时间依赖摩擦问题的区域分解法及其收敛性分析  

Domain decomposition method for solution of time dependent friction problem and its convergence analysis

作　　者：刘乐春[1] 陈娟[1] 郝琪伟[2] 仪明旭[1] 陈一鸣[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004 [2]燕山大学电气工程学院,河北秦皇岛066004

出　　处：《燕山大学学报》2013年第3期260-264,共5页Journal of Yanshan University

基　　金：河北省自然科学基金资助项目(A2012203047);秦皇岛市科学技术研究与发展计划项目(201201B019)

摘　　要：以力学中的时间依赖摩擦问题为背景,就第二类抛物型变分不等式构造了区域分解算法。通过对含有时间的导数项采用半离散和隐格式方法,将抛物型变分不等式转化为椭圆型变分不等式,对有限元离散中不容易计算的不可微项采用数值积分近似,使得计算简化,针对其等价的优化问题给出了区域分解算法并进行了收敛性证明。文中数值算例进一步说明了该方法的可行性与有效性。In this paper,domain decomposition algorithm is constructed to solve the solution of the second type parabolic variational inequalities on the background of time dependent friction problem in mechanics.The parabolic variational inequality can be formulated as an elliptic variational inequality by using semi-discretization and implicit method in time,then the numerical integrals is adopted to approximate the non-differentiable term which cannot be calculated easily in finite element discretization,and the calculation becomes more convenient.Based on the equivalent optimization problem,the domain decomposition method was proposed and its convergence is also given.The numerical example is presented to illustrate the feasibility and effectiveness of the method.

关 键 词：时间依赖摩擦 第二类变分不等式 区域分解法 收敛性分析 

分 类 号：O175.2[理学—数学]