Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity

Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity

In this work we propose and analyze a numerical method for electrical impedance tomography to recover a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suit...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Inverse problems 2020-01, Vol.36 (1), p.14003
Hauptverfasser: Jin, Bangti, Xu, Yifeng
Format: Artikel
Sprache:eng
Schlagworte:
a posteriori error estimator
adaptive finite element method
convergence analysis
electrical impedance tomography
Modica-Mortola functional
piecewise constant conductivity
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 1
container_start_page 14003
container_title Inverse problems
container_volume 36
creator Jin, Bangti
Xu, Yifeng
description In this work we propose and analyze a numerical method for electrical impedance tomography to recover a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.
doi_str_mv 10.1088/1361-6420/ab261e
format Article
fullrecord <record><control><sourceid>iop_cross</sourceid><recordid>TN_cdi_iop_journals_10_1088_1361_6420_ab261e</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>ipab261e</sourcerecordid><originalsourceid>FETCH-LOGICAL-c322t-51ecf75b5df03342804db41543db9c21f407ee8166ed3d466a8a8351644ed763</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWKt3j_kBrs0k2Ww8luIXFLz0HrLJrE1pN0sSW_rv7Vrx5mmG4X0fhoeQe2CPwLSegVBQKcnZzLZcAV6Qyd_pkkwYV6qqFcA1ucl5wxiAhmZC2rm3Qwl7pAld7HNJX66E2NMuJopbdCUFZ7c07Ab0tndIS9zFz2SH9ZEeQllTS4eADg8hI_0h2L6Mix9B-1COt-Sqs9uMd79zSlYvz6vFW7X8eH1fzJeVE5yXqgZ0XVO3te-YEJJrJn0roZbCt0-OQydZg6hBKfTCS6WstlrUoKRE3ygxJeyMdSnmnLAzQwo7m44GmBkVmdGHGX2Ys6JT5eFcCXEwm_iV-tN__8e_AYEYafA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><creator>Jin, Bangti ; Xu, Yifeng</creator><creatorcontrib>Jin, Bangti ; Xu, Yifeng</creatorcontrib><description>In this work we propose and analyze a numerical method for electrical impedance tomography to recover a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.</description><identifier>ISSN: 0266-5611</identifier><identifier>EISSN: 1361-6420</identifier><identifier>DOI: 10.1088/1361-6420/ab261e</identifier><identifier>CODEN: INPEEY</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>a posteriori error estimator ; adaptive finite element method ; convergence analysis ; electrical impedance tomography ; Modica-Mortola functional ; piecewise constant conductivity</subject><ispartof>Inverse problems, 2020-01, Vol.36 (1), p.14003</ispartof><rights>2019 IOP Publishing Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c322t-51ecf75b5df03342804db41543db9c21f407ee8166ed3d466a8a8351644ed763</citedby><cites>FETCH-LOGICAL-c322t-51ecf75b5df03342804db41543db9c21f407ee8166ed3d466a8a8351644ed763</cites><orcidid>0000-0002-3775-9155</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1361-6420/ab261e/pdf$$EPDF$$P50$$Giop$$Hfree_for_read</linktopdf><link.rule.ids>314,780,784,27922,27923,53844,53891</link.rule.ids></links><search><creatorcontrib>Jin, Bangti</creatorcontrib><creatorcontrib>Xu, Yifeng</creatorcontrib><title>Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity</title><title>Inverse problems</title><addtitle>IP</addtitle><addtitle>Inverse Problems</addtitle><description>In this work we propose and analyze a numerical method for electrical impedance tomography to recover a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.</description><subject>a posteriori error estimator</subject><subject>adaptive finite element method</subject><subject>convergence analysis</subject><subject>electrical impedance tomography</subject><subject>Modica-Mortola functional</subject><subject>piecewise constant conductivity</subject><issn>0266-5611</issn><issn>1361-6420</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>O3W</sourceid><recordid>eNp1kE1LAzEQhoMoWKt3j_kBrs0k2Ww8luIXFLz0HrLJrE1pN0sSW_rv7Vrx5mmG4X0fhoeQe2CPwLSegVBQKcnZzLZcAV6Qyd_pkkwYV6qqFcA1ucl5wxiAhmZC2rm3Qwl7pAld7HNJX66E2NMuJopbdCUFZ7c07Ab0tndIS9zFz2SH9ZEeQllTS4eADg8hI_0h2L6Mix9B-1COt-Sqs9uMd79zSlYvz6vFW7X8eH1fzJeVE5yXqgZ0XVO3te-YEJJrJn0roZbCt0-OQydZg6hBKfTCS6WstlrUoKRE3ygxJeyMdSnmnLAzQwo7m44GmBkVmdGHGX2Ys6JT5eFcCXEwm_iV-tN__8e_AYEYafA</recordid><startdate>20200101</startdate><enddate>20200101</enddate><creator>Jin, Bangti</creator><creator>Xu, Yifeng</creator><general>IOP Publishing</general><scope>O3W</scope><scope>TSCCA</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3775-9155</orcidid></search><sort><creationdate>20200101</creationdate><title>Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity</title><author>Jin, Bangti ; Xu, Yifeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-51ecf75b5df03342804db41543db9c21f407ee8166ed3d466a8a8351644ed763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>a posteriori error estimator</topic><topic>adaptive finite element method</topic><topic>convergence analysis</topic><topic>electrical impedance tomography</topic><topic>Modica-Mortola functional</topic><topic>piecewise constant conductivity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jin, Bangti</creatorcontrib><creatorcontrib>Xu, Yifeng</creatorcontrib><collection>IOP Publishing Free Content</collection><collection>IOPscience (Open Access)</collection><collection>CrossRef</collection><jtitle>Inverse problems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jin, Bangti</au><au>Xu, Yifeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity</atitle><jtitle>Inverse problems</jtitle><stitle>IP</stitle><addtitle>Inverse Problems</addtitle><date>2020-01-01</date><risdate>2020</risdate><volume>36</volume><issue>1</issue><spage>14003</spage><pages>14003-</pages><issn>0266-5611</issn><eissn>1361-6420</eissn><coden>INPEEY</coden><abstract>In this work we propose and analyze a numerical method for electrical impedance tomography to recover a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.</abstract><pub>IOP Publishing</pub><doi>10.1088/1361-6420/ab261e</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0002-3775-9155</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0266-5611
ispartof Inverse problems, 2020-01, Vol.36 (1), p.14003
issn 0266-5611
1361-6420
language eng
recordid cdi_iop_journals_10_1088_1361_6420_ab261e
source IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link
subjects a posteriori error estimator
adaptive finite element method
convergence analysis
electrical impedance tomography
Modica-Mortola functional
piecewise constant conductivity
title Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T08%3A39%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-iop_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Adaptive%20reconstruction%20for%20electrical%20impedance%20tomography%20with%20a%20piecewise%20constant%20conductivity&rft.jtitle=Inverse%20problems&rft.au=Jin,%20Bangti&rft.date=2020-01-01&rft.volume=36&rft.issue=1&rft.spage=14003&rft.pages=14003-&rft.issn=0266-5611&rft.eissn=1361-6420&rft.coden=INPEEY&rft_id=info:doi/10.1088/1361-6420/ab261e&rft_dat=%3Ciop_cross%3Eipab261e%3C/iop_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true