| 求解半空间中Helmholtz方程Cauchy问题的投影法 |
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| 引用本文： | 马云云,马富明.求解半空间中Helmholtz方程Cauchy问题的投影法[J].吉林大学学报(理学版),2012,50(2):157-166. |
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| 作者姓名： | 马云云 马富明 |
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| 作者单位： | 吉林大学 数学研究所, 长春 130012 |
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| 基金项目： | 国家自然科学基金(批准号:10971083) |
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| 摘 要： | 针对Helmholtz方程Cauchy问题提出一种数值计算方法. 借助于Dirichlet to Neumann映射, 将Cauchy问题转化为求解散射场初值的紧算子方程. 先讨论紧算子奇异值的渐近性质, 然后将投影法与Tikhonov正则化方法相结合, 提出一种求解相应紧算子方程的带有正则化技巧的投影法, 并通过数值实验验证了算法的有效性.
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| 关 键 词： | Helmholtz方程 Cauchy问题 投影法 正则化 |
| 收稿时间： | 2011-06-01 |
Projection Method for the Cauchy Problem of Helmholtz Equation in Half-Space |
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| MA Yun-yun,MA Fu-ming.Projection Method for the Cauchy Problem of Helmholtz Equation in Half-Space[J].Journal of Jilin University: Sci Ed,2012,50(2):157-166. |
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| Authors: | MA Yun-yun MA Fu-ming |
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| Institution: | Institute of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | A numerical method was proposed for the Cauchy problem in accordance with the Helmholtz equation in the half-space.With the help of Dirichlet-to-Neumann map,this problem was transformed into a compact opera tor equation for the initial value of the wave field.The asymptotic behavior of the singular values of the compact operator was rigorously justified firstly.Th en a projection method with regularization was applied to solving the operator e quation.Finally,several numerical examples were presented to illustrate the approach.The results show that the algorithm is effective. |
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| Keywords: | Helmholtz equation Cauchy problem projection method regularization |
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