| 二维稳态各向异性介质渗透率的反演问题 |
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| 引用本文： | 许作良,张关泉.二维稳态各向异性介质渗透率的反演问题[J].计算数学,2003,25(2):145-156. |
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| 作者姓名： | 许作良 张关泉 |
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| 作者单位： | 1. 中国人民大学信息学院,北京,100872
2. 中国科学院数学与系统科学研究院,计算数学与科学工程计算研究所;科学与工程计算国家重点实验室,北京,100080 |
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| 基金项目： | 国家重点基础研究规划项目资助(G1999,0328). |
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| 摘 要： | 1.引 言由多孔介质的渗流理论,二维稳态各向异性介质的渗流问题满足下列偏微分方程 -div(u(x,y)(?)u(x,y))=f(x,y),(x,y)∈Ω(?)R2, (1.1)
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| 关 键 词： | 多孔介质渗流 二维稳态各向异性介质 渗透率 反演问题 椭圆型方程 Dirichlet条件 凸泛函 极小化子 正交异性 |
| 修稿时间： | 2001年12月11 |
IDENTIFICATION OF THE STEADY-STATE PERMEABILITY FOR TWO DIMENSIONAL ANISOTROPIC MEDIUM |
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| Xu Zuoliang.IDENTIFICATION OF THE STEADY-STATE PERMEABILITY FOR TWO DIMENSIONAL ANISOTROPIC MEDIUM[J].Mathematica Numerica Sinica,2003,25(2):145-156. |
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| Authors: | Xu Zuoliang |
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| Institution: | Xu Zuoliang (Information School, Renmin University of China, Beijing, 100872)
Zhang Guanquan
(State Key Laboratory of Scientific & Engineering Computing, Institute of Computational
Mathematics and Scientific /Engineering Computing, Academy of Mathematics
and System Science, Chinese Academy of Sciences, Beijing, 100080) |
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| Abstract: | This paper seeks to identify the coefficient v in the steady-state diffusion equa-tion -div(v gradu) = f for two dimensional anisotropic medium in a boundeddomain Ω from two known solutions u1, u2 of the corresponding Dirichlet prob-lems, where f is known, v takes diagonal matrix values, which are given at theboundary of Ω, and may have mild discontinuities. This problem is solved byminimization of an associated functional. We propose an alternating Neubergergradient algorithm, and show the results of numerical experiments. |
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| Keywords: | Elliptic equations Inverse problems Parameter identification Anisotropic |
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