## 留言板

 引用本文: 饶玲. 单调迭代结合虚拟区域法求解非线性障碍问题[J]. 应用数学和力学, 2018, 39(4): 485-492.
RAO Ling. Monotone Iterations Combined With Fictitious Domain Methods for Numerical Solution of Nonlinear Obstacle Problems[J]. Applied Mathematics and Mechanics, 2018, 39(4): 485-492. doi: 10.21656/1000-0887.380109
 Citation: RAO Ling. Monotone Iterations Combined With Fictitious Domain Methods for Numerical Solution of Nonlinear Obstacle Problems[J]. Applied Mathematics and Mechanics, 2018, 39(4): 485-492.

## 单调迭代结合虚拟区域法求解非线性障碍问题

##### doi: 10.21656/1000-0887.380109

###### 作者简介:饶玲(1968—), 女, 副教授, 博士(E-mail: lingrao@sina.com).
• 中图分类号: O357.41

## Monotone Iterations Combined With Fictitious Domain Methods for Numerical Solution of Nonlinear Obstacle Problems

• 摘要: 讨论了二阶半线性椭圆方程障碍问题的数值求解问题.用单调迭代算法求解障碍问题，并用改进的虚拟区域法求解相关的不规则区域上具有Dirichlet边界条件的椭圆方程.在计算过程中，传统的有限元离散会导致用扩展区域规则网格计算不规则物体边界上积分的困难.为了克服此困难，给出了一种新的基于有限差分的算法，从而使得偏微分快速算法可用.算法结构简单，易于编程实现.对有扩散和增长障碍的logistic人口模型数值模拟说明算法可行且高效.
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##### 出版历程
• 收稿日期:  2017-04-24
• 修回日期:  2017-08-09
• 刊出日期:  2018-04-15

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