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Fast Preconditioned Solver for Truncated Saddle Point Problem in Nonsmooth Cahn–Hilliard Model

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Recent Advances in Computational Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 655))

Abstract

The discretization of Cahn–Hilliard equation with obstacle potential leads to a block \(2 \times 2\) non-linear system, where the (1, 1) block has a non-linear and non-smooth term. Recently a globally convergent Newton Schur method was proposed for the non-linear Schur complement corresponding to this non-linear system. The proposed method is similar to an inexact active set method in the sense that the active sets are first approximately identified by solving a quadratic obstacle problem corresponding to the (1, 1) block of the block \(2 \times 2\) system, and later solving a reduced linear system by annihilating the rows and columns corresponding to identified active sets. For solving the quadratic obstacle problem, various optimal multigrid like methods have been proposed. In this paper, we study a block tridiagonal Schur complement preconditioner for solving the reduced linear system. The preconditioner shows robustness with respect to problem parameters and truncations of domain.

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Acknowledgments

This research was carried out in the framework of Matheon supported by Einstein Foundation Berlin.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195, Berlin, Germany

    Pawan Kumar

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  1. Pawan Kumar
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Correspondence to Pawan Kumar .

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Editors and Affiliations

  1. Department of Parallel Algorithms, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Kumar, P. (2016). Fast Preconditioned Solver for Truncated Saddle Point Problem in Nonsmooth Cahn–Hilliard Model. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 655. Springer, Cham. https://doi.org/10.1007/978-3-319-40132-4_10

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  • DOI: https://doi.org/10.1007/978-3-319-40132-4_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40131-7

  • Online ISBN: 978-3-319-40132-4

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