On the Application of Mosaic-Skeleton Approximations of Matrices in Electrodynamics Problems with Impedance Boundary Conditions
A boundary value problem for Maxwell’s equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing weakly and strongly singular integrals. For the numerical solution of a system of integr...
Uloženo v:
| Vydáno v: | Lobachevskii journal of mathematics Ročník 44; číslo 9; s. 4062 - 4069 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Moscow
Pleiades Publishing
01.09.2023
|
| Témata: | |
| ISSN: | 1995-0802, 1818-9962 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | A boundary value problem for Maxwell’s equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing weakly and strongly singular integrals. For the numerical solution of a system of integral equations, the paper presents a numerical solution method based on piecewise constant approximation and collocation methods. Thus, the original problem is reduced to solving a system of linear algebraic equations with a dense matrix. To effectively solve a system of linear equations, the method of mosaic-skeleton approximations of matrices is used. The specifics of applying the method of mosaic-skeleton approximations in this problem are analyzed. |
|---|---|
| AbstractList | A boundary value problem for Maxwell’s equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing weakly and strongly singular integrals. For the numerical solution of a system of integral equations, the paper presents a numerical solution method based on piecewise constant approximation and collocation methods. Thus, the original problem is reduced to solving a system of linear algebraic equations with a dense matrix. To effectively solve a system of linear equations, the method of mosaic-skeleton approximations of matrices is used. The specifics of applying the method of mosaic-skeleton approximations in this problem are analyzed. |
| Author | Setukha, A. V. Stavtsev, S. L. |
| Author_xml | – sequence: 1 givenname: A. V. surname: Setukha fullname: Setukha, A. V. email: setuhaav@rambler.ru organization: Moscow State University, Marchuk Institute of Numerical Mathematics, Russian Academy of Science – sequence: 2 givenname: S. L. surname: Stavtsev fullname: Stavtsev, S. L. email: sstass2000@mail.ru organization: Marchuk Institute of Numerical Mathematics, Russian Academy of Science |
| BookMark | eNp9kE1OwzAQhS1UJNrCAdj5AgH_pGm8LFWBSkVFKkjsIseeUJfEjuxUkBVXx23ZIbGa0bzvjWbeCA2ss4DQNSU3lPL0dkOFmJCcMMaJIDx_O0NDmtM8ESJjg9hHOTnoF2gUwo5EMMuyIfpeW9xtAc_atjZKdsZZ7Cr85II0Ktl8QA1dHEXZuy_THIFwJGTnjYKAjcWLGlTnne6tbIwK-Nm7soYm4E_TbfGyaUFLqwDfub3V0vd47qw2x1WX6LySdYCr3zpGr_eLl_ljslo_LOezVaJYSrpEk1RkwIEwogmTkrJ8qicZY7LUuiS6VLQERiXXqaZcyGk1YTmDDPIpr5gAPkb0tFd5F4KHqmh9fMf3BSXFIcHiT4LRw06eEFn7Dr7Yub238cx_TD_D0ne7 |
| Cites_doi | 10.1139/p62-067 10.1016/j.jcp.2018.07.013 10.1049/SBEW045E 10.1134/S1995080219110064 10.1134/S0012266120090062 10.1515/rnam-2017-0035 10.1134/S0012266114090110 10.1007/s006070070031 10.1134/S1995080218040029 10.1137/1.9781611973167 |
| ContentType | Journal Article |
