Detection of cavities using the method of fundamental solutions

The determination of the boundary of a cavity, defined here as a perfectly insulated inclusion, within a conducting medium from a single voltage and current flux measurements on the accessible boundary of the medium, can be modelled as an inverse boundary value problem for harmonic functions. We pro...

Full description

Saved in:
Bibliographic Details
Published in:Inverse problems in science and engineering Vol. 17; no. 6; pp. 803 - 820
Main Authors: Karageorghis, A., Lesnic, D.
Format: Journal Article
Language:English
Published: Taylor & Francis 01.01.2009
Subjects:
cavity detection
inverse problem
method of fundamental solutions
Primary 65N35
Secondary 65N21
ISSN:1741-5977, 1741-5985
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The determination of the boundary of a cavity, defined here as a perfectly insulated inclusion, within a conducting medium from a single voltage and current flux measurements on the accessible boundary of the medium, can be modelled as an inverse boundary value problem for harmonic functions. We propose a novel numerical solution method for this inverse problem based on the method of fundamental solutions. The algorithm for imaging the interior of the medium also makes use of radial polar parametrization of the unknown cavity shape in two dimensions (or spherical parametrization in three dimensions). This discretization yields a highly non-linear and ill-conditioned system of equations. The system is recast as a non-linear least-squares problem with penalty regularizing terms included in order to improve the stability of the numerical solution with respect to random noise introduced in the measured error-contaminated input data. The feasibility of this new method is illustrated by some numerical examples.
AbstractList The determination of the boundary of a cavity, defined here as a perfectly insulated inclusion, within a conducting medium from a single voltage and current flux measurements on the accessible boundary of the medium, can be modelled as an inverse boundary value problem for harmonic functions. We propose a novel numerical solution method for this inverse problem based on the method of fundamental solutions. The algorithm for imaging the interior of the medium also makes use of radial polar parametrization of the unknown cavity shape in two dimensions (or spherical parametrization in three dimensions). This discretization yields a highly non-linear and ill-conditioned system of equations. The system is recast as a non-linear least-squares problem with penalty regularizing terms included in order to improve the stability of the numerical solution with respect to random noise introduced in the measured error-contaminated input data. The feasibility of this new method is illustrated by some numerical examples.
Author Lesnic, D.
Karageorghis, A.
Author_xml – sequence: 1
  givenname: A.
  surname: Karageorghis
  fullname: Karageorghis, A.
  organization: Department of Mathematics and Statistics, University of Cyprus
– sequence: 2
  givenname: D.
  surname: Lesnic
  fullname: Lesnic, D.
  organization: Department of Applied Mathematics, University of Leeds
