Computation of the Sommerfeld Integral tails using the matrix pencil method
The oscillating infinite domain Sommerfeld integrals (SI) are difficult to integrate using a numerical procedure when dealing with structures in a layered media, even though several researchers have attempted to do that. Generally, integration along the real axis is used to compute the SI. However,...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on antennas and propagation Jg. 54; H. 4; S. 1358 - 1362 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
IEEE
01.04.2006
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Schlagworte: | |
| ISSN: | 0018-926X, 1558-2221 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The oscillating infinite domain Sommerfeld integrals (SI) are difficult to integrate using a numerical procedure when dealing with structures in a layered media, even though several researchers have attempted to do that. Generally, integration along the real axis is used to compute the SI. However, significant computational effort is required to integrate the oscillating and slowly decaying function along the tail. Extrapolation methods are generally applied to accelerate the rate of convergence of these integrals. However, there are difficulties with the extrapolation methods, such as locations for the breakpoints. In this paper, we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the SI. In this paper, we fit the tail by a sum of finite (usually 10 to 20) complex exponentials using the matrix pencil method (MPM). The integral of the tail of the SI is then simply calculated by summing some complex numbers. No numerical integration is needed in this process, as the integrals can be done analytically. Good accuracy is achieved with a small number of evaluations for the integral kernel (60 points for the MPM as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods) along the tails of the SI. Simulation results show that to obtain the similar accuracy in the evaluation of the SI, the MPM is approximately 10 times faster than the traditional extrapolation methods. Moreover, since the MPM is robust to the effects of noise, this method is more stable, especially for large values of the horizontal distances. The method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the Green's function for a layered media in the spatial domain. |
|---|---|
| AbstractList | The oscillating infinite domain Sommerfeld integrals (SI) are difficult to integrate using a numerical procedure when dealing with structures in a layered media, even though several researchers have attempted to do that. Generally, integration along the real axis is used to compute the SI. However, significant computational effort is required to integrate the oscillating and slowly decaying function along the tail. Extrapolation methods are generally applied to accelerate the rate of convergence of these integrals. However, there are difficulties with the extrapolation methods, such as locations for the breakpoints. In this paper, we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the SI. In this paper, we fit the tail by a sum of finite (usually 10 to 20) complex exponentials using the matrix pencil method (MPM). The integral of the tail of the SI is then simply calculated by summing some complex numbers. No numerical integration is needed in this process, as the integrals can be done analytically. Good accuracy is achieved with a small number of evaluations for the integral kernel (60 points for the MPM as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods) along the tails of the SI. Simulation results show that to obtain the similar accuracy in the evaluation of the SI, the MPM is