摘要
参数差分线法是一种求解曲线围域上偏微分方程的有效算法,但是在退化线处存在边界条件"缺失"的问题。该文"找到"了退化线处的边界条件,解决了这个问题。文中以二维Poisson方程为例,给出了具体的公式推导,所给出的数值算例验证了该边界条件处理的正确性。
The parametric finite difference method of lines is an effective numerical method for solving the partial differential equations in the domains with curved boundaries. However, for the degenerate lines on the boundary, how rationally to deal with required boundary conditions remains an open problem. This paper resolves the problem and "finds out" the needed boundary conditions on degenerate lines. Taking a two-dimensional Poisson equation as an example, the detailed derivation of related formulas is presented, and the validity, rationality, and accuracy of derived boundary conditions are demonstrated by the numerical results of computational examples.
作者
林永静
袁驷
LIN Yong-jing YUAN Si(Department of Architectural Engineering, Wenzhou Vocational Technical College, Wenzhou 325035, China Department of Civil Engineering, Tsinghua University, Beijing 100084, China)
出处
《工程力学》
EI
CSCD
北大核心
2017年第4期1-4,共4页
Engineering Mechanics
基金
浙江省教育厅科研项目(Y201225911)
温州市科技局科研项目(S20110002)
国家自然科学基金项目(51378293
51078199)
关键词
参数差分线法
曲线围域
退化线
边界条件
POISSON方程
parametric finite difference method of lines
curved domain
degenerate lines
boundary conditions
Poisson equation