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On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraints

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Domain Decomposition Methods in Science and Engineering XVI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 55))

Abstract

We consider preconditioned Uzawa iterations for a saddle point problem with inequality constraints as arising from an implicit time discretization of the Cahn-Hilliard equation with an obstacle potential. We present a new class of preconditioners based on linear Schur complements associated with successive approximations of the coincidence set. In numerical experiments, we found superlinear convergence and finite termination.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 14, Berlin, D-14195, Germany

    Carsten Gräser & Ralf Kornhuber

Authors
  1. Carsten Gräser
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  2. Ralf Kornhuber
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Editor information

Editors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012-1185, New York, NY, USA

    Olof B. Widlund

  2. Department of Applied Physics & Mathematics, Columbia University, 500 W. 120th Street, MC 4701, 10027, New York, NY, USA

    David E. Keyes

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Gräser, C., Kornhuber, R. (2007). On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraints. In: Widlund, O.B., Keyes, D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34469-8_8

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