approximately 10 times faster than the traditional extrapolation methods. Moreover, since the MPM is robust to the effects of noise, this method is more stable, especially for large values of the horizontal distances. The method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the Green's function for a layered media in the spatial domain. Simulation results show that to obtain the similar accuracy in the evaluation of the SI, the MPM is approximately 10 times faster than the traditional extrapolation methods. [...] since the MPM is robust to the effects of noise, this method is more stable, especially for large values of the horizontal distances. |
| Author | Mengtao Yuan Sarkar, T.K. |
| Author_xml | – sequence: 1 surname: Mengtao Yuan fullname: Mengtao Yuan organization: EECS Dept., Syracuse Univ., NY, USA – sequence: 2 givenname: T.K. surname: Sarkar fullname: Sarkar, T.K. organization: EECS Dept., Syracuse Univ., NY, USA |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17683445$$DView record in Pascal Francis |
| BookMark | eNqNkcFLHTEQh0NR6NP23EMvS6HtaZ-ZbDabHOVRrVSwUAu9hWzeRCO7m9ckC_rfm9cVBA_SUwj5fjOT-Y7IwRQmJOQD0DUAVSfXpz_XjFKxlh0TrXhDVtC2smaMwQFZUQqyVkz8eUuOUrorVy45X5EfmzDu5myyD1MVXJVvsfoVxhGjw2FbXUwZb6IZqmz8kKo5-enmHzOaHP19tcPJ-qEaMd-G7Tty6MyQ8P3TeUx-n3273nyvL6_OLzanl7XlwHKNClDSrTNgjBPOsL6zxvYgoFdGWGmE64WRLbNSqha3gvVMMdkiyqYpL80x-brU3cXwd8aU9eiTxWEwE4Y56RLjTduJtpBfXiWZBNpJgP8Ay8IEUwX89AK8C3Ocyne1AgYNk5wW6PMTZJI1g4umbCnpXfSjiQ8aOiEbzvfjnSycjSGliO4ZoXovVRepei9VL1JLon2RsH6Rl2Mx9Eru45LziPjcRQAHpZpHw02vww |
| CODEN | IETPAK |
| CitedBy_id | crossref_primary_10_1016_j_aeue_2009_05_006 crossref_primary_10_1002_mop_23283 crossref_primary_10_1016_j_camwa_2009_06_044 crossref_primary_10_1109_JLT_2008_2005914 crossref_primary_10_1029_2007RS003731 crossref_primary_10_1109_TGRS_2014_2329995 crossref_primary_10_1109_JMMCT_2016_2613868 crossref_primary_10_1109_TCPMT_2014_2372771 crossref_primary_10_1109_TAP_2009_2037761 crossref_primary_10_1109_TAP_2013_2265377 crossref_primary_10_1109_TAP_2012_2186244 crossref_primary_10_1109_TAP_2015_2477414 crossref_primary_10_1109_LMWC_2012_2188020 crossref_primary_10_1007_s11432_010_4093_7 crossref_primary_10_1109_TAP_2012_2210179 crossref_primary_10_1109_TAP_2022_3227799 crossref_primary_10_1109_TAP_2008_922176 crossref_primary_10_1109_TAP_2022_3161316 crossref_primary_10_1109_TMTT_2012_2195025 crossref_primary_10_1109_TMTT_2012_2231424 crossref_primary_10_1109_TAP_2019_2938675 crossref_primary_10_1109_TAP_2013_2238211 crossref_primary_10_1049_iet_map_2009_0033 crossref_primary_10_1109_LMWC_2007_911971 crossref_primary_10_1109_TAP_2010_2096187 |
| Cites_doi | 10.1109/22.75309 10.1023/A:1022318402393 10.1109/36.752208 10.1109/TMTT.1986.1133357 10.1109/8.56988 10.1109/8.725271 10.1109/22.493917 10.21236/ADA020991 10.1109/29.56027 10.1002/(SICI)1522-6301(199709)7:5<330::AID-MMCE3>3.0.CO;2-L 10.56021/9781421407944 10.1109/TMTT.2002.1006417 10.1109/74.370583 10.1109/22.775434 10.1109/8.558666 10.1109/TAP.2004.829849 10.1109/75.877225 |
| ContentType | Journal Article |
| Copyright | 2006 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2006 |
| Copyright_xml | – notice: 2006 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2006 |
| DBID | 97E RIA RIE AAYXX CITATION IQODW 7SP 8FD L7M H8D F28 FR3 |
| DOI | 10.1109/TAP.2006.872656 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) - NZ CrossRef Pascal-Francis Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace Aerospace Database ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