| Copyright | Pleiades Publishing, Ltd. 2023 |
| Copyright_xml | – notice: Pleiades Publishing, Ltd. 2023 |
| DBID | AAYXX CITATION |
| DOI | 10.1134/S199508022309038X |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1818-9962 |
| EndPage | 4069 |
| ExternalDocumentID | 10_1134_S199508022309038X |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~9 -~C .VR 06D 0R~ 0VY 1N0 29L 2J2 2JN 2JY 2KG 2KM 2LR 2VQ 2WC 2~H 30V 4.4 408 40D 40E 5GY 5IG 5VS 642 6NX 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABDZT ABECU ABFTV ABHQN ABJNI ABJOX ABKCH ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACDTI ACGFO ACGFS ACHSB ACHXU ACIPV ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AEOHA AEPYU AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGJBK AGMZJ AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AZFZN B-. BA0 BAPOH BDATZ BGNMA C1A CAG COF CS3 CSCUP DDRTE DNIVK DPUIP E4X EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 H13 HF~ HG6 HLICF HMJXF HRMNR HVGLF HZ~ IJ- IKXTQ IWAJR IXC IXD I~X I~Z J-C J9A JBSCW JZLTJ KOV LLZTM LO0 M4Y MA- NPVJJ NQJWS NU0 O9- O93 O9J OK1 P2P P9R PF0 PT4 QOS R89 R9I REM RIG ROL RSV S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TR2 TSG TUC UG4 UOJIU UTJUX UZXMN VFIZW W48 WK8 XSB XU3 YLTOR ZMTXR ~A9 AAPKM AAYXX ABDBE ABFSG ABRTQ ACSTC AEZWR AFDZB AFHIU AFOHR AHPBZ AHWEU AIXLP ATHPR CITATION OVT |
| ID | FETCH-LOGICAL-c240t-d0496e3e020d02aa1287d5622abddb0dbc1be21a3d4d139a7f5282e6e873f29e3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001156509800024&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1995-0802 |
| IngestDate | Sat Nov 29 05:39:40 EST 2025 Fri Feb 21 02:41:09 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 9 |
| Keywords | integral equations impedance boundary condition fast matrix algorithms Maxwell’s equations |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c240t-d0496e3e020d02aa1287d5622abddb0dbc1be21a3d4d139a7f5282e6e873f29e3 |
| PageCount | 8 |
| ParticipantIDs | crossref_primary_10_1134_S199508022309038X springer_journals_10_1134_S199508022309038X |
| PublicationCentury | 2000 |
| PublicationDate | 20230900 2023-09-00 |
| PublicationDateYYYYMMDD | 2023-09-01 |
| PublicationDate_xml | – month: 9 year: 2023 text: 20230900 |
| PublicationDecade | 2020 |
| PublicationPlace | Moscow |
| PublicationPlace_xml | – name: Moscow |
| PublicationTitle | Lobachevskii journal of mathematics |
| PublicationTitleAbbrev | Lobachevskii J Math |
| PublicationYear | 2023 |
| Publisher | Pleiades Publishing |
| Publisher_xml | – name: Pleiades Publishing |
| References | SeniorT. B. A.A note on impedance boundary conditionsCanad. J. Phys.19624066366510.1139/p62-067 SetukhaA.FetisovS.The method of relocation of boundary condition for the problem of electromagnetic wave scattering by perfectly conducting thin objectsJ. Comput. Phys.2018373631647385416110.1016/j.jcp.2018.07.0131416.65549 HoppeD. J.Rahmat-SamiiY.Impedance Boundary Conditions in Electromagnetics1995Washington DCTaylor and Francis VolakisJ. L.SertelK.Integral Equation Methods for