Blank, Luise and Garcke, Harald and Sarbu, Lavinia and Styles, Vanessa (2013) Nonlocal Allen-Cahn systems: analysis and a primal-dual active set method. IMA JOURNAL OF NUMERICAL ANALYSIS, 33 (4). pp. 1126-1155. ISSN 0272-4979,
Full text not available from this repository. (Request a copy)Abstract
We show the existence and uniqueness of a solution for the nonlocal vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and nonlocal constraints. Furthermore, we propose and analyse a primal-dual active set (PDAS) method for local and nonlocal vector-valued Allen-Cahn variational inequalities. The local convergence behaviour of the PDAS algorithm is studied by interpreting the approach as a semismooth Newton method and numerical simulations are presented demonstrating its efficiency.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; PHASE-FIELD MODEL; NUMERICAL SIMULATIONS; IMAGE SEGMENTATION; BOUNDARY MOTION; NEWTON METHOD; EQUATION; CONSTRAINTS; INEQUALITY; SEPARATION; Allen-Cahn systems; nonlocal constraints; variational inequality; vector-valued obstacle problems; primal-dual active set method; semismooth Newton method |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Mar 2020 12:58 |
| Last Modified: | 30 Mar 2020 12:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15985 |
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