A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS

This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholt...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational mathematics 2018-01, Vol.36 (1), p.1-16
Main Author: Li, Peijun
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c343t-b17232c7208cd5b7aab017ab517021d4c3d70270f3f6eeb31480fbb7f2de13e53
cites
container_end_page 16
container_issue 1
container_start_page 1
container_title Journal of computational mathematics
container_volume 36
creator Li, Peijun
description This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.
doi_str_mv 10.4208/jcm.1605-m2015-0407
format article
fullrecord <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_4208_jcm_1605_m2015_0407</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cqvip_id>674130753</cqvip_id><jstor_id>45151756</jstor_id><sourcerecordid>45151756</sourcerecordid><originalsourceid>FETCH-LOGICAL-c343t-b17232c7208cd5b7aab017ab517021d4c3d70270f3f6eeb31480fbb7f2de13e53</originalsourceid><addsrcrecordid>eNo9j01PwkAQhjdGExH9Bcak8WoWZ3Z2u_RYm4IkSElbSDhtuv1AiAVtufjvLUI4zSQzzzvzMPaIMJAChq_bvB6gC4rXAlBxkKCvWA89D7lG8q5ZD4SS3JPg3bK7tt0CAAmpe-zFd5JFvAxXTjRyonk4cwJ_OUlXThL4aRrGk9nYmcfR2zT8SO7ZTZV9teXDufbZYhSmwTufRuNJ4E95TpIO3KIWJHLdPZYXyuoss4A6swo1CCxkTkXXaKiocsvSEsohVNbqShQlUqmoz-iUmzf7tm3Kynw3mzprfg2COfqaztccfc2_rzn6dtTTidq2h31zQaTC7rByu_nzOfVzv1v_bHbry46rJRJoRfQH0XpZjg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS</title><source>JSTOR Journals and Primary Sources</source><creator>Li, Peijun</creator><creatorcontrib>Li, Peijun</creatorcontrib><description>This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.</description><identifier>ISSN: 0254-9409</identifier><identifier>EISSN: 1991-7139</identifier><identifier>DOI: 10.4208/jcm.1605-m2015-0407</identifier><language>eng</language><publisher>Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy of Sciences</publisher><ispartof>Journal of computational mathematics, 2018-01, Vol.36 (1), p.1-16</ispartof><rights>Copyright 2018 AMSS, Chinese Academy of Sciences</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c343t-b17232c7208cd5b7aab017ab517021d4c3d70270f3f6eeb31480fbb7f2de13e53</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/85761X/85761X.jpg</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/45151756$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/45151756$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,58237,58470</link.rule.ids></links><search><creatorcontrib>Li, Peijun</creatorcontrib><title>A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS</title><title>Journal of computational mathematics</title><addtitle>Journal of Computational Mathematics</addtitle><description>This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.</description><issn>0254-9409</issn><issn>1991-7139</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNo9j01PwkAQhjdGExH9Bcak8WoWZ3Z2u_RYm4IkSElbSDhtuv1AiAVtufjvLUI4zSQzzzvzMPaIMJAChq_bvB6gC4rXAlBxkKCvWA89D7lG8q5ZD4SS3JPg3bK7tt0CAAmpe-zFd5JFvAxXTjRyonk4cwJ_OUlXThL4aRrGk9nYmcfR2zT8SO7ZTZV9teXDufbZYhSmwTufRuNJ4E95TpIO3KIWJHLdPZYXyuoss4A6swo1CCxkTkXXaKiocsvSEsohVNbqShQlUqmoz-iUmzf7tm3Kynw3mzprfg2COfqaztccfc2_rzn6dtTTidq2h31zQaTC7rByu_nzOfVzv1v_bHbry46rJRJoRfQH0XpZjg</recordid><startdate>20180101</startdate><enddate>20180101</enddate><creator>Li, Peijun</creator><general>Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy of Sciences</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180101</creationdate><title>A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS</title><author>Li, Peijun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-b17232c7208cd5b7aab017ab517021d4c3d70270f3f6eeb31480fbb7f2de13e53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Peijun</creatorcontrib><collection>维普_期刊</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>维普中文期刊数据库</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><jtitle>Journal of computational mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Peijun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS</atitle><jtitle>Journal of computational mathematics</jtitle><addtitle>Journal of Computational Mathematics</addtitle><date>2018-01-01</date><risdate>2018</risdate><volume>36</volume><issue>1</issue><spage>1</spage><epage>16</epage><pages>1-16</pages><issn>0254-9409</issn><eissn>1991-7139</eissn><abstract>This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.</abstract><pub>Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy of Sciences</pub><doi>10.4208/jcm.1605-m2015-0407</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0254-9409
ispartof Journal of computational mathematics, 2018-01, Vol.36 (1), p.1-16
issn 0254-9409
1991-7139
language eng
recordid cdi_crossref_primary_10_4208_jcm_1605_m2015_0407
source JSTOR Journals and Primary Sources
title A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T04%3A29%3A43IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20SURVEY%20OF%20OPEN%20CAVITY%20SCATTERING%20PROBLEMS&rft.jtitle=Journal%20of%20computational%20mathematics&rft.au=Li,%20Peijun&rft.date=2018-01-01&rft.volume=36&rft.issue=1&rft.spage=1&rft.epage=16&rft.pages=1-16&rft.issn=0254-9409&rft.eissn=1991-7139&rft_id=info:doi/10.4208/jcm.1605-m2015-0407&rft_dat=%3Cjstor_cross%3E45151756%3C/jstor_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c343t-b17232c7208cd5b7aab017ab517021d4c3d70270f3f6eeb31480fbb7f2de13e53%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_cqvip_id=674130753&rft_jstor_id=45151756&rfr_iscdi=true