时间分数阶二维对流扩散方程多点源强的数值反演  

Numerical determination of multi-point sources magnitude in 2-D time fractional advection-dispersion equation

作　　者：李慧玲[1] 李功胜[1] 贾现正[1] 池光胜[2] 

机构地区：[1]山东理工大学理学院,山东淄博255091 [2]山东凯文科技职业学院本科教育学院,山东济南250200

出　　处：《山东理工大学学报（自然科学版）》2013年第6期1-6,共6页Journal of Shandong University of Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(11071148);山东省自然科学基金资助项目(ZR2011AQ014)

摘　　要：对于一类带有多个点源的二维反常扩散问题,基于Caputo意义下时间分数阶导数的离散,给出了一个有限差分求解格式.在已知点源个数及位置的前提下,根据终止时刻的浓度观测数据,应用最佳摄动量正则化算法对源强度识别反问题进行了有效的数值反演,并讨论了正则参数、分数微分阶数及数据扰动等因素对反演算法的影响.A finite difference scheme is introduced to solve the 2-D time fractional diffusion equation with multiple point sources based on Caputo’s discretization to the time fractional derivative , and numerical test is presented .Furthermore ,the optimal perturbation regularization algorithm is applied to determine the magnitudes of the multi-point sources using measurements at the final time .Numerical inversions are performed to demonstrate the effectiveness of the proposed algorithm ,and influences of the regularization parameter ,the fractional order and the data noises on the inversion algorithm are discussed .

关 键 词：时间分数阶导数 二维对流扩散 多点源 反问题 最佳摄动量正则化算法 数值模拟 

分 类 号：O175[理学—数学]