Preconditioning for Allen–Cahn variational inequalities with non-local constraints

Luise Blank; Lavinia Sarbu; Martin Stoll

doi:10.1016/j.jcp.2012.04.035

Preconditioning for Allen–Cahn variational inequalities with non-local constraints

Luise Blank, Lavinia Sarbu, Martin Stoll

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach. © 2012 Elsevier Inc.

Original language	English (US)
Pages (from-to)	5406-5420
Number of pages	15
Journal	Journal of Computational Physics
Volume	231
Issue number	16
DOIs	https://doi.org/10.1016/j.jcp.2012.04.035
State	Published - Jun 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is partially based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.jcp.2012.04.035

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title = "Preconditioning for Allen–Cahn variational inequalities with non-local constraints",

abstract = "The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach. {\textcopyright} 2012 Elsevier Inc.",

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doi = "10.1016/j.jcp.2012.04.035",

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AU - Sarbu, Lavinia

AU - Stoll, Martin

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AB - The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach. © 2012 Elsevier Inc.

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Preconditioning for Allen–Cahn variational inequalities with non-local constraints

Abstract

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