Numerical recovering of a density by the BC-method

Pestov, Leonid; Bolgova, Victoria; Kazarina, Oksana

doi:10.3934/ipi.2010.4.703

Cited by 26 publications

(28 citation statements)

References 8 publications

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“…In addition to [5], the only multidimensional implementation of a variant of the BC method, that we are aware of, is [31]. This variant is based on solving the control problem (3.4) without the constraint supp(f ) ⊂ S τ .…”

Section: Overview Of Bc Methods Variantsmentioning

confidence: 99%

On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map

Hoop¹,

Kepley²,

Oksanen³

2016

SIAM J. Appl. Math.

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We introduce a new algorithm to construct travel time distances between a point in the interior of a Riemannian manifold and points on the boundary of the manifold, and describe a numerical implementation of the algorithm. It is known that the travel time distances for all interior points determine the Riemannian manifold in a stable manner. We do not assume that there are sources or receivers in the interior, and use the hyperbolic Neumann-to-Dirichlet map, or its restriction, as our data. Our algorithm is a variant of the Boundary Control method, and to our knowledge, this is the first numerical implementation of the method in a geometric setting.

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Section: Overview Of Bc Methods Variantsmentioning

confidence: 99%

On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map

Hoop¹,

Kepley²,

Oksanen³

2016

SIAM J. Appl. Math.

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“…Over the last decades, the BC method has been exploited extensively and has now become an important tool in dealing with the coefficient identification in distributed parameter systems. Actually, it has been successfully applied to the wave equations in [9][10][11], the Schrödinger equation in [12], the heat equation in [13], and the beam equation in [14]. In particular, in [15], it establishes the connections between the dynamics and the spectral data, where the local version of the classical Gelfand-Levitan equations (see, e.g., [16]) is also derived.…”

Section: Introductionmentioning

confidence: 98%

Boundary control method to identification of elastic modulus of string equation from Neumann-Dirichlet map

Zhao

Guo

2015

J Syst Sci Complex

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This paper considers identification for the spatial variable coefficient of a vibrating string with Neumann boundary control from the measured boundary displacement. The reconstruction algorithm consists of two steps: The first step is to recover the spectral data from the measured boundary displacement by showing that the system is spectral controllable; the second step is to reconstruct the coefficient from the recovered spectral data using the boundary control method, for which the required exact controllability is also verified.

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“…These results are based on the so-called Boundary Control method. Computational aspects of this method have been studied recently in [7], [12], [24], see also [6] for the first computational implementation of the method. Uniqueness up to diffeomorphism in anisotropic materials has been shown in [5], [8].…”

Section: Introductionmentioning

confidence: 99%

Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain

Cârstea¹,

Nakamura²,

Oksanen³

2020

Trans. Amer. Math. Soc.

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We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumannto-Dirichlet map for the elasticity equation in the space-time domain. We derive uniqueness for identifying these tensor and density on all domains of homogeneity that may be reached from the part of the boundary where the measurements are taken by a chain of subdomains whose successive interfaces contain a curved portion.

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Numerical recovering of a density by the BC-method

Abstract: In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.

Cited by 26 publications

References 8 publications

On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map

On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map

Boundary control method to identification of elastic modulus of string equation from Neumann-Dirichlet map

Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain

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