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Inverse parameter and shape problem for an isotropic scatterer with two conductivity coefficients

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Abstract

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident direction for multiple frequencies. Then, we address the inverse shape problem for recovering the scatterer for the measured far-field data at a fixed frequency. Furthermore, we examine the direct sampling method for recovering the scatterer by studying the factorization for the far-field operator. The direct sampling method is stable with respect to noisy data and valid in two dimensions for partial aperture data. The theoretical results are verified with numerical examples to analyze the performance by the direct sampling method.

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Acknowledgements

The research of R. Ceja Ayala and I. Harris is partially supported by the NSF DMS Grant 2107891.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Rafael Ceja Ayala & Isaac Harris

  2. Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Wilhelm-Johnen-Straße, 52425, Jülich, Germany

    Andreas Kleefeld

  3. Faculty of Medical Engineering and Technomathematics, University of Applied Sciences Aachen, Heinrich-Mußmann-Str. 1, 52428, Jülich, Germany

    Andreas Kleefeld

Authors
  1. Rafael Ceja Ayala
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  2. Isaac Harris
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  3. Andreas Kleefeld
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Contributions

I.H. worked on the analysis and editing of the main document R.C-A. worked on the analysis, numerical examples, and writing of the main document A.K. worked on the numerical examples and editing of the main document

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Correspondence to Isaac Harris.

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Ayala, R.C., Harris, I. & Kleefeld, A. Inverse parameter and shape problem for an isotropic scatterer with two conductivity coefficients. Anal.Math.Phys. 14, 90 (2024). https://doi.org/10.1007/s13324-024-00950-x

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  • DOI: https://doi.org/10.1007/s13324-024-00950-x

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