| 椭球外区域问题的自然边界元法 |
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| 引用本文： | 黄红英.椭球外区域问题的自然边界元法[J].浙江海洋学院学报(自然科学版),2009,28(1). |
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| 作者姓名： | 黄红英 |
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| 作者单位： | 浙江海洋学院数理与信息学院,浙江舟山,316004 |
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| 基金项目： | 浙江省科技厅项目，浙江省教育厅资助项目，浙江海洋学院研究项目 |
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| 摘 要： | 主要讨论了椭球面外部区域Laplace方程的自然边界元法.首先引入椭球坐标,通过分离变量法导出了Poisson积分公式和自然积分算子的无穷级数显示表达式.这样原无界区域问题就归化为椭球面上边界积分方程,然后再数值求解该积分方程.给出了该积分方程的变分问题的适定性和逼近解的误差估计,且该误差估计不仅依赖于网格参数而且依赖与级数截断后的项数.数值例子说明了该方法的有效性和理论分析的正确性.
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| 关 键 词： | 椭球面 自然边界归化 有限元法 无界区域问题 |
A Natural Boundary Element Method for Laplace Equation Outside an Ellipsoid |
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| HUANG Hong-ying.A Natural Boundary Element Method for Laplace Equation Outside an Ellipsoid[J].Journal of Zhejiang Ocean University(Natural Science Edition),2009,28(1). |
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| Authors: | HUANG Hong-ying |
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| Institution: | School of Mathematics;Physics and Information Science of Zhejiang Ocean University;Zhoushan 316004;China |
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| Abstract: | In this paper,we study the natural boundary reduction for Laplace equation with the Dirichlet or Neumann boundary condition outside an ellipsoid.We express explicitly the Poisson integral formula and natural integral operator in a series form.Thus the original problem is reduced to a boundary integral equation on an ellipsoidal surface and then the boundary integral equation is solved numerically.Error estimate is pre-sent and the error depends on the mesh size and the number of the term after truncating th... |
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| Keywords: | ellipsoid natural boundary reduction finite elements unbounded domain problem |
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