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Some Preconditioning Techniques for Saddle Point Problems

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Model Order Reduction: Theory, Research Aspects and Applications

Part of the book series: Mathematics in Industry ((TECMI,volume 13))

Saddle point problems arise frequently in many applications in science and engineering, including constrained optimization, mixed finite element formulations of partial differential equations, circuit analysis, and so forth. Indeed the formulation of most problems with constraints gives rise to saddle point systems. This paper provides a concise overview of iterative approaches for the solution of such systems which are of particular importance in the context of large scale computation. In particular we describe some of the most useful preconditioning techniques for Krylov subspace solvers applied to saddle point problems, including block and constraint preconditioners.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia, 30322, USA

    Michele Benzi

  2. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    Andrew J. Wathen

Authors
  1. Michele Benzi
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  2. Andrew J. Wathen
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Editor information

Editors and Affiliations

  1. Physical Design Methods – Mathematics, NXP Semiconductors Corporate I&T/DTF/Design Methods, High Tech Campus 37, 5656, AE Eindhoven, The Netherlands

    Wilhelmus H. A. Schilders

  2. Physical Design Mothods, NXP Semiconductors Corporate I&T/DTF/Design Methods, High Tech Campus 37, 5656, AE Eindhoven, The Netherlands

    Henk A. van der Vorst

  3. Mathematical Institute, Utrecht University, Budapestlaan 6, 3508, TA Utrecht, The Netherlands

    Joost Rommes

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Benzi, M., Wathen, A.J. (2008). Some Preconditioning Techniques for Saddle Point Problems. In: Schilders, W.H.A., van der Vorst, H.A., Rommes, J. (eds) Model Order Reduction: Theory, Research Aspects and Applications. Mathematics in Industry, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78841-6_10

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