Numerical testing in determination of sound speed from a part of boundary by the BC-method

2015/05/20 by Belishev, M. I., Ivanov, I. B., Kubyshkin, I. V. +1
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1505.06176

Abstract

We present the results of numerical testing on determination of the sound speed c in the acoustic equation u_tt-c²Δu=0 by the \it boundary control method. The inverse data is a response operator (a hyperbolic Dirichlet-to-Neumann map) given on controls, which are supported on \it a part of the boundary. The speed is determined in the subdomain covered by acoustic rays, which are emanated from the points of this part orthogonally to the boundary. The determination is \it time-optimal: the longer is the observation time, the larger is the subdomain, in which c is recovered. The numerical results are preceded with brief exposition of the relevant variant of the BC-method.

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