Electromagnetic2012Raleigh, NCSciTech10.1049/SBEW045E ZakharovE. V.RyzhakovG. V.SetukhaA. V.Numerical solution of 3D problems of electromagnetic wave diffraction on a system of ideally conducting surfaces by the method of hypersingular integral equationsDiffer. Equat.20145012401251337186710.1134/S00122661140901101308.78011 SetukhaA.BezobrazovaE.The method of hypersingularintegral equations in the problem of electromagnetic wave diffraction by a dielectric body with a partial perfectly conducting coatingRuss. J. Numer. Anal. Math. Model.20173237138010.1515/rnam-2017-00351375.78038 ColtonD.KressR.Integral Equation Methods in Scattering Theory2013PhiladelphiaSIAM10.1137/1.97816119731671291.35003 TyrtyshnikovE.Incomplete cross approximation in the mosaic-skeleton methodComputing200064367380178346810.1007/s0060700700310964.65048 LeontovichM. A.Investigations on Radiowave Propagation, Part II1948MoscowAkad. Nauk ZakharovE. V.SetukhaA. V.Method of boundary integral equations in the problem of diffraction of a monochromatic electromagnetic wave by a system of perfectly conducting and piecewise homogeneous dielectric objectsDiffer. Equat.20205611531166416524310.1134/S00122661200900621451.78024 AparinovA.SetukhaA.StavtsevS.Parallel implementation for some applications of integral equations methodLobachevskii J. Math.201839477485381194110.1134/S19950802180400291483.65211 GibsonW.The Method of Moments in Electromagnetics2008Boca RatonChapman and Hall/CRC1175.78002 AparinovA. A.SetukhaA. V.StavtsevS. L.Low rank methods of approximations in an electromagnetic problemLobachevskii J. Math.20194017711780404362210.1134/S19950802191100641434.65052 A. Setukha (7430_CR5) 2018; 373 E. Tyrtyshnikov (7430_CR6) 2000; 64 A. Setukha (7430_CR12) 2017; 32 A. A. Aparinov (7430_CR13) 2019; 40 M. A. Leontovich (7430_CR1) 1948 W. Gibson (7430_CR9) 2008 E. V. Zakharov (7430_CR4) 2020; 56 D. Colton (7430_CR11) 2013 J. L. Volakis (7430_CR8) 2012 E. V. Zakharov (7430_CR10) 2014; 50 A. Aparinov (7430_CR7) 2018; 39 D. J. Hoppe (7430_CR3) 1995 T. B. A. Senior (7430_CR2) 1962; 40 |
| References_xml | – reference: SeniorT. B. A.A note on impedance boundary conditionsCanad. J. Phys.19624066366510.1139/p62-067 – reference: AparinovA. A.SetukhaA. V.StavtsevS. L.Low rank methods of approximations in an electromagnetic problemLobachevskii J. Math.20194017711780404362210.1134/S19950802191100641434.65052 – reference: ZakharovE. V.SetukhaA. V.Method of boundary integral equations in the problem of diffraction of a monochromatic electromagnetic wave by a system of perfectly conducting and piecewise homogeneous dielectric objectsDiffer. Equat.20205611531166416524310.1134/S00122661200900621451.78024 – reference: SetukhaA.FetisovS.The method of relocation of boundary condition for the problem of electromagnetic wave scattering by perfectly conducting thin objectsJ. Comput. Phys.2018373631647385416110.1016/j.jcp.2018.07.0131416.65549 – reference: TyrtyshnikovE.Incomplete cross approximation in the mosaic-skeleton methodComputing200064367380178346810.1007/s0060700700310964.65048 – reference: