一种求解Robin反问题的边界型无网格方法

O242.82; 给出一种求解非齐次稳态热传导方程Robin反问题的边界型无网格方法.该方法首先利用Newton法则将Robin反问题转化为Cauchy问题,然后用边界粒子法处理非齐次项以避免区域内部的离散节点,并结合基本解方法分别求得近似特解以及相应齐次问题的近似解.鉴于所考虑问题的不适定性,引入截断奇异值分解和L-曲线准则来求解离散后得到的高度病态的线性方程组.最后给出数值例子说明该方法的稳定性和有效性....

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Published in浙江大学学报（理学版） Vol. 40; no. 1; pp. 29 - 34
Main Author 董超峰
Format Journal Article
LanguageChinese
Published 嘉兴学院数理与信息工程学院,浙江嘉兴,314001 2013
Subjects
meshless method
基本解方法
边界粒子法
截断奇异值分解
Robin反问题
method of fundamental solutions
无网格方法
Robin inverse problem
boundary particle method
truncated singular value decomposition
Online AccessGet full text
ISSN1008-9497
DOI10.3785/j.issn.1008-9497.2013.01.008

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Abstract O242.82; 给出一种求解非齐次稳态热传导方程Robin反问题的边界型无网格方法.该方法首先利用Newton法则将Robin反问题转化为Cauchy问题,然后用边界粒子法处理非齐次项以避免区域内部的离散节点,并结合基本解方法分别求得近似特解以及相应齐次问题的近似解.鉴于所考虑问题的不适定性,引入截断奇异值分解和L-曲线准则来求解离散后得到的高度病态的线性方程组.最后给出数值例子说明该方法的稳定性和有效性.
AbstractList O242.82; 给出一种求解非齐次稳态热传导方程Robin反问题的边界型无网格方法.该方法首先利用Newton法则将Robin反问题转化为Cauchy问题,然后用边界粒子法处理非齐次项以避免区域内部的离散节点,并结合基本解方法分别求得近似特解以及相应齐次问题的近似解.鉴于所考虑问题的不适定性,引入截断奇异值分解和L-曲线准则来求解离散后得到的高度病态的线性方程组.最后给出数值例子说明该方法的稳定性和有效性.
Author 董超峰
AuthorAffiliation 嘉兴学院数理与信息工程学院,浙江嘉兴,314001
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DocumentTitle_FL A boundary-type meshless method for the Robin inverse problem
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Keywords meshless method
基本解方法
边界粒子法
截断奇异值分解
Robin反问题
method of fundamental solutions
无网格方法
Robin inverse problem
boundary particle method
truncated singular value decomposition
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Title 一种求解Robin反问题的边界型无网格方法
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