三维声波方程逆问题的共轭梯度法求解  

Application of the conjugate gradient method to the inverse problem of 3-D acoustic equation

作　　者：应金品[1] 包康 

机构地区：[1]渐江大学物理系,杭州310027 [2]浙江大学现代光学仪器国家重点实验室,杭州310027

出　　处：《声学学报》1998年第4期340-348,共9页Acta Acustica

基　　金：浙江大学现代光学仪器国家重点实验室开放课题

摘　　要：考虑一个完整的三维声波方程的逆问题．通过构造一个表面声压偏差平方和形式的目标泛函，把声波方程的逆问题转化为一个控制声学特性参数分布使得目标泛函达到最小伍的优化问题．采用共轭梯度法来求解这个优化问题．通过引入一个对偶函数u（x，t），文中用微扰法求得了目标泛函梯度值的解析表达式，从而克服了以往用共轭梯度法求解偏微分方程控制的优化问题时计算目标活函梯度的困难，大大压缩了共轭梯度法计算目标泛函梯度的时间，而且提高了梯度值的计算精度．还进一步进行了反演声学特性参数三维分布的数值仿真计算．共轭梯度法完整解决了三维声波方程的逆问题．The inverse problem of 3-D acoustic equation is considered in the time-domain. By constructing the objective functional, the inverse problem is thereby reduced to an optimization problem where the profiles of the velocity and the density minimizing the functional are to be found. A conjugate gradient method is employed to solve the optimization problem. By introducing a dual function, the gradient of the objective functional is found with an explicit expression. The inverse problem of 3-D acoustic equation is solved successfully by the conjugate gradient method. The numerical example of reconstructing acoustic parameters is provided.

关 键 词：共轭梯度法 三维 声波方程 逆问题 

分 类 号：O422[理学—声学]