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Live load matrix recovery from scattering data in linear elasticity

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Abstract

We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown linear load given by a square matrix. For both backscattering data and fixed-angle scattering data, we show how to obtain numerical approximations of the so-called Born approximations and propose new iterative algorithms that provide sequences of approximations to the unknown load. Numerical evidences of the convergence for not too large loads are also given.

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Data Availability

Not applicable, but the necessary programs to replicate the experiments are available.

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Funding

This work is supported by the Spanish Grant PID2021-124195NB-C31.

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Authors and Affiliations

  1. M2ASAI, ETSI de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    Juan Antonio Barceló & Carlos Castro

  2. M2ASAI, ETSI Navales, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    Mari Cruz Vilela

Authors
  1. Juan Antonio Barceló
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  2. Carlos Castro
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  3. Mari Cruz Vilela
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Correspondence to Mari Cruz Vilela.

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Barceló, J.A., Castro, C. & Vilela, M.C. Live load matrix recovery from scattering data in linear elasticity. Adv Comput Math 49, 88 (2023). https://doi.org/10.1007/s10444-023-10087-3

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