| DatabaseTitle | CrossRef Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts Aerospace Database Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database Technology Research Database Engineering Research Database Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) - NZ url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Applied Sciences |
| EISSN | 1558-2221 |
| EndPage | 1362 |
| ExternalDocumentID | 2544100001 17683445 10_1109_TAP_2006_872656 1614199 |
| Genre | orig-research |
| GroupedDBID | -~X 0R~ 29I 4.4 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACIWK ACKIV ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 E.L EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RNS RXW TAE TAF TN5 VH1 VJK VOH AAYXX CITATION IQODW RIG 7SP 8FD L7M H8D F28 FR3 |
| ID | FETCH-LOGICAL-c412t-e91e80dfa1aaf6fa2b7cacb161b9a6c8a6fb6a852c8895ed62b29285ee833b6a3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 36 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000236745300040&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0018-926X |
| IngestDate | Sat Sep 27 20:15:39 EDT 2025 Sat Sep 27 19:44:54 EDT 2025 Mon Sep 29 02:44:26 EDT 2025 Sun Nov 09 06:50:44 EST 2025 Mon Jul 21 09:16:51 EDT 2025 Sat Nov 29 08:00:34 EST 2025 Tue Nov 18 21:45:26 EST 2025 Tue Aug 26 16:36:56 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Breakpoint Numerical integration Extrapolation methods Moment method method of moments (MoM) Computational complexity Green function Integral method Stratified medium Accuracy matrix pencil method (MPM) Infinite medium Simulation Sommerfeld integrals Convergence rate Sommerfeld integration (SI) Computational electromagnetics Matrix method Localization |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c412t-e91e80dfa1aaf6fa2b7cacb161b9a6c8a6fb6a852c8895ed62b29285ee833b6a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| PQID | 912132840 |
| PQPubID | 23500 |
| PageCount | 5 |
| ParticipantIDs | proquest_journals_912132840 proquest_miscellaneous_28014629 pascalfrancis_primary_17683445 proquest_miscellaneous_28107811 crossref_primary_10_1109_TAP_2006_872656 proquest_miscellaneous_889435765 crossref_citationtrail_10_1109_TAP_2006_872656 ieee_primary_1614199 |
| PublicationCentury | 2000 |
| PublicationDate | 2006-04-01 |
| PublicationDateYYYYMMDD | 2006-04-01 |
| PublicationDate_xml | – month: 04 year: 2006 text: 2006-04-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY – name: New York |
| PublicationTitle | IEEE transactions on antennas and propagation |
| PublicationTitleAbbrev | TAP |
| PublicationYear | 2006 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref12 ref15 ref14 ref20 ref11 ref10 ref1 ref17 ref16 Chow (ref6) 1990 ref19 ref18 ref8 ref7 ref9 Gander (ref21) 2000; 40 (ref3) 2004 ref5 Yuan (ref2) Sommerfeld (ref4) 1969 |
| References_xml | – ident: ref10 doi: 10.1109/22.75309 – volume: 40 start-page: 84 issue: 1 year: 2000 ident: ref21 article-title: Adaptive Quadrature - Revisited publication-title: BIT doi: 10.1023/A:1022318402393 – ident: ref14 doi: 10.1109/36.752208 – ident: ref18 doi: 10.1109/TMTT.1986.1133357 – ident: ref8 doi: 10.1109/8.56988 – ident: ref2 article-title: Modeling large and complex structures in computational electromagnetics publication-title: IEEE Antennas Propagat Mag – ident: ref15 doi: 10.1109/8.725271 – volume-title: Waves and Fields in Inhomogeneous Media year: 1990 ident: ref6 – ident: ref11 doi: 10.1109/22.493917 – ident: ref5 doi: 10.21236/ADA020991 – volume-title: WIPL-D Pro User’s Manual year: 2004 ident: ref3 – volume-title: Partial Differential Equations in Physics year: 1969 ident: ref4 – ident: ref20 doi: 10.1109/29.56027 – ident: ref17 doi: 10.1002/(SICI)1522-6301(199709)7:5<330::AID-MMCE3>3.0.CO;2-L – ident: ref19 doi: 10.56021/9781421407944 – ident: ref13 doi: 10.1109/TMTT.2002.1006417 – ident: ref16 doi: 10.1109/74.370583 – ident: ref1 doi: 10.1109/22.775434 – ident: ref7 doi: 10.1109/8.558666 – ident: ref9 doi: 10.1109/TAP.2004.829849 – ident: ref12 doi: 10.1109/75.877225 |
