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
![]() |
PDF
- Accepted Version
Restricted to SRO admin only Download (2MB) |
Abstract
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 |
URI: | http://sro.sussex.ac.uk/id/eprint/41122 |
View download statistics for this item
📧 Request an update