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

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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)
 

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