Non-local Allen-Cahn systems: analysis and a primal-dual active set method

Blank, Luise, Garcke, Harald, Sarbu, Lavinia and Styles, Vanessa (2013) Non-local Allen-Cahn systems: analysis and a primal-dual active set method. IMA Journal of Numerical Analysis, 33 (4). pp. 1126-1155. ISSN 0272-4979

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We show existence and uniqueness of a solution for the non-local vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and non-local constraints. Furthermore, we propose and analyze a primal-dual active set method for local and non-local vector-valued Allen-Cahn variational inequalities. The local convergence behaviour of the primal-dual active set algorithm is studied by interpreting the approach as a semi-smooth Newton method and numerical simulations are presented demonstrating its efficiency.

Item Type: Article
Keywords: Allen–Cahn systems nonlocal constraints variational inequality vector-valued obstacle problems primal–dual active set method semismooth Newton method
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Vanessa Styles
Date Deposited: 08 Mar 2013 14:15
Last Modified: 02 Jul 2019 22:21

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