Obstacle Problems with Cohesion: A Hemivariational Inequality Approach and Its Efficient Numerical Solution
Obstacle Problems with Cohesion: A Hemivariational Inequality Approach and Its Efficient Numerical Solution
复制标题
内聚障碍问题：半变分不等式方法及其有效的数值解
DOI：
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发表时间：
2011
影响因子：
3.1
通讯作者：
K. Kunisch
中科院分区：
文献类型：
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作者：
M. Hintermüller;V. A. Kovtunenko;K. Kunisch
出于一个障碍问题的膜受到凝聚力，约束最小化问题，涉及一个非凸和不可微的目标功能代表总势能被认为是。相应的一阶最优性系统导致了一个半变分不等式，它也可以解释为函数空间中的一个特殊的互补问题。除了一阶最优性的分析调查，一个原始-对偶有效集求解器。它与一个半光滑牛顿法的一个正则化版本的基本问题类的极限情况。对于本文研究的数值算法，全球以及局部收敛性推导和数值验证。
Motivated by an obstacle problem for a membrane subject to cohesion forces, constrained minimization problems involving a nonconvex and nondifferentiable objective functional representing the total potential energy are considered. The associated first-order optimality system leads to a hemivariational inequality, which can also be interpreted as a special complementarity problem in function space. Besides an analytical investigation of first-order optimality, a primal-dual active set solver is introduced. It is associated to a limit case of a semismooth Newton method for a regularized version of the underlying problem class. For the numerical algorithms studied in this paper, global as well as local convergence properties are derived and verified numerically.