SetukhaA.BezobrazovaE.The method of hypersingularintegral equations in the problem of electromagnetic wave diffraction by a dielectric body with a partial perfectly conducting coatingRuss. J. Numer. Anal. Math. Model.20173237138010.1515/rnam-2017-00351375.78038 – reference: AparinovA.SetukhaA.StavtsevS.Parallel implementation for some applications of integral equations methodLobachevskii J. Math.201839477485381194110.1134/S19950802180400291483.65211 – reference: VolakisJ. L.SertelK.Integral Equation Methods for Electromagnetic2012Raleigh, NCSciTech10.1049/SBEW045E – reference: GibsonW.The Method of Moments in Electromagnetics2008Boca RatonChapman and Hall/CRC1175.78002 – reference: ZakharovE. V.RyzhakovG. V.SetukhaA. V.Numerical solution of 3D problems of electromagnetic wave diffraction on a system of ideally conducting surfaces by the method of hypersingular integral equationsDiffer. Equat.20145012401251337186710.1134/S00122661140901101308.78011 – reference: ColtonD.KressR.Integral Equation Methods in Scattering Theory2013PhiladelphiaSIAM10.1137/1.97816119731671291.35003 – reference: LeontovichM. A.Investigations on Radiowave Propagation, Part II1948MoscowAkad. Nauk – reference: HoppeD. J.Rahmat-SamiiY.Impedance Boundary Conditions in Electromagnetics1995Washington DCTaylor and Francis – volume: 40 start-page: 663 year: 1962 ident: 7430_CR2 publication-title: Canad. J. Phys. doi: 10.1139/p62-067 – volume: 373 start-page: 631 year: 2018 ident: 7430_CR5 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2018.07.013 – volume-title: Integral Equation Methods for Electromagnetic year: 2012 ident: 7430_CR8 doi: 10.1049/SBEW045E – volume: 40 start-page: 1771 year: 2019 ident: 7430_CR13 publication-title: Lobachevskii J. Math. doi: 10.1134/S1995080219110064 – volume: 56 start-page: 1153 year: 2020 ident: 7430_CR4 publication-title: Differ. Equat. doi: 10.1134/S0012266120090062 – volume: 32 start-page: 371 year: 2017 ident: 7430_CR12 publication-title: Russ. J. Numer. Anal. Math. Model. doi: 10.1515/rnam-2017-0035 – volume: 50 start-page: 1240 year: 2014 ident: 7430_CR10 publication-title: Differ. Equat. doi: 10.1134/S0012266114090110 – volume-title: The Method of Moments in Electromagnetics year: 2008 ident: 7430_CR9 – volume-title: Investigations on Radiowave Propagation, Part II year: 1948 ident: 7430_CR1 – volume-title: Impedance Boundary Conditions in Electromagnetics year: 1995 ident: 7430_CR3 – volume: 64 start-page: 367 year: 2000 ident: 7430_CR6 publication-title: Computing doi: 10.1007/s006070070031 – volume: 39 start-page: 477 year: 2018 ident: 7430_CR7 publication-title: Lobachevskii J. Math. doi: 10.1134/S1995080218040029 – volume-title: Integral Equation Methods in Scattering Theory year: 2013 ident: 7430_CR11 doi: 10.1137/1.9781611973167 |
| SSID | ssj0022666 |
| Score | 2.2632778 |
| Snippet | A boundary value problem for Maxwell’s equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a... |
| SourceID | crossref springer |
| SourceType | Index Database Publisher |
| StartPage | 4062 |
