二维流Boussinesq方程渗透系数反演的变分伴随方法.pdf

30 6 2010 12 Vol. 30 No. 6 Advances in Science and Technology of Water Resour ces Dec. 2010 DOI 10. 3880/ j . issn . 2010 . 06. 004 二维流Boussinesq 方程渗透系数反演的变分伴随方法 1, 2 1, 2 3 2 王兵贤 , 王泽文 , 徐定华, 胡康秀 ( 1. ( ) , 330013; 2 . , 344000 ; 3. , 3100 18) 用偏微分方程最优控制中的变分伴随方法研究平面二维流Boussinsq 方程渗透系数反演问 题, 据正则化方法改造最小二乘方法并构造目标泛函, 依据变分伴随方法构造迭代算法, 迭代过 程中有哪些信誉好的足球投注网站方向选取泛函下降最快的负梯度方向数值模拟结果表明该算法用于渗透系数的反演是 可行的 Boussinesq 方程; 渗透系数; 变分伴随方法; 反问题 O17529 A 2010) Variational adj oint method for inversion of permeability coefficient of twodimensional flow Boussinesq equation/ / WANG 1, 2 1, 2 3 2 Bingxian , WANG Zew en , XU Dinghu a , HU Kangxiu ( 1. State Key Laboratory Breeding Base of Nuclear Resources and Environment, East China Institute of echnology, Nanchang 330013, China; 2. School of Mathematics and Inf ormational Sciences, East ChinaInstitute of echnology, Fuzhou 344000, China; 3. Institute of Mathematics, Zhej iang University of Science and echnology, Hangzhou 310018, China) Abstract The inversion of permeability coeff icient of tw odim ensional flow Boussinesq equation w as discussed by use of the variational adjoint method proposed in the optimization control for partial differential equations. The least squared m ethod w as modif ied by means of the idea of regularization, and a target arbitrary function w as established. A new iteration algorithm w as derived by using the variational adjoint m ethod . The negative gradient direction w as selected as the iteration direction. The results of num erical simulations indicate that the pr