Abstract
The aim of the article is to solve an inverse problem in order to determine the presence and some properties of an elastic “inclusion” (an unknown object, characterized by elastic properties discriminant from the surrounding medium) from partial observations of acoustic waves, scattered by the inclusion. The method will require developing techniques based on Time Reversal methods. A finite element method based on acousto-elastodynamics equations will be derived and used to solve the inverse problem. Our approach will be applied to configurations modeling breast cancer detection, using simulated ultrasound waves.
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Notes
- 1.
u(x, t) is the velocity, that is the time derivative of the displacement. This formulation allows us to derive a pressure-velocity fluid-solid formulation, which will make easier the derivation of the variational formulation, see below.
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Assous, F., Lin, M. (2019). Time-Reversal Methods in Acousto-Elastodynamics. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_20
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DOI: https://doi.org/10.1007/978-3-030-27550-1_20
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