热方程未知源识别的计算方法

兰州大学机构库 >数学与统计学院

	热方程未知源识别的计算方法
Alternative Title	Computational method for determining an unknown heat source in heat equation
	胡勇
Thesis Advisor	魏婷
	2013-06-02
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	基本解方法热源识别问题反初值问题正则化
Abstract	本文采用基本解方法对热方程的未知源识别问题进行求解. 基本解方法是一种无网格方法，其基本思想是用热方程基本解的线性组合来近似表示问题的解，避免了对区域的离散. 为了能够直接利用基本解方法，首先通过变换将原问题转化成齐次反初值问题，由于热源识别问题为不适定问题，利用基本解方法所得到的插值矩阵具有高度病态性，本文采用Tikhonov正则化结合GCV方法对病态方程组进行处理. 最后通过一维和二维的数值算例说明了所采用方法的有效性．
Other Abstract	In this paper, the method of fundamental solutions(MFS) is used to determine an unknown heat source term in a heat equation from overspecified boundary measurement data. The MFS is an inherently meshless technique for solving partial differential equations and the basic idea is to approximate the solution of the problem by a linear combination of fundamental solutions for the governing differential equation. By a function transformation, the inverse source problem is changed into an inverse initial data problem. Since the matrix arising from the MFS discretization is severely ill-conditioned, the standard Tikhonov regularization technique with the generalized cross-validation criterion for choosing the regularization parameter is adopted for solving the resulting ill-conditioned system of linear algebraic equations. The effectiveness of the algorithm is illustrated by five numerical examples in one-dimensional and two dimensional cases.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/224774
Collection	数学与统计学院
Recommended Citation GB/T 7714	胡勇. 热方程未知源识别的计算方法[D]. 兰州. 兰州大学,2013.

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