Commun. Comput. Phys., 6 (2009), pp. 793-803. |
A Level Set Method for the Inverse Problem of Wave Equation in the Fluid-Saturated Porous Media Ying He ^{1}, Bo Han ^{2*} 1 Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China; School of Mathematical Sciences, Heilongjiang University, Harbin, 150080, China.2 Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China. Received 17 June 2008; Accepted (in revised version) 19 January 2009 Available online 5 March 2009 Abstract In this paper, a level set method is applied to the inverse problem of 2-D wave equation in the fluid-saturated media. We only consider the situation that the parameter to be recovered takes two different values, which leads to a shape reconstruction problem. A level set function is used to present the discontinuous parameter, and a regularization functional is applied to the level set function for the ill-posed problem. Then the resulting inverse problem with respect to the level set function is solved by using the damped Gauss-Newton method. Numerical experiments show that the method can recover parameter with complicated geometry and the noise in the observation data. AMS subject classifications: 35R30, 34K28 Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164 Key words: Level set method, fluid-saturated porous media, parameter recovery, damped Gauss-Newton method. *Corresponding author. Email: happybirdzhp@sohu.com (Y. He), bohan@hit.edu.cn (B. Han) |