一种求解双障碍问题的迭代解法

摘要

An iterative algorithm for solving the double obstacles problem is proposed basing on the finite difference method,which obtains the approximate solution by solving 2 subproblems including a locally upper obstacle subproblem and a locally lower obstacle subproblem alternately.In the iterative process,the solution is approximated by enlarging the contact regions of the upper and lower obstacle successively.The iterative sequences generated by each subproblem are monotonic convergent respectively.The iterative method proposed is convergent globally and stops in a finite number of iterations.Numerical experiments show that the algorithm puts up a good performance.%基于有限差分法,给出了一种求解双障碍问题的迭代方法,通过交替求解上障碍和下障碍两个子问题得到双障碍问题的近似解.迭代过程中,与上、下障碍的接触面积连续扩大并渐逼近问题的解.各子问题产生的迭代序列分别单调收敛.所构造的迭代方法全局收敛并有限步终止,数值实验显示该算法有较好的性能.