An estimation method for point sources of multidimensional diffusion equation

Yamatani, Katsu; Ohnaka, Kohzaburo

doi:10.1016/s0307-904x(96)00148-5

Cited by 7 publications

(5 citation statements)

References 5 publications

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“…In addition, specialized strategies have been proposed in e.g. [19] (where the convex hull of a set of sources is reconstructed) and [26] (an algorithm we found, by conducting preliminary numerical experiments, to be highly sensitive to imperfect data).…”

Section: Physical Motivationmentioning

confidence: 99%

Identification of transient heat sources using the reciprocity gap

Auffray

Bonnet

Pagano

2012

Inverse Problems in Science and Engineering

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International audienceThe deformation of solid materials is nearly always accompanied with temperature variations, induced by intrinsic dissipation and thermomechanical coupling. Heat sources give precious information on the thermomechanical behavior of materials. They can be indirectly observed from thermal measurements on the specimen boundary, obtained e.g. via infrared thermography. To solve the inverse problem of identifying heat sources from such observations, a non-iterative algebraical method based on the Reciprocity Gap Method is proposed. This approach, used elsewhere mainly for time-independent identification, is applied here to transient measurements. Under appropriate modelling assumptions the number of heat sources, their spatial locations and energies are retrieved, as demonstrated on numerical experiments where the robustness of the method to measurement noise is also studied

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Section: Physical Motivationmentioning

confidence: 99%

Identification of transient heat sources using the reciprocity gap

Auffray

Bonnet

Pagano

2012

Inverse Problems in Science and Engineering

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“…It is well known that one can not uniquely determine general source f (x, t) from the data. However, it is also known that under some a priori assumption on the form of f (x, t) one can extract the full or partial information about the source, e. g., see [38,192].…”

Section: Inverse Source Problem For the Heat Equationmentioning

confidence: 99%

Extracting discontinuity using the probe and enclosure methods

Ikehata¹

2020

Preprint

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“…While some authors assume that the number of sources is known a priori [10,12], some suppose that it is bounded by a known integer [4,5] and others consider finding this quantity as part of the problem [11,16], lemma 2 demonstrates an advantage of collecting boundary data in the form (p, Dp), namely that the number of sources counting multiplicity is given by formula (11).…”

Section: Proofmentioning

confidence: 99%

“…In particular, Ohe and Ohnaka [13] proposed a method for estimating the unknown number and locations of point masses corresponding to monopoles in dimension 2 based on an algebraic relation between the Fourier coefficients of the logarithmic potential and the parameters of the point mass model. Yamatani and Ohnaka [16] introduced a weighted residual approach to estimate the unknown parameters for the corresponding parabolic problem. In [4], El Badia and Ha-Duong proved that the sources are identifiable from boundary measurements, that is, they established uniqueness for the class of admissible sources in the form (2).…”

Section: Introductionmentioning

confidence: 99%

A boundary value transformation for an inverse source problem with point sources

Glotov¹

2010

Inverse Problems

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We consider an inverse problem for the Poisson equation with point sources in dimension 2. This problem has been studied extensively for the data in the form of the values of both the solution and its normal derivative given on the boundary. Our focus is on another type of data, namely the absolute value of the gradient and its derivatives. We present a method for converting the boundary data of the latter type to the boundary data of the former type. For the resulting system of ordinary differential equations, we establish the necessary and sufficient conditions for the existence of periodic solutions. To guarantee the uniqueness of the solution we introduce an additional constraint. Next, we present some numerical examples to illustrate the method and comment on the rate of convergence of the algorithm. Finally, we show that the method in its present form cannot be extended to dimension 3.

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An estimation method for point sources of multidimensional diffusion equation

Cited by 7 publications

References 5 publications

Identification of transient heat sources using the reciprocity gap

Identification of transient heat sources using the reciprocity gap

Extracting discontinuity using the probe and enclosure methods

A boundary value transformation for an inverse source problem with point sources

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