Numerical approximation of the scattering amplitude in elasticity

• Autores: Juan Antonio Barceló Varcárcel , Carlos Manuel Castro Barbero
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 79, Nº. 4, 2022, págs. 549-570
• Idioma: inglés
• DOI: 10.1007/s40324-021-00270-1
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• Resumen

  • 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 Vainikko (Res Rep A 387:3–18, 1997) to solve such equations when considering the Lamé operator. Convergence is proved for sufficiently smooth potentials. Implementation details and numerical examples are also given.