| 三维Helmholtz方程Dirichlet问题的边界元法及其收敛性分析 |
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| 引用本文： | 丁方允.三维Helmholtz方程Dirichlet问题的边界元法及其收敛性分析[J].兰州大学学报(自然科学版),1995,31(3):30-38. |
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| 作者姓名： | 丁方允 |
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| 作者单位： | 兰州大学数学系 |
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| 摘 要： | 本文把三维Ｈｅｌｍｈｏｌｔｚ方程Ｄｉｒｉｃｈｌｅｔ内外值问题结合起来讨论，得到统一形式的边界积分方程，首先，据拟微分算子的理论，讨论了积分算子的性质及问题弱解的存在唯一性，接着采用边界元方法，离散积分方程得到数值解，最后，给出了解的全局误差估计及内部超收敛估计。
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| 关 键 词： | 边界元 Helmholtz方程 狄利克雷问题 收敛性 |
The BEM for Dirichlet Problems of Three Dimensional Helmholtz Equation and Its Convergence |
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| Ding Fangyun.The BEM for Dirichlet Problems of Three Dimensional Helmholtz Equation and Its Convergence[J].Journal of Lanzhou University(Natural Science),1995,31(3):30-38. |
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| Authors: | Ding Fangyun |
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| Abstract: | In this paper, we discuss the combination of the interior and exterior boundary values of Dirichlet problem for three dimensional Helmholtz equation, and get the uniform boundary integral equations. First, according to the theory of pseudo-differential operator,we study the properties of integral operator and the existence of weak solution, secondly, by use of BEM, we discret the integral equation and obtain the numerical solution. Finally, the global error estimation and interior superconvergence estimation are given. |
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| Keywords: | pseudo-differential operator BEM Galerkin's method |
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