconditioner for the saddle point system and is based on the parareal algorithm. Theoretical results show that the preconditioned algorithm has optimal convergence properties and parallel scalability. Numerical experiments are ...
Tarek P. Mathew, Marcus Sarkis, Christian E. Schae
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SIAMSC
Authors Tarek P. Mathew, Marcus Sarkis, Christian E. Schaerer
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