Nonlocal Allen-Cahn systems: analysis and a primal-dual active set method
Nonlocal Allen-Cahn systems: analysis and a primal-dual active set method
复制标题
非局部 Allen-Cahn 系统：分析和原始对偶活动集方法
DOI：
10.1093/imanum/drs039
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发表时间：
2013
影响因子：
2.1
通讯作者：
Blank L
中科院分区：
文献类型：
--
作者：
Blank L
我们证明了非局部向量值Allen-Cahn变分不等式解的存在性和唯一性，该变分不等式在局部和非局部约束下包含拉格朗日乘子.此外，我们提出并分析了一个原始-对偶有效集（PDAS）方法的局部和非局部向量值Allen-Cahn变分不等式。PDAS算法的局部收敛行为进行了研究，通过解释的方法作为一个半光滑牛顿法和数值模拟证明其效率。
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.