Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method
In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Ma...
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| Veröffentlicht in: | IEEE transactions on microwave theory and techniques 2007-06, Vol.55 (6), p.1322-1331 |
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| creator | Movahhedi, M. Abdipour, A. Nentchev, A. Dehghan, M. Selberherr, S. |
| description | In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Maxwell curl equations in order to obtain an unconditionally stable FETD approach, unlike the conventional FETD method, which is conditionally stable. A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived. Investigation of the proposed method formulation shows that it does not generally lead to a tri-diagonal system of equations. Therefore, the Crank-Nicolson FETD method is introduced as another alternative in order to obtain an unconditionally stable method. Numerical results are presented to demonstrate the effectiveness of the proposed methods and are compared to those obtained using the conventional FETD method. |
| doi_str_mv | 10.1109/TMTT.2007.897777 |
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The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Maxwell curl equations in order to obtain an unconditionally stable FETD approach, unlike the conventional FETD method, which is conditionally stable. A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived. Investigation of the proposed method formulation shows that it does not generally lead to a tri-diagonal system of equations. Therefore, the Crank-Nicolson FETD method is introduced as another alternative in order to obtain an unconditionally stable method. Numerical results are presented to demonstrate the effectiveness of the proposed methods and are compared to those obtained using the conventional FETD method.</description><identifier>ISSN: 0018-9480</identifier><identifier>EISSN: 1557-9670</identifier><identifier>DOI: 10.1109/TMTT.2007.897777</identifier><identifier>CODEN: IETMAB</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Alternating-direction implicit (ADI) technique ; Amplification ; Applied classical electromagnetism ; Crank-Nicolson (CN) method ; Electromagnetic transients ; Electromagnetic wave propagation, radiowave propagation ; Electromagnetism; electron and ion optics ; Exact sciences and technology ; Finite difference methods ; Finite element method ; Finite element methods ; finite-element time-domain (FETD) method ; Fundamental areas of phenomenology (including applications) ; instability ; Mathematical analysis ; Mathematical models ; Maxwell equation ; Maxwell equations ; Maxwell's equations ; Microwaves ; Nodular iron ; Nonlinear equations ; Partial differential equations ; Perfectly matched layers ; Physics ; Stability analysis ; Time domain analysis ; Transient analysis ; unconditional stability</subject><ispartof>IEEE transactions on microwave theory and techniques, 2007-06, Vol.55 (6), p.1322-1331</ispartof><rights>2007 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c383t-ac266991262e8f0b8b02773f2d3a85029d8b0bc8e03c003f15739f49a15772e33</citedby><cites>FETCH-LOGICAL-c383t-ac266991262e8f0b8b02773f2d3a85029d8b0bc8e03c003f15739f49a15772e33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4230880$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,314,780,784,789,790,796,23930,23931,25140,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4230880$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18910477$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Movahhedi, M.</creatorcontrib><creatorcontrib>Abdipour, A.</creatorcontrib><creatorcontrib>Nentchev, A.</creatorcontrib><creatorcontrib>Dehghan, M.</creatorcontrib><creatorcontrib>Selberherr, S.</creatorcontrib><title>Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method</title><title>IEEE transactions on microwave theory and techniques</title><addtitle>TMTT</addtitle><description>In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Maxwell curl equations in order to obtain an unconditionally stable FETD approach, unlike the conventional FETD method, which is conditionally stable. A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived. Investigation of the proposed method formulation shows that it does not generally lead to a tri-diagonal system of equations. Therefore, the Crank-Nicolson FETD method is introduced as another alternative in order to obtain an unconditionally stable method. Numerical results are presented to demonstrate the effectiveness of the proposed methods and are compared to those obtained using the conventional FETD method.