| 求解双侧障碍问题的自适应投影算法 |
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| 引用本文： | 程兰,张霖森,张守贵. 求解双侧障碍问题的自适应投影算法[J]. 重庆师范大学学报(自然科学版), 2023, 40(4): 23-31 |
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| 作者姓名： | 程兰 张霖森 张守贵 |
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| 作者单位： | 重庆师范大学 数学科学学院， 重庆 401331 |
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| 基金项目： | 国家自然科学基金面上项目(No.11971085); 重庆市自然科学基金面上项目(No.cstc2020jcyj-msxmX0066);重庆市研究生教育优质课程项目(No.201949); 重庆市研究生教育教学改革研究项目(No.yjg213071) |
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| 摘 要： | 对一类具有双侧障碍的自由边界问题得到求它的数值解的自适应投影迭代算法。采用有限差分法将障碍问题离散为有限维双侧障碍问题,该问题等价于一个新的投影不动点问题,可得到双侧障碍问题的投影算法。并通过迭代数据自动调整投影算法的参数,加快其收敛速度。从而提出求解双侧障碍问题的自适应投影算法,给出算法过程和收敛性分析。理论分析和数值算例结果都表明该算法的有效性。
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| 关 键 词： | 双侧障碍问题；有限差分；投影算法；自适应法则 |
A Self-Adaptive Projection Algorithm for the Bilateral Obstacle Problem |
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| CHENG Lan,ZHANG Linsen,ZHANG Shougui. A Self-Adaptive Projection Algorithm for the Bilateral Obstacle Problem[J]. Journal of Chongqing Normal University:Natural Science Edition, 2023, 40(4): 23-31 |
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| Authors: | CHENG Lan ZHANG Linsen ZHANG Shougui |
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| Affiliation: | School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China |
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| Abstract: | An adaptive projection iterative algorithm for solving a class of free boundary problems with bilateral obstacles was developed. The finite difference method was used to discretize the obstacle problem into a finite dimensional two-sided obstacle problem, which was equivalent to a new projection fixed point problem, and the projection algorithm for the two-sided obstacle problem was obtained. The parameters are automatically adjusted by iterating data to accelerate convergence. An adaptive projection algorithm for solving bilateral obstacle problem was proposed, and the algorithm process and convergence analysis were given. Both theoretical analysis and numerical examples demonstrate the effectiveness of the proposed algorithm. |
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| Keywords: | bilateral disorder finite difference projection algorithm self-adaptive rule |
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