Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method
When a finite-difference time-domain (FDTD) method is constructed by applying the Crank-Nicolson (CN) scheme to discretize Maxwell's equations, a huge sparse irreducible matrix results, which cannot be solved efficiently. This paper proposes a factorization-splitting scheme using two substeps t...
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| Veröffentlicht in: | IEEE transactions on microwave theory and techniques 2006-05, Vol.54 (5), p.2275-2284 |
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| creator | Guilin Sun Trueman, C.W. |
| description | When a finite-difference time-domain (FDTD) method is constructed by applying the Crank-Nicolson (CN) scheme to discretize Maxwell's equations, a huge sparse irreducible matrix results, which cannot be solved efficiently. This paper proposes a factorization-splitting scheme using two substeps to decompose the generalized CN matrix into two simple matrices with the terms not factored confined to one sub-step. Two unconditionally stable methods are developed: one has the same numerical dispersion relation as the alternating-direction implicit FDTD method, and the other has a much more isotropic numerical velocity. The limit on the time-step size to avoid numerical attenuation is investigated, and is shown to be below the Nyquist sampling rate. The intrinsic temporal numerical dispersion is discussed, which is the fundamental accuracy limit of the methods. |
| doi_str_mv | 10.1109/TMTT.2006.873639 |
| format | Article |
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This paper proposes a factorization-splitting scheme using two substeps to decompose the generalized CN matrix into two simple matrices with the terms not factored confined to one sub-step. Two unconditionally stable methods are developed: one has the same numerical dispersion relation as the alternating-direction implicit FDTD method, and the other has a much more isotropic numerical velocity. The limit on the time-step size to avoid numerical attenuation is investigated, and is shown to be below the Nyquist sampling rate. The intrinsic temporal numerical dispersion is discussed, which is the fundamental accuracy limit of the methods.</description><identifier>ISSN: 0018-9480</identifier><identifier>EISSN: 1557-9670</identifier><identifier>DOI: 10.1109/TMTT.2006.873639</identifier><identifier>CODEN: IETMAB</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Anisotropic magnetoresistance ; Applied sciences ; Attenuation ; Computational electromagnetics ; Crank-Nicolson (CN) scheme ; Dispersions ; Electric, optical and optoelectronic circuits ; Electronics ; Exact sciences and technology ; Finite difference method ; Finite difference methods ; Finite difference time domain method ; finite-difference time-domain (FDTD) method ; Geometry ; Magnetoelectric, magnetostrictive, magnetoacoustic, magnetooptic and magnetothermal devices. Spintronics ; Mathematical analysis ; Mathematical models ; Matrix decomposition ; Maxwell's equations ; Microwave filters ; Microwaves ; numerical anisotropy ; numerical dispersion ; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices ; Sparse matrices ; Sun ; Theoretical study. Circuits analysis and design ; Time domain analysis ; Transmission line matrix methods ; unconditionally stable method</subject><ispartof>IEEE transactions on microwave theory and techniques, 2006-05, Vol.54 (5), p.2275-2284</ispartof><rights>2006 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2006</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c449t-c3917d755a1083c0d3b3394a4a61e626b56152fec712791a9edbd1cd5f188923</citedby><cites>FETCH-LOGICAL-c449t-c3917d755a1083c0d3b3394a4a61e626b56152fec712791a9edbd1cd5f188923</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1629072$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27923,27924,54757</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1629072$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17795241$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Guilin Sun</creatorcontrib><creatorcontrib>Trueman, C.W.</creatorcontrib><title>Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method</title><title>IEEE transactions on microwave theory and techniques</title><addtitle>TMTT</addtitle><description>When a finite-difference time-domain (FDTD) method is constructed by applying the Crank-Nicolson (CN) scheme to discretize Maxwell's equations, a huge sparse irreducible matrix results, which cannot be solved efficiently. This paper proposes a factorization-splitting scheme using two substeps to decompose the generalized CN matrix into two simple matrices with the terms not factored confined to one sub-step. Two unconditionally stable methods are developed: one has the same numerical dispersion relation as the alternating-direction implicit FDTD method, and the other has a much more isotropic numerical velocity. The limit on the time-step size to avoid numerical attenuation is investigated, and is shown to be below the Nyquist sampling rate. The intrinsic temporal numerical dispersion is discussed, which is the fundamental accuracy limit of the methods.</description><subject>Anisotropic magnetoresistance</subject><subject>Applied sciences</subject><subject>Attenuation</subject><subject>Computational electromagnetics</subject><subject>Crank-Nicolson (CN) scheme</subject><subject>Dispersions</subject><subject>Electric, optical and optoelectronic circuits</subject><subject>Electronics</subject><subject>Exact sciences and technology</subject><subject>Finite difference method</subject><subject>Finite difference methods</subject><subject>Finite difference time domain method</subject><subject>finite-difference time-domain (FDTD) method</subject><subject>Geometry</subject><subject>Magnetoelectric, magnetostrictive, magnetoacoustic, magnetooptic and magnetothermal devices. Spintronics</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Matrix decomposition</subject><subject>Maxwell's equations</subject><subject>Microwave filters</subject><subject>Microwaves</subject><subject>numerical anisotropy</subject><subject>numerical dispersion</subject><subject>Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices</subject><subject>Sparse matrices</subject><subject>Sun</subject><subject>Theoretical study. Circuits analysis and design</subject><subject>Time domain analysis</subject><subject>Transmission line matrix methods</subject><subject>unconditionally stable method</subject><issn>0018-9480</issn><issn>1557-9670</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp90U2LFDEQBuAgCo6rd8FLI6inHlP5zlGG1V1Y9dL3JpOuMFm7kzHpOfjvN-MsLHjwlBT1VEHyEvIW6BaA2s_D92HYMkrV1miuuH1GNiCl7q3S9DnZUAqmt8LQl-RVrfetFJKaDfHXIUQfMa1dXI4zLu3m1phT7XLo1gN2u-LSr_5H9HmuOXXVHxrqQi5_uyGmuGI_xRCwYPLYrXFpdV5cTN2C6yFPr8mL4OaKbx7PKzJ8vR52N_3dz2-3uy93vRfCrr3nFvSkpXRADfd04nvOrXDCKUDF1F4qkCyg18C0BWdx2k_gJxnAGMv4Ffl0WXss-fcJ6zousXqcZ5cwn-rYEDecS9nkx_9KZiiA5aLB9__A-3wqqT1iNEoKZkGcEb0gX3KtBcN4LHFx5c8IdDxnM56zGc_ZjJds2siHx72uejeH9sU-1qc5ra1kApp7d3EREZ_ailmqGX8AvHeXSg</recordid><startdate>20060501</startdate><enddate>20060501</enddate><creator>Guilin Sun</creator><creator>Trueman, C.W.</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>20060501</creationdate><title>Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method</title><author>Guilin Sun ; Trueman, C.W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c449t-c3917d755a1083c0d3b3394a4a61e626b56152fec712791a9edbd1cd5f188923</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Anisotropic magnetoresistance</topic><topic>Applied sciences</topic><topic>Attenuation</topic><topic>Computational electromagnetics</topic><topic>Crank-Nicolson (CN) scheme</topic><topic>Dispersions</topic><topic>Electