The Enclosure Method and its Applications

Ikehata, Masaru

doi:10.1007/978-1-4757-3298-6_7

Cited by 28 publications

(23 citation statements)

References 27 publications

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“…Impenetrable obstacles have also been reconstructed, see [26] and the references therein. For more details see Section 2.2 of [24] and also Section 5 in this article.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Nonradiating Sources and Transmission Eigenfunctions Vanish at Corners and Edges

Blåsten

2018

SIAM J. Math. Anal.

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We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far-or nearfield measurement. We show that nonradiating sources having a convex or non-convex corner or edge on their boundary must vanish there. The same holds true for smooth enough transmission eigenfunctions. The proof is based on an energy identity from the enclosure method and the construction of a new type of planar complex geometrical optics solution whose logarithm is a branch of the square root. The latter allows us to deal with non-convex corners and edges.

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“…Impenetrable obstacles have also been reconstructed, see [26] and the references therein. For more details see Section 2.2 of [24] and also Section 5 in this article.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Nonradiating Sources and Transmission Eigenfunctions Vanish at Corners and Edges

Blåsten

2018

SIAM J. Math. Anal.

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“…This is treated theoretically for example by [61] and numerically in [62]. A practical example is the location of the air core of a hydrocyclone, a device used in chemical engineering [114].…”

Section: The Reconstruction Problem Locating Objects and Boundariesmentioning

confidence: 99%

Electrical Impedance Tomography

Adler¹,

Gaburro²,

Lionheart³

2015

Handbook of Mathematical Methods in Imaging

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“…The CGO solutions constructed in Theorem 1.3 have been applied to determine inclusions for Helmholtz equations in [84] and Maxwell's equations in [209] using the enclosure method [83,84].…”

Section: Other Applicationsmentioning

confidence: 99%

Inverse problems: seeing the unseen

2014

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This survey article deals mainly with two inverse problems and the relation between them. The first inverse problem we consider is whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. This is called electrical impedance tomography and also Calderón's problem since the famous analyst proposed it in the mathematical literature (Calderón in On an inverse boundary value problem. Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980), Soc Brasil Mat. Rio de Janeiro, pp. [65][66][67][68][69][70][71][72][73] 1980). The second is on travel time tomography. The question is whether one can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as a geometry problem, the boundary rigidity problem. Can we determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points? These two inverse problems concern visibility, that is whether we can determine the internal properties of a medium by making measurements at the boundary. The last topic of this paper considers the opposite issue: invisibility: Can one make objects invisible to different types of waves, including light?Communicated by Ari Laptev.

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The Enclosure Method and its Applications

Cited by 28 publications

References 27 publications

Nonradiating Sources and Transmission Eigenfunctions Vanish at Corners and Edges

Nonradiating Sources and Transmission Eigenfunctions Vanish at Corners and Edges

Electrical Impedance Tomography

Inverse problems: seeing the unseen

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