Numerical testing in determination of sound speed from a part of boundary by the BC-method
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Mikhail I. Belishev
,
Ivan B. Ivanov
Abstract
We present the results of numerical testing on determination of the sound speed c in the acoustic equation utt - c2Δu = 0 by the boundary control method. The inverse data is a response operator (a hyperbolic Dirichlet-to-Neumann map) given on controls, which are supported on 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 time-optimal: the longer the observation time is, the larger the subdomain is, in which c is recovered. The numerical results are preceded with a brief exposition of the relevant variant of the BC-method.
Funding source: RFBR
Award Identifier / Grant number: 14-01-00535À
Funding source: SPbGU
Award Identifier / Grant number: 6.38.670.2013
Funding source: St. Petersburg State University
Award Identifier / Grant number: leading scientific schools 2836.2014.5
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Preface
- In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)
- An inverse source problem for a damped wave equation with memory
- On the Cauchy problem for semilinear elliptic equations
- A unified approach to convergence rates for ℓ1-regularization and lacking sparsity
- Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives
- Numerical testing in determination of sound speed from a part of boundary by the BC-method
- Inverse determination of spatially varying material coefficients in solid objects
- Determination of the initial condition in parabolic equations from boundary observations
Artikel in diesem Heft
- Frontmatter
- Preface
- In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)
- An inverse source problem for a damped wave equation with memory
- On the Cauchy problem for semilinear elliptic equations
- A unified approach to convergence rates for ℓ1-regularization and lacking sparsity
- Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives
- Numerical testing in determination of sound speed from a part of boundary by the BC-method
- Inverse determination of spatially varying material coefficients in solid objects
- Determination of the initial condition in parabolic equations from boundary observations