| SSID | ssj0014844 |
| Score | 2.008035 |
| Snippet | The oscillating infinite domain Sommerfeld integrals (SI) are difficult to integrate using a numerical procedure when dealing with structures in a layered... Simulation results show that to obtain the similar accuracy in the evaluation of the SI, the MPM is approximately 10 times faster than the traditional... |
| SourceID | proquest pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1358 |
| SubjectTerms | Acceleration Accuracy Applied sciences Computation Convergence Dealing Exact sciences and technology Extrapolation Extrapolation methods Filling Integral equations Integrals Kernel Mathematical analysis Mathematical models matrix pencil method (MPM) Media method of moments (MoM) Moment methods Nonhomogeneous media Radiocommunications Radiowave propagation Sommerfeld integration (SI) Studies Tail Telecommunications Telecommunications and information theory Transmission line matrix methods |
| Title | Computation of the Sommerfeld Integral tails using the matrix pencil method |
| URI | https://ieeexplore.ieee.org/document/1614199 https://www.proquest.com/docview/912132840 https://www.proquest.com/docview/28014629 https://www.proquest.com/docview/28107811 https://www.proquest.com/docview/889435765 |
| Volume | 54 |
| WOSCitedRecordID | wos000236745300040&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: PRVIEE databaseName: IEEE Electronic Library (IEL) - NZ customDbUrl: eissn: 1558-2221 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014844 issn: 0018-926X databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Na9wwEB2S0EN7aNKmpW4-qkMPPdSJJcuydAwhoSEQAk1hb0bSjkpgsw7xbunPr0ZyNiltCr0ZNAYxb-SRNOP3AD4Sabhxvi2d46aUjfNlDOUISKixjum3atEnsYn24kJPJuZyDT6v_oVBxNR8hgf0mGr5094v6arsMO5OJDdmHdbbts3_aq0qBlLLzLjM4wIWajLS-PDKHF4dXeaqg26FIqXqRxkoSapQQ6Qdok9CFrP447ucks3p5v9NcwtejptKdpSj4BWs4fw1vHhENbgN51m-IeHA-sDivo997enWOuBsys4ya8SMUUPpwKgb_nuyuSEK_5_sNgbz9Yxlvek38O305Or4SzkKKZRecrEo0XDU1TRYbm1QwQrXeutdnKczVnltVXDK6kZ4rU2DUyWcMEI3iLqu40j9Fjbm_RzfAZOyVj4CWEvhpDXBoZC6Ctpq1XiudQEH987t_MgyTmIXsy6dNirTRTRI-1J1GY0CPq1euM0EG0-bbpOzH8yynwvY_w29h_F4lIrx1hSwcw9nN67QoTPEZRdzc1XAh9VoXFpUL7Fz7JdDJxKzjjD_suBElsQLYE9YaOK3j2e65v3fJ78Dz_OlDvUC7cLG4m6Je_DM_1hcD3f7KcR_AQ9G-k0 |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1RSxwxEB6sFto-2Fot3Wo1Dz70oaubbDabPIooinoIvcK9LUkuEeG8Ffeu9Oc3k6ynYi30bSGzEOab7CSZ2e8D2EXScGVsnRtDVc4rY_MQygEQX7oypN-idjaKTdSDgRyN1OUSfF_8C-Oci81nbg8fYy1_3No5XpXth90Jp0q9gpWKc0bT31qLmgGXPHEu07CEmRj1RD60UPvDg8tUd5A1E6hV_SgHRVEVbInUXfCKT3IWz77MMd0cv_-_iX6A1X5bSQ5SHKzBkpt-hHePyAbX4SwJOEQkSOtJ2PmRHy3eW3s3GZPTxBsxIdhS2hHsh7-KNjdI4v-b3IZwvp6QpDi9AT-Pj4aHJ3kvpZBbTtksd4o6WYy9plp74TUztdXWhHkapYWVWngjtKyYlVJVbiyYYYrJyjlZlmGk_ATL03bqPgPhvBQ2QFhyZrhW3jjGZeGllqKyVMoM9u6d29ieZxzlLiZNPG8UqglooPqlaBIaGXxbvHCbKDZeNl1HZz-YJT9nsP0EvYfxcJgKEVdlsHkPZ9Ov0a5RyGYXsnORwc5iNCwurJjoqWvnXcMitw5T_7KgSJdEMyAvWEhkuA-nuurL3ye_A29Ohhfnzfnp4GwT3qYrHuwM2oLl2d3cfYXX9tfsurvbjuH-BzGm_ZQ |
| 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=Computation+of+the+Sommerfeld+Integral+tails+using+the+matrix+pencil+method&rft.jtitle=IEEE+transactions+on+antennas+and+propagation&rft.au=Mengtao+Yuan&rft.au=Sarkar%2C+T.K.&rft.date=2006-04-01&rft.pub=IEEE&rft.issn=0018-926X&rft.volume=54&rft.issue=4&rft.spage=1358&rft.epage=1362&rft_id=info:doi/10.1109%2FTAP.2006.872656&rft.externalDocID=1614199 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-926X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-926X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-926X&client=summon |