求解单侧障碍问题的隐式投影方法

An Implicit Projection Methods for the Unilateral Obstacle Problem

利用不动点原理,得到了求解一类障碍问题的隐式投影算法.采用中心差分格式将障碍问题离散为一个线性互补问题,从而得到了基于投影形式的隐式算法.该方法的每一步迭代只需要求解一个线性方程组.用投影性质很容易证明算法收敛性.给出了具体的算法过程,数值算例结果和理论分析是一致的.

An implicit projection method based on fixed point principle is analyzed for the unitateral obstacle problem in this paper. Central difference scheme is introduced to approximate the problem. This results in a linear complementarity problem,which deduces to an implicit algorithm with projection form. Our method only needs to solve a system of linear equations for each iteration. It is very simple for us to prove the convergence results with projection properties. The detail process of the algorithm is presented, and the numerical results are in good agreement with the theory.