二维位势边界条件反识别TSVD正则化法  

Inverse identification of 2-D potential boundary conditions by using TSVD regularization method

作　　者：卞步喜[1] 周焕林[1] 程长征[1] 牛忠荣[1] 

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2014年第9期1097-1101,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11072073)

摘　　要：二维各向同性材料Cauchy位势边界条件反识别问题是不适定的,通过边界元方法得到线性方程组的系数矩阵呈现病态,测量数据的随机偏差会影响分析结果的稳定性和精确性。文章运用截断奇异值分解正则化方法来处理该反问题,借助L曲线法选择奇异值截断位置,进一步可求解得到未知边界条件。圆环和方形板区域热传导2个算例结果分析表明:获取数据的偏差越小,边界划分单元越细密,数值解越接近解析值,正则误差也越小。Inverse identification of Cauchy potential boundary conditions for 2-D isotropic material is ill-posed .The coefficient matrix of the linear equation obtained from the boundary element method is ill-conditioned .T he random noises of the measurable data affect the stability and accuracy of numerical results .In this paper ,the truncated singular value decomposition （TSVD ） regularization method is applied to dealing with the inverse problem ,and the optimal truncation number is chosen according to the L-curve method .Then the unknown boundary conditions can be determined .The numerical re-sults of two examples about heat conduction in a ring and a square domain show that decreasing the data noise and fining the mesh size can improve the accuracy of numerical solutions and reduce the reg-ularization error at the same time .

关 键 词：位势问题 反问题 边界条件 L曲线法 截断奇异值分解法 

分 类 号：O343.1[理学—固体力学]