| 基于MIB方法求解一维泊松方程有关界面问题的插值逼近 |
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| 引用本文： | 李建晶,冯艳秋.基于MIB方法求解一维泊松方程有关界面问题的插值逼近[J].宁夏师范学院学报,2014,35(3):41-49. |
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| 作者姓名： | 李建晶 冯艳秋 |
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| 作者单位： | 宁夏大学数学计算机科学学院,宁夏银川,750021 |
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| 摘 要： | 针对一维带有不连续系数和奇异源项的椭圆型方程,采用MIB方法通过插值逼近处理界面处不规则点进行求解.该方法对微分方程的离散和跳跃条件的离散是分离的,反复处理低阶跳跃条件可以提高MIB格式的精度.该MIB方法对一维椭圆型方程的求解,其结果比IIM方法、BCCM方法求得的结果误差小,稳定性好.
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| 关 键 词： | 椭圆型方程 跳跃条件 插值法 虚拟点 MIB方法 |
Based on MIB Method for Solving One-dimensional Poisson Equation about Interface Problem of the Interpolation Approximation |
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| LI Jianjing,FENG Yanqiu.Based on MIB Method for Solving One-dimensional Poisson Equation about Interface Problem of the Interpolation Approximation[J].Journal of Ningxia Teachers College,2014,35(3):41-49. |
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| Authors: | LI Jianjing FENG Yanqiu |
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| Institution: | (School of Mathematics and Computer Science,Ningxia University, Yinchuan, Ningxia 750021 ) |
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| Abstract: | In this paper,MIB（Matched Interface and Boundary） method by interpolation processing irregular point in the interface are proposed for solving one-dimensional Elliptic equations with discontinuous coefficient and singular source term. This method in the discretization of the differential equations and the jump conditions are separated. Dealing with low order jump condition for several times can improve the accuracy of the high order MIB scheme. The feature of this new method is to improve numerical order and reduce errors,thus,it takes little effort to replace the dirichlet boundary conditions with neumann boundary conditions. |
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| Keywords: | Elliptic equations Jump condition Interpolation method Ghost point MIB method |
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