BookMark eNqNkEtLxDAQx4MoqKsfwFtP3laTpmlSEER8w4IXPZfsZKKRNtEk9fHtbVnx4IJ4GGaYmd88_rtk0wePhBwwesSoosdMVkw0cgxLMVrNN8jOlJuLRonNn1jKbbKb0jOlvKwrvkNOLzAjZBd8EWwB-s1lh6kYkvOPRX7Cosf8FMxUtIM3ukefdVek0A0TlPbIltVdwv1vPyMPV5f35zfzxd317fnZYg5cyjw3sKyNrSkqI0XVAIIolwyYtoJaMJwaaDiCVKoBSREtAlVLIStR1aYEy2fkcDX3JYbXAVNue5cAu057DENqeaVqphQfG9mqEWJIKaJtX6LrdfxsGW0nqdo1qUZG_mLAZT39l6N23Z_kyYp03obY6_cQO9Nm_dmFaKP24MbT_rH4D3yNavNH5l-DxZUq
CitedBy_id crossref_primary_10_1016_j_enganabound_2023_05_019
crossref_primary_10_1016_j_enganabound_2022_11_022
crossref_primary_10_3934_ipi_2024043
crossref_primary_10_1080_00207160_2013_868447
crossref_primary_10_1002_num_21739
crossref_primary_10_1108_HFF_08_2011_0153
crossref_primary_10_1007_s11075_024_01831_x
crossref_primary_10_1016_j_enganabound_2010_11_010
crossref_primary_10_1137_24M170716X
crossref_primary_10_1016_j_cam_2011_10_020
crossref_primary_10_1016_j_ijmecsci_2014_05_015
crossref_primary_10_1016_j_enganabound_2016_02_011
crossref_primary_10_1016_j_enganabound_2017_10_012
crossref_primary_10_3390_math10081324
crossref_primary_10_1016_j_matcom_2012_02_002
crossref_primary_10_1016_j_compstruc_2012_05_001
crossref_primary_10_1007_s00707_019_02473_0
crossref_primary_10_1016_j_apm_2017_01_021
crossref_primary_10_1016_j_enganabound_2010_05_008
crossref_primary_10_1080_00207160_2012_689290
crossref_primary_10_1016_j_amc_2021_126402
crossref_primary_10_1016_j_enganabound_2010_09_014
crossref_primary_10_1080_19475705_2018_1547324
crossref_primary_10_1016_j_compstruc_2015_01_002
crossref_primary_10_1016_j_ijsolstr_2019_06_001
crossref_primary_10_1080_10407790_2013_849979
crossref_primary_10_1016_j_enganabound_2012_02_001
crossref_primary_10_1016_j_enganabound_2020_08_013
Cites_doi 10.1016/S0009-2509(97)00044-4
10.1016/S0895-7177(99)00233-2
10.1016/0041-5553(64)90006-0
10.1007/s10444-004-1782-z
10.1016/0377-0427(91)90175-J
10.1515/1569394053583711
10.1002/num.20104
10.1088/0266-5611/18/4/314
10.1088/0266-5611/2/2/003
10.1080/10407790490436624
10.1007/1-4020-5370-3_522
10.1016/0045-7949(78)90166-9
10.1023/A:1012873712701
10.1016/j.camwa.2005.02.021
10.1016/j.enganabound.2006.06.005
10.1002/nme.1763
10.1016/j.enganabound.2003.07.005
10.1016/0021-9991(92)90178-2
10.1109/10.844230
10.1023/A:1018981221740
10.1093/imanum/18.2.273
10.1137/S003613990037090X
10.1109/38.674972
10.1016/j.jcp.2005.03.007
10.1088/0143-0815/13/A/029
10.1016/j.matcom.2004.02.006
10.1137/0722040
10.1002/nme.1620230105
10.1016/0898-1221(95)00186-3
10.1002/(SICI)1097-0207(19990420)44:11<1653::AID-NME558>3.0.CO;2-1
10.1016/S0955-7997(01)00007-8
10.1088/0266-5611/19/5/308
10.1216/jiea/1181075363
10.1147/sj.353.0587
10.1006/jdeq.2000.3987
10.1088/0266-5611/18/5/308
10.1016/0045-7949(78)90023-8
10.1016/j.enganabound.2007.05.004
10.1137/0714043
10.1088/0266-5611/21/3/009
10.1002/num.10500
10.1137/0508038
10.1016/0045-7949(84)90169-X
10.1088/0266-5611/21/4/002
ContentType Journal Article
Copyright Copyright Taylor & Francis 2009
Copyright_xml – notice: Copyright Taylor & Francis 2009
DBID AAYXX
CITATION
7SC
7TB
8FD
FR3
H8D
JQ2
KR7
L7M
L~C
L~D
DOI 10.1080/17415970802580263
DatabaseName CrossRef
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
Aerospace Database
ProQuest Computer Science Collection
Civil Engineering Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Aerospace Database
Civil Engineering Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList Aerospace Database
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
EISSN 1741-5985
EndPage 820
ExternalDocumentID 10_1080_17415970802580263
358194
Genre Article
GroupedDBID .7F
