二维流Boussinesq方程渗透系数反演的变分伴随方法  

Variational adjoint method for inversion of permeability coefficient of two-dimensional flow Boussinesq equation

作　　者：王兵贤[1,2] 王泽文[1,2] 徐定华[3] 胡康秀[2] 

机构地区：[1]核资源与环境省部共建国家重点实验室培育基地(东华理工大学),江西南昌330013 [2]东华理工大学数学与信息科学学院,江西抚州344000 [3]浙江理工大学数学研究所,浙江杭州310018

出　　处：《水利水电科技进展》2010年第6期11-14,共4页Advances in Science and Technology of Water Resources

基　　金：国家自然科学基金(10861001)

摘　　要：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,根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,迭代过程中搜索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。The inversion of permeability coefficient of two-dimensional flow Boussinesq equation was discussed by use of the variational adjoint method proposed in the optimization control for partial differential equations.The least squared method was modified by means of the idea of regularization,and a target arbitrary function was established.A new iteration algorithm was derived by using the variational adjoint method.The negative gradient direction was selected as the iteration direction.The results of numerical simulations indicate that the proposed algorithm is applicable to the inversion of the permeability coefficient.

关 键 词：BOUSSINESQ方程 渗透系数 变分伴随方法 反问题 

分 类 号：O175.29[理学—数学]