Numerical approximation of the scattering amplitude in elasticity

2021/05/12 by Barceló, Juan A., Castro, Carlos · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2105.05741

Abstract

We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions d=2 and 3. This requires to approximate first the scattering field, for some incident waves, which can be written as the solution of a suitable Lippmann-Schwinger equation. In this work we adapt the method introduced by G. Vainikko in \citeV to solve such equations when considering the Lamé operator. Convergence is proved for sufficiently smooth potentials. Implementation details and numerical examples are also given.

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