.QJ
29J
2DF
30N
4.4
5GY
5VS
AAENE
AAJMT
ABCCY
ABDBF
ABFIM
ABHAV
ABPEM
ABTAI
ACGEJ
ACGFO
ACGFS
ACGOD
ACIWK
ACTIO
ACUHS
ADCVX
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AGMYJ
AIJEM
AIYEW
AJWEG
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AQRUH
AQTUD
AVBZW
AWYRJ
BLEHA
CAG
CCCUG
CE4
COF
CS3
DGEBU
DKSSO
DU5
EAP
EBS
EJD
EMK
EPL
EST
ESX
E~A
E~B
GTTXZ
H13
HF~
HZ~
H~P
I-F
IPNFZ
J.P
KYCEM
M4Z
MK~
NA5
NY~
O9-
PQQKQ
RIG
S-T
SNACF
TDBHL
TFL
TFW
TN5
TTHFI
TUS
TWF
UT5
UU3
~S~
AAYXX
CITATION
7SC
7TB
8FD
FR3
H8D
JQ2
KR7
L7M
L~C
L~D
ID FETCH-LOGICAL-c377t-dcb6df60e8d7549cec52b1c1af50fcd30dc93ec7889c70eefec08b574546d2cf3
IEDL.DBID TFW
ISICitedReferencesCount 41
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000268758200006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1741-5977
IngestDate Thu Jul 10 19:09:36 EDT 2025
Sat Nov 29 02:42:02 EST 2025
Tue Nov 18 22:26:58 EST 2025
Mon May 13 12:09:02 EDT 2019
Mon Oct 20 23:48:23 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 6
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c377t-dcb6df60e8d7549cec52b1c1af50fcd30dc93ec7889c70eefec08b574546d2cf3
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
PQID 34861883
PQPubID 23500
PageCount 18
ParticipantIDs crossref_primary_10_1080_17415970802580263
crossref_citationtrail_10_1080_17415970802580263
proquest_miscellaneous_34861883
informaworld_taylorfrancis_310_1080_17415970802580263
PublicationCentury 2000
PublicationDate 2009-01-01
PublicationDateYYYYMMDD 2009-01-01
PublicationDate_xml – month: 01
  year: 2009
  text: 2009-01-01
  day: 01
PublicationDecade 2000
PublicationTitle Inverse problems in science and engineering
PublicationYear 2009
Publisher Taylor & Francis
Publisher_xml – name: Taylor & Francis
References CIT0030
CIT0032
CIT0031
CIT0034
CIT0033
Ladyzenskaya OA (CIT0014) 1968; 23
CIT0036
CIT0035
CIT0038
CIT0037
CIT0039
CIT0041
CIT0040
CIT0043
CIT0042
CIT0001
CIT0045
CIT0044
Garbow BS (CIT0049) 1980
Borman D (CIT0011)
McLean W (CIT0013) 2000
CIT0003
CIT0047
CIT0002
CIT0046
CIT0005
CIT0004
CIT0007
CIT0006
CIT0009
CIT0008
CIT0050
CIT0051
CIT0010
CIT0012
(CIT0048) 2007
Golberg MA (CIT0022) 1999
CIT0016
CIT0015
CIT0018
CIT0017
CIT0019
Golberg MA (CIT0021) 1997
CIT0020
CIT0023
CIT0025
CIT0024
Morozov A (CIT0052) 1966; 7
CIT0027
CIT0026
CIT0029
CIT0028
References_xml – ident: CIT0007
  doi: 10.1016/S0009-2509(97)00044-4
– ident: CIT0041
  doi: 10.1016/S0895-7177(99)00233-2
– ident: CIT0029
  doi: 10.1016/0041-5553(64)90006-0
– ident: CIT0030
  doi: 10.1007/s10444-004-1782-z
– ident: CIT0028
  doi: 10.1016/0377-0427(91)90175-J
– ident: CIT0003
  doi: 10.1515/1569394053583711
– ident: CIT0033
  doi: 10.1002/num.20104
– ident: CIT0051
  doi: 10.1088/0266-5611/18/4/314
– volume: 23
  volume-title: Transactions of the Mathematical Monographs
  year: 1968
  ident: CIT0014
– ident: CIT0042
  doi: 10.1088/0266-5611/2/2/003
– ident: CIT0004
  doi: 10.1080/10407790490436624
– ident: CIT0046
  doi: 10.1007/1-4020-5370-3_522
– ident: CIT0024
  doi: 10.1016/0045-7949(78)90166-9
– ident: CIT0032
  doi: 10.1023/A:1012873712701
– ident: CIT0043
  doi: 10.1016/j.camwa.2005.02.021
– ident: CIT0045
  doi: 10.1016/j.enganabound.2006.06.005
– volume-title: MINPACK Project
  year: 1980
  ident: CIT0049
– ident: CIT0050
  doi: 10.1002/nme.1763
– volume: 7
  start-page: 414
  year: 1966
  ident: CIT0052
  publication-title: Soviet Math. Dokl.
