Physics, mathematics, and technology

2013 Issue №4

Back to the list Download the article

Numerical solving the linearized inverse problem for two-parameter acoustic equation



In this paper we develop а numerical algorithm for solving inverse dynamical problem: recovering two parameters of the acoustical medium (density and compressibility modulus) by boundary measurements (response operator). The solution is based on a linearized version of the Boundary Control method: the response operator explicitly determined some bilinear energy forms w. r. t. boundary controls. We use linearized presentations of these forms w. r. t. to background. The results of numerical experiments are represented.


1. Belishev M. I. Boundary control in reconstruction of manifolds and metrics (the BC-method) // Inverse Problems. 1997. № 13. P. 1—45.
2. Belishev M. I. Boundary Control Method in Dynamical Inverse Problems — An Introductory Course by M. I. Belishev. Gladwell G. M. L., Morassi A., Editors // Dynamical Inverse Problems: Theory and Application. CISM Courses and Lectures.Wien, Springer, 2011. Vol. 529. P. 85—150.
3. Pestov L., Bolgova V., Kazarina O. Numerical recovering a density by BC-method // Inverse Problems and Imaging (American Institute of Mathematical Sciences).2010. Vol. 4, № 4. P. 703—712. URL:
4. Филатова В. М. Численное восстановление коэффициента поглощения методом граничного управления // Вестник Балтийского федерального университета им. И. Канта. 2012. Вып. 10. С. 153—159.