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Conference Papers Year : 2022

Inverse problem for the Helmholtz equation and singular sources in the divergence form

Abstract

We shall discuss an inverse problem where the underlying model is related to sources generated by currents on an anisotropic layer. This problem is a generalization of another motivated by the recovering of magnetization distribution in a rock sample from outer measurements of the generated static magnetic field. The original problem can be formulated as inverse source problem for the Laplace equation [1,2] with sources being the divergence of the magnetization whereas the generalization comes from taking the Helmholtz equation. Either inverse problem is non uniquely solvable with a kernel of infinite dimension. We shall present a decomposition of the space of sources that will allow us to discuss constraints that may restore uniqueness and propose regularization schemes adapted to these assumptions. We then present some validating experiments and some related open questions.
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hal-03899189 , version 1 (14-12-2022)

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  • HAL Id : hal-03899189 , version 1

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Laurent Baratchart, Houssem Haddar, Cristóbal Villalobos Guillén. Inverse problem for the Helmholtz equation and singular sources in the divergence form. WAVES 2022 - 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jul 2022, Palaiseau, France. ⟨hal-03899189⟩
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