– ident: CIT0031
  doi: 10.1016/j.enganabound.2003.07.005
– ident: CIT0034
  doi: 10.1016/0021-9991(92)90178-2
– ident: CIT0010
  doi: 10.1109/10.844230
– ident: CIT0020
  doi: 10.1023/A:1018981221740
– ident: CIT0037
  doi: 10.1093/imanum/18.2.273
– ident: CIT0005
  doi: 10.1137/S003613990037090X
– ident: CIT0011
  publication-title: J. Integral Eqns. Appl.
– ident: CIT0016
  doi: 10.1109/38.674972
– ident: CIT0044
  doi: 10.1016/j.jcp.2005.03.007
– start-page: 103
  volume-title: Boundary Integral Methods: Numerical and Mathematical Aspects, vol. 1 of Comput. Eng
  year: 1999
  ident: CIT0022
– ident: CIT0047
  doi: 10.1088/0143-0815/13/A/029
– ident: CIT0001
  doi: 10.1016/j.matcom.2004.02.006
– ident: CIT0026
  doi: 10.1137/0722040
– ident: CIT0009
  doi: 10.1002/nme.1620230105
– ident: CIT0027
  doi: 10.1016/0898-1221(95)00186-3
– volume-title: Strongly Elliptic Systems and Boundary Integral Equations
  year: 2000
  ident: CIT0013
– ident: CIT0036
  doi: 10.1002/(SICI)1097-0207(19990420)44:11<1653::AID-NME558>3.0.CO;2-1
– ident: CIT0038
  doi: 10.1016/S0955-7997(01)00007-8
– ident: CIT0002
  doi: 10.1088/0266-5611/19/5/308
– ident: CIT0008
  doi: 10.1216/jiea/1181075363
– ident: CIT0015
  doi: 10.1147/sj.353.0587
– ident: CIT0018
  doi: 10.1006/jdeq.2000.3987
– ident: CIT0019
  doi: 10.1088/0266-5611/18/5/308
– ident: CIT0023
  doi: 10.1016/0045-7949(78)90023-8
– ident: CIT0040
  doi: 10.1016/j.enganabound.2007.05.004
– volume-title: NAG(UK) Ltd
  year: 2007
  ident: CIT0048
– ident: CIT0039
  doi: 10.1137/0714043
– ident: CIT0017
  doi: 10.1088/0266-5611/21/3/009
– ident: CIT0035
  doi: 10.1002/num.10500
– ident: CIT0012
  doi: 10.1137/0508038
– ident: CIT0025
  doi: 10.1016/0045-7949(84)90169-X
– volume-title: Discrete Projection Methods for Integral Equations
  year: 1997
  ident: CIT0021
– ident: CIT0006
  doi: 10.1088/0266-5611/21/4/002
SSID ssj0032643
Score 1.9532112
Snippet The determination of the boundary of a cavity, defined here as a perfectly insulated inclusion, within a conducting medium from a single voltage and current...
