On the simultaneous reconstruction of t...

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Title:	On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation
Subtitle:
Abstract:	AbstractThis paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameterκ(x)often referred to asB/Ain the acoustics literature and the wave speedc0(x). The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. For a reformulation of the problem in terms of the squared slownesss=1/c02and the combined coefficientη=κc02we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples.
Keywords:	Applied Mathematics, Computer Science Applications, Mathematical Physics, Signal Processing, Theoretical Computer Science

Publication type:	Article in journal (Authorship)
Publication date:	23.08.2023 (Online)
Published by:	Inverse Problems Inverse Problems to publication  ( IOP Publishing Ltd.; )
Title of the series:	-
Volume number:	39
Issue:	10
First publication:	Yes
Version:	-
Page:	-
Total number of pages:	105001 pp.

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Publication date:	23.08.2023
ISBN (e-book):	-
eISSN:	1361-6420
DOI:	http://dx.doi.org/10.1088/1361-6420/aceef2
Homepage:	-
Open access	Stored in a repository

Publication date:	01.10.2023
ISBN:	-
ISSN:	0266-5611
Homepage:	-

Authors

Barbara Kaltenbacher Barbara.Kaltenbacher@aau.at Institut für Mathematik Research activities To visiting card (internal)

William Rundell United States of America rundell@math.tamu.edu Research activities (external)

Assignment

Organisation	Address
Fakultät für Technische Wissenschaften   Institut für Mathematik Universitätsstraße 65-67 9020 Klagenfurt am Wörthersee Austria    math@aau.at https://www.aau.at/mathematik To organisation	Universitätsstraße 65-67 AT - 9020  Klagenfurt am Wörthersee

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Subject areas	101002 - Analysis 101014 - Numerical mathematics
Research Cluster	No research Research Cluster selected
Citation index	Science Citation Index Expanded (SCI Expanded) Information about the citation index: Master Journal List
Peer reviewed	Yes
Publication focus	Science to Science (Quality indicator: I) Classification raster of the assigned organisational units: Institut für Mathematik
working groups	Inverse Probleme

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Texas A&M University 400 Bizzell St TX 77843 College Station United States of America	400 Bizzell St US - TX 77843  College Station

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