An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods
type: Item
instance of: scholarly article
title: An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods
zbMATH Open document ID: 1029.74028
DOI: 10.1155/S1110757X0210903X
author: Shinuk Kim
author: K. L. Kreider
published in: Journal of Applied Mathematics
publication date: 2003-03-18T00:00:00Z
full work available at URL: https://eudml.org/doc/50532
review text: Summary: Elastic wave propagation in weakly nonlinear elastic rods is considered in time domain. The method of wave splitting is employed to formulate a standard scattering problem, forming the mathematical basis for both direct and inverse problems. A quasi-linear version of Wendroff scheme (FDTD) is used to solve the direct problem. To solve the inverse problem, an asymptotic expansion is used for the wave field; this linearizes the order equations, allowing the use of standard numerical techniques. Analysis and numerical results are presented for three model inverse problems: (i) recovery of a nonlinear parameter in stress-strain relation for a homogeneous elastic rod, (ii) recovery of cross-sectional area for a homogeneous elastic rod, (iii) recovery of elastic modulus for an inhomogeneous elastic rod.
Mathematics Subject Classification ID: 74J25
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 74H10
Mathematics Subject Classification ID: 74S20
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 1884077
zbMATH Keywords: elastic wave
zbMATH Keywords: method of wave splitting
zbMATH Keywords: scattering
zbMATH Keywords: quasi-linear Wendroff scheme
zbMATH Keywords: direct problem
zbMATH Keywords: inverse problem
zbMATH Keywords: asymptotic expasion
zbMATH Keywords: stress-strain relation
zbMATH Keywords: homogeneous elastic rod
zbMATH Keywords: elastic modulus
zbMATH Keywords: inhomogeneous elastic rod
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1884077