SourceID proquest
crossref
informaworld
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 803
SubjectTerms cavity detection
inverse problem
method of fundamental solutions
Primary 65N35
Secondary 65N21
Title Detection of cavities using the method of fundamental solutions
URI https://www.tandfonline.com/doi/abs/10.1080/17415970802580263
https://www.proquest.com/docview/34861883
Volume 17
WOSCitedRecordID wos000268758200006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor and Francis Online Journals
  customDbUrl:
  eissn: 1741-5985
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0032643
  issn: 1741-5977
  databaseCode: TFW
  dateStart: 20040201
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELZQxcDCG1GeHpiQLJw4jp0JIaBiqhiK6Bb5iZBQipq04udjx05FVdQBhky5cyL7znfnO38HwFVhFcOCGZSmmKNMYYxERgXCGbNGSEk1kW2zCTYc8vG4eI61OXUsq_QxtA1AEe1e7ZVbyLqriLtJvBUsmL8lSt2Te6xPZ_a9Wo4Gr90-7PySUF7vqJFHWetymr-NsGSVljBLV_bo1vAMdv75y7tgO3qc8C6IyB7YMNU-2IneJ4y6XR-A2wfTtHVZFZxYqMS8xVqFvjD-DTo3EYZm0_6l9ddHQlcAuJDdQ_AyeBzdP6HYXgEpwliDtJK5tjk2XDMXJSqjaCoTlQhLsVWaYK0KYpSLkQu3nsZYozCXlGU0y3WqLDkCvWpSmWMAqU5IIhRz3plwEaLgjorTzORMWilx3ge4m95SRexx3wLjo0wiROnKBPXB9YLlMwBvrCPGP9esbNrTDhtak6ySl81X0wd0DQtZ86nLTh5Kp4k-vSIqM5k5noznCefk5I8jn4KtkKry5ztnoNdMZ-YcbKp5815PL1rZ_gawwPXG
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NS8MwFH_oFPTi_MT5tRw8CcW0aZr0JKKOiXN4mOitJGkignSydcM_36QfwzHZQQ899SUtyfvOy-8BnMdGMSyY9oIAcy9UGHsipMLDITNaSElTIotmE6zf56-v8VOVcBtXZZUuhjYlUEShq51wu2R0XRJ36TszGDN3TZTaJyKrsEatnXXY-YPOS62JrWdSFthbcs_hrNWnmr9NMWeX5lBLF7R0YXo6zf_-9DZsVU4nui65ZAdWdLYLzcoBRZV4j_fg6lbnRWlWhoYGKTEt4FaRq41_Q9ZTRGW_affSuBskZWMANGPffXju3A1uul7VYcFThLHcS5WMUhNhzVNmA0WlFQ2kr3xhKDYqJThVMdHKhsmx3VKtjVaYS8pCGkZpoAw5gEY2zPQhIJr6xBeKWQdN2CBRcEvFaagjJo2UOGoBrtc3URX8uOuC8ZH4FUrpwgK14GI25LPE3lhGjH9uWpIXCQ9TdidZJE_yr7wFdMkQsuRT7ZohEiuM7oRFZHo4sWNCHvmck6M_ztyGje7gsZf07vsPx7BZnly5dM8JNPLRRJ_Cuprm7-PRWcHo30T7-fA
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB58IV58i-szB09CMW2aR08i6qIoiwdFbyVPEaS77HYXf75JH6Ks7EEPPXUmLcnMZCYz-QbgJHOaY8ltlCRYRKnGOJIplRFOubNSKWqIqppN8F5PvLxkD01tzqgpqwwxtKuBIipbHZR7YFxbEXcWh10w4-GWKPUPI_Ow6N1mFgT8sfvcGmLvmNT19Z48CjBrbVLztyF-bEs_QEunjHS183TX_vnP67DauJzoopaRDZizxSasNe4napR7tAXnV7asCrMK1HdIy0kFtopCZfwr8n4iqrtNh5cu3B-p2wKgL-Hdhqfu9ePlTdT0V4g04byMjFbMOIatMNyHidpqmqhYx9JR7LQh2OiMWO2D5MwvqLXOaiwU5SlNmUm0IzuwUPQLuwuImpjEUnPvnkkfIkrhqQRNLePKKYVZB3A7vbluwMdDD4z3PG4wSqcmqAOnXyyDGnljFjH-vmZ5WR13uLo3yTR5Xn6UHaAzWMiMTx238pB7VQz5FVnY_tjzpILFQpC9P458DMsPV938_rZ3tw8rddoqnPUcwEI5HNtDWNKT8m00PKrE_BNVIPii
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Detection+of+cavities+using+the+method+of+fundamental+solutions&rft.jtitle=Inverse+problems+in+science+and+engineering&rft.au=Karageorghis%2C+A.&rft.au=Lesnic%2C+D.&rft.date=2009-01-01&rft.pub=Taylor+%26+Francis&rft.issn=1741-5977&rft.eissn=1741-5985&rft.volume=17&rft.issue=6&rft.spage=803&rft.epage=820&rft_id=info:doi/10.1080%2F17415970802580263&rft.externalDocID=358194
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1741-5977&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1741-5977&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1741-5977&client=summon