Solution of linear systems from an optimal control problem arising in wind simulation

Several solution strategies for a class of large, sparse linear systems with a block 2 × 2 structure arising from the finite element discretization of an optimal control problem in wind simulation are introduced and analyzed. Block preconditioners and a sparse direct solver on the original coupled s...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2010-12, Vol.17 (6), p.895-915
Main Authors: Benzi, M., Ferragut, L., Pennacchio, M., Simoncini, V.
Format: Article
Language:English
Subjects:
AMG
block preconditioning
Blocking
Computer simulation
eigenvalue bounds
Linear systems
Mathematical analysis
Mathematical models
Optimal control
Schur complement
Solvers
sparse direct solvers
Strategy
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Summary:Several solution strategies for a class of large, sparse linear systems with a block 2 × 2 structure arising from the finite element discretization of an optimal control problem in wind simulation are introduced and analyzed. Block preconditioners and a sparse direct solver on the original coupled system are compared with a preconditioned GMRES iteration applied to a reduced system (Schur complement). Theoretical and experimental results demonstrate the effectiveness of the reduced system approach. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:1070-5325
1099-1506
1099-1506
DOI:10.1002/nla.679