Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题)
将用于求解椭圆型偏微分方程边值问题的基本解方法应用于求解一个三维线弹性反问题，即Navier方程组的Cauchy问题.基本解方法离散方程所得的线性方程组是高度病态的，常见的求解方法如最小二乘法等无法得到合理的解.文中应用Tikhonov正则化和截断奇异值分解这两种正则化方法求解线性方程组，所需正则化参数则根据L-曲线确定，克服了问题的病态性.数值算例表明，本文方法能有效地求解三维线弹性力学反问题，而且这两种正则化方法所得到的结果精度相当....
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2006-03-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/zjup/1008-9497.2006.33.2.134-138 |
| _version_ | 1797236303500148736 |
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| author | WANGJun(王钧) SUNFang-yu(孙方裕) JINBang-ti(金邦梯) |
| author_facet | WANGJun(王钧) SUNFang-yu(孙方裕) JINBang-ti(金邦梯) |
| author_sort | WANGJun(王钧) |
| collection | DOAJ |
| description | 将用于求解椭圆型偏微分方程边值问题的基本解方法应用于求解一个三维线弹性反问题，即Navier方程组的Cauchy问题.基本解方法离散方程所得的线性方程组是高度病态的，常见的求解方法如最小二乘法等无法得到合理的解.文中应用Tikhonov正则化和截断奇异值分解这两种正则化方法求解线性方程组，所需正则化参数则根据L-曲线确定，克服了问题的病态性.数值算例表明，本文方法能有效地求解三维线弹性力学反问题，而且这两种正则化方法所得到的结果精度相当. |
| first_indexed | 2024-04-24T17:01:43Z |
| format | Article |
| id | doaj.art-a19573f0e3094656a2f41c9daf188614 |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T17:01:43Z |
| publishDate | 2006-03-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-a19573f0e3094656a2f41c9daf1886142024-03-29T01:58:23ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972006-03-01332134138zjup/1008-9497.2006.33.2.134-138Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题)WANGJun(王钧)0SUNFang-yu(孙方裕)1JINBang-ti(金邦梯)2Department of Mathematics, Zhejiang University, Hangzhou 310027, China(浙江大学数学系，浙江 杭州 310027)Department of Mathematics, Zhejiang University, Hangzhou 310027, China(浙江大学数学系，浙江 杭州 310027)Department of Mathematics, Zhejiang University, Hangzhou 310027, China(浙江大学数学系，浙江 杭州 310027)将用于求解椭圆型偏微分方程边值问题的基本解方法应用于求解一个三维线弹性反问题，即Navier方程组的Cauchy问题.基本解方法离散方程所得的线性方程组是高度病态的，常见的求解方法如最小二乘法等无法得到合理的解.文中应用Tikhonov正则化和截断奇异值分解这两种正则化方法求解线性方程组，所需正则化参数则根据L-曲线确定，克服了问题的病态性.数值算例表明，本文方法能有效地求解三维线弹性力学反问题，而且这两种正则化方法所得到的结果精度相当.https://doi.org/zjup/1008-9497.2006.33.2.134-138基本解方法cauchy问题正则化方法线弹性力学反问题 |
| spellingShingle | WANGJun(王钧) SUNFang-yu(孙方裕) JINBang-ti(金邦梯) Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题) Zhejiang Daxue xuebao. Lixue ban 基本解方法 cauchy问题 正则化方法 线弹性力学 反问题 |
| title | Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题) |
| title_full | Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题) |
| title_fullStr | Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题) |
| title_full_unstemmed | Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题) |
| title_short | Method of fundamental solutions for a three-dimensional inverse problem in linear elasticity(基本解方法求解一个三维线弹性力学反问题) |
| title_sort | method of fundamental solutions for a three dimensional inverse problem in linear elasticity 基本解方法求解一个三维线弹性力学反问题 |
| topic | 基本解方法 cauchy问题 正则化方法 线弹性力学 反问题 |
| url | https://doi.org/zjup/1008-9497.2006.33.2.134-138 |
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