CAJ | 학술논문

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。
이역학중적시간의뢰마찰문제위배경，취제이류포물형변분불등식구조료구역분해산법。통과대함유시간적도수항채용반리산화은격식방법，장포물형변분불등식전화위타원형변분불등식，대유한원리산중불용역계산적불가미항채용수치적분근사，사득계산간화，침대기등개적우화문제급출료구역분해산법병진행료수렴성증명。문중수치산례진일보설명료해방법적가행성여유효성。
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 for-mulated 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 cal-culation 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.