</description><subject>Alternating-direction implicit (ADI) technique</subject><subject>Amplification</subject><subject>Applied classical electromagnetism</subject><subject>Crank-Nicolson (CN) method</subject><subject>Electromagnetic transients</subject><subject>Electromagnetic wave propagation, radiowave propagation</subject><subject>Electromagnetism; electron and ion optics</subject><subject>Exact sciences and technology</subject><subject>Finite difference methods</subject><subject>Finite element method</subject><subject>Finite element methods</subject><subject>finite-element time-domain (FETD) method</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>instability</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Maxwell equation</subject><subject>Maxwell equations</subject><subject>Maxwell's equations</subject><subject>Microwaves</subject><subject>Nodular iron</subject><subject>Nonlinear equations</subject><subject>Partial differential equations</subject><subject>Perfectly matched layers</subject><subject>Physics</subject><subject>Stability analysis</subject><subject>Time domain analysis</subject><subject>Transient analysis</subject><subject>unconditional stability</subject><issn>0018-9480</issn><issn>1557-9670</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kUFP3DAQha2KSiy0d6ReIqS2pyxjO3HsIwIWkEA9kJ4jr3fS9cqJt7Zz4N_jsKhIHDoXj8ffe5LnEXJGYUkpqIv2sW2XDKBZStXk-kQWtK6bUokGjsgCgMpSVRKOyUmMu3ytapAL8nTpEoZRJzv-Ka9tQJOsH4v7Ye-ssalY-TBMTr8OfV-kLRYrO9qE5Y3DAcdUtHbA8toP2o7FI6at33whn3vtIn59O0_J79VNe3VXPvy6vb-6fCgNlzyV2jAhlKJMMJQ9rOUaWNPwnm24ljUwtcmTtZEI3ADwntYNV32ldG4ahpyfkp8H333wfyeMqRtsNOicHtFPsZMShKilmMkf_yV5JYDm7WTw_AO481Nej8tuoqIVQD1DcIBM8DEG7Lt9sIMOzx2Fbg6jm8Po5jC6QxhZ8v3NV0ejXR_0aGx810lFoXrlvh04i4j_nivGIX-GvwBqlZDL</recordid><startdate>20070601</startdate><enddate>20070601</enddate><creator>Movahhedi, M.</creator><creator>Abdipour, A.</creator><creator>Nentchev, A.</creator><creator>Dehghan, M.</creator><creator>Selberherr, S.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>L7M</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20070601</creationdate><title>Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method</title><author>Movahhedi, M. ; Abdipour, A. ; Nentchev, A. ; Dehghan, M. ; Selberherr, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c383t-ac266991262e8f0b8b02773f2d3a85029d8b0bc8e03c003f15739f49a15772e33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Alternating-direction implicit (ADI) technique</topic><topic>Amplification</topic><topic>Applied classical electromagnetism</topic><topic>Crank-Nicolson (CN) method</topic><topic>Electromagnetic transients</topic><topic>Electromagnetic wave propagation, radiowave propagation</topic><topic>Electromagnetism; electron and ion optics</topic><topic>Exact sciences and technology</topic><topic>Finite difference methods</topic><topic>Finite element method</topic><topic>Finite element methods</topic><topic>finite-element time-domain (FETD) method</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>instability</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Maxwell equation</topic><topic>Maxwell equations</topic><topic>Maxwell's equations</topic><topic>Microwaves</topic><topic>Nodular iron</topic><topic>Nonlinear equations</topic><topic>Partial differential equations</topic><topic>Perfectly matched layers</topic><topic>Physics</topic><topic>Stability analysis</topic><topic>Time domain analysis</topic><topic>Transient analysis</topic><topic>unconditional stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Movahhedi, M.</creatorcontrib><creatorcontrib>Abdipour, A.</creatorcontrib><creatorcontrib>Nentchev, A.</creatorcontrib><creatorcontrib>Dehghan, M.</creatorcontrib><creatorcontrib>Selberherr, S.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on microwave theory and techniques</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Movahhedi, M.</au><au>Abdipour, A.</au><au>Nentchev, A.</au><au>Dehghan, M.</au><au>Selberherr, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method</atitle><jtitle>IEEE transactions on microwave theory and techniques</jtitle><stitle>TMTT</stitle><date>2007-06-01</date><risdate>2007</risdate><volume>55</volume><issue>6</issue><spage>1322</spage><epage>1331</epage><pages>1322-1331</pages><issn>0018-9480</issn><eissn>1557-9670</eissn><coden>IETMAB</coden><abstract>In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Maxwell curl equations in order to obtain an unconditionally stable FETD approach, unlike the conventional FETD method, which is conditionally stable. A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived. Investigation of the proposed method formulation shows that it does not generally lead to a tri-diagonal system of equations. Therefore, the Crank-Nicolson FETD method is introduced as another alternative in order to obtain an unconditionally stable method. Numerical results are presented to demonstrate the effectiveness of the proposed methods and are compared to those obtained using the conventional FETD method.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TMTT.2007.897777</doi><tpages>10</tpages></addata></record> |
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| subjects | Alternating-direction implicit (ADI) technique Amplification Applied classical electromagnetism Crank-Nicolson (CN) method Electromagnetic transients Electromagnetic wave propagation, radiowave propagation Electromagnetism electron and ion optics Exact sciences and technology Finite difference methods Finite element method Finite element methods finite-element time-domain (FETD) method Fundamental areas of phenomenology (including applications) instability Mathematical analysis Mathematical models Maxwell equation Maxwell equations Maxwell's equations Microwaves Nodular iron Nonlinear equations Partial differential equations Perfectly matched layers Physics Stability analysis Time domain analysis Transient analysis unconditional stability |
| title | Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method |
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