椭圆外区域上Helmholtz问题的耦合法 |
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引用本文: | 赵自霞,杨桦,杜其奎.椭圆外区域上Helmholtz问题的耦合法[J].数学的实践与认识,2014(18). |
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作者姓名: | 赵自霞 杨桦 杜其奎 |
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作者单位: | 安阳第三十九中;南京师范大学数学与计算机科学学院;安阳工学院数理学院; |
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基金项目: | 国家自然科学基金(10471067);江苏省基础研究计划(自然科学基金)(BK2006215) |
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摘 要: | 以椭圆外区域上Helmholtz方程为例,研究一种带有椭圆人工边界的自然边界元与有限元耦合法,给出了耦合变分问题的适定性及误差分析并给出数值例子.理论分析及数值结果表明,用方法求解椭圆外问题是十分有效的.为求解具有长条型内边界外Helmholtz问题提供了一种很好的数值方法.
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关 键 词: | 椭圆边界 Helmholtz方程 自然边界元 耦合法 Mathieu函数 |
The Coupling of NBE and FEM for Helmholtz Problem in an Exterior Elliptic Domain |
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Abstract: | In this paper,the couphng method is discussed of natural boundary element and finite element method for solving 2D exterior Helmholtz problem with elliptic artifical boundary.The well-posdeness is studied of the variational problem,and error estimates of the approximate solution is given.A numerical example is presented.Theoretical analysis and numerical examples show that our method is effective. |
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Keywords: | elliptic boundary Helmholtz equation natural boundary element coupling Mathieu functions |
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