Numerical approximation of the scattering amplitude in elasticity

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-07
Main Authors: Barceló, Juan A, Castro, Carlos
Format: Article
Language:English
Subjects:
Approximation
Elasticity
Incident waves
Mathematical analysis
Numerical methods
Scattering amplitude
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 \cite{V} to solve such equations when considering the Lamé operator. Convergence is proved for sufficiently smooth potentials. Implementation details and numerical examples are also given.
ISSN:2331-8422