求解自由边界问题的自适应投影方法

A Self-adaptive Projection Algorithm for Solving Free Boundary Problem

对一类自由边界问题,提出了基于线性互补问题的自适应投影算法.采用有限差分格式将自由边界问题离散为一个线性互补问题,然后用自适应投影迭代算法求其数值解,该方法在迭代过程中自动调整参数,达到加快收敛速度的目的,每一步迭代只需要求解一个线性方程组.给出了具体算法过程,并利用投影性质得到了它们的收敛性分析.最后用数值算例对算法验证,与已有的算法比较,结果表明:参数对自适应投影算法影响较小,该方法收敛速度更快.

According to a class of free boundary problems,a self-adaptive projection algorithm based on linear complementarity problem is put forward,The free boundary problem is discretized by the finite difference method and formulated as a linear complementarity problem,then the self-adaptive projection iteration algorithm is used to obtain its numerical solution,this method automatically adjusts parameters in iterative process to attain the goal of accelerating the convergence speed,and this method only needs to solve a system of linear equations for each iteration. The detailed algorithm process is given,their convergence analysis is obtained by projection properties.Finally,the numerical examples are used to test the algorithm,compared with the existed algorithms,this method has more rapid convergence speed because the parameter has little effect on the self-adaptive projection algorithm.