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arXiv · 2112.14071

Determining kernels in linear viscoelasticity

Barbara Kaltenbacher·Ustim Khristenko·Vanja Nikolić·Mabel Lizzy Rajendran·Barbara Wohlmuth
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Abstract

In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal viscoelastic wave equation. To this end, we minimize a tracking-type data misfit function under this PDE constraint. We perform the well-posedness analysis of the state and adjoint problems and, using these results, rigorously derive the first-order sensitivities. Numerical experiments in a three-dimensional setting illustrate the method.

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Barbara Kaltenbacher, Ustim Khristenko, Vanja Nikolić, Mabel Lizzy Rajendran, Barbara Wohlmuth. 2021-12-28. Determining kernels in linear viscoelasticity. https://doi.org/10.1016/j.jcp.2022.111331

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