| SubjectTerms | Algebra Analysis Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes |
| Title | On the Application of Mosaic-Skeleton Approximations of Matrices in Electrodynamics Problems with Impedance Boundary Conditions |
| URI | https://link.springer.com/article/10.1134/S199508022309038X |
| Volume | 44 |
| WOSCitedRecordID | wos001156509800024&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: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1818-9962 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0022666 issn: 1995-0802 databaseCode: RSV dateStart: 20080101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB60etCDb7G-2IMnJZhmN016rKWiYGuhWnoLm-wGgpBItoqe_OvO7iaVoh70GDIsYTPJfN_O4wM489NUchm2nLjthg4TPHA41UWONOBSg_zQVFVO7oLhMJxOO6Oqj1vV1e51StL8qa3uCLsc62Zi0xlK9dlCOF2GFV8Pm9EUfTyZsyyMOKalyLQeh65XpTJ_XGIxGC1mQk2Aud7816NtwUaFJ0nXOsA2LMl8B9YH82Gsahc-7nOCl6T7lasmRUoGheJZ4oyfMPAgANS3y-Its62MyliY8f1SkSwnfSuXI6yAvSIjK0SjiD7IJbcIvoX2H3JlZJrKd9IrdDJcL7UHj9f9h96NU-kuOAnG95kjkDW0JZWIJIXrcY4hLBCIkzweCxG7Ik5asfRanAomEEDyIPWRuMm2DAOaeh1J96GRF7k8ACI1BeZJkKAZ66QC0WbKYua7Anllwv0mnNcvIHq24zUiQ0soi77tahMu6u2Pqi9N_W59-CfrI1jTQvK2euwYGrPyRZ7AavI6y1R5ajzsE3d6zGE |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB60CurBt1ife_CkBNPspkmPtbS02NZCa-ktbLIbCEIi2Sp68q-7j6RS1IMeQ4YlbCaZ79t5fABXbhxzyv2aFdZt3yKMehbFqsgRe5QrkO_rqspp3xsO_dmsMSr6uEVZ7V6mJPWf2uiOkNuxaibWnaFYnS34s1VYI0plR1H08XTBsmTE0S1FuvXYt50ilfnjEsvBaDkTqgNMZ-dfj7YL2wWeRE3jAHuwwtN92BoshrGKA_h4SJG8RM2vXDXKYjTIBE0ia_wkA48EgOp2nr0lppVRaAs9vp8LlKSobeRymBGwF2hkhGgEUge5qCfBN1P-g-60TFP-jlqZSoarpQ7hsdOetLpWobtgRTK-zy0mWUOdYy6RJLMdSmUI85jESQ4NGQttFka1kDs1ihlhEkBSL3YlceN17ns4dhocH0ElzVJ-DIgrCkwjL5JmpBEziTZjEhLXZpJXRtStwnX5AoJnM14j0LQEk-Dbrlbhptz-oPjSxO_WJ3-yvoSN7mTQD_q94f0pbCpReVNJdgaVef7Cz2E9ep0nIr_Q3vYJFfnPRQ |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFA46RfTBuzivefBJKeuadO0e59xwuM3hdOytpE0CRWhHU0Wf_Ovm0k6G-iA-lh5CaU4435dz-QC4cDlnhPl1K2zYvoUp8SyCVJEj8ghTIN_XVZWTvjcc-tNpc1TonIqy2r1MSZqeBjWlKclrM8oLDRJcG6vGYt0litQ9gz9dBitYEhlV0_UwnswZl4w-ur1ItyH7tlOkNX9cYjEwLWZFdbDpbv37M7fBZoEzYcs4xg5YYsku2BjMh7SKPfBxn0D5CFtfOWyYcjhIBYkja_wsA5IEhup1lr7FpsVRaAs91p8JGCewY2R0qBG2F3BkBGoEVBe8sCdBOVV-Ba-1fFP2DtupSpKrpfbBU7fz2L61Cj0GK5JxP7eoZBMNhphEmNR2CJGhzaMSPzkkpDS0aRjVQ-bUCaKYSmBJPO5KQscazPcQd5oMHYBKkibsEECmqDGJvEia4SanEoVyHGLXppJvRsStgstyM4KZGbsRaLqCcPDtr1bBVbkVQXECxe_WR3-yPgdro5tu0O8N747ButKaNwVmJ6CSZy_sFKxGr3kssjPteJ-D79gp |
| 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=On+the+Application+of+Mosaic-Skeleton+Approximations+of+Matrices+in+Electrodynamics+Problems+with+Impedance+Boundary+Conditions&rft.jtitle=Lobachevskii+journal+of+mathematics&rft.au=Setukha%2C+A.+V.&rft.au=Stavtsev%2C+S.+L.&rft.date=2023-09-01&rft.pub=Pleiades+Publishing&rft.issn=1995-0802&rft.eissn=1818-9962&rft.volume=44&rft.issue=9&rft.spage=4062&rft.epage=4069&rft_id=info:doi/10.1134%2FS199508022309038X&rft.externalDocID=10_1134_S199508022309038X |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1995-0802&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1995-0802&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1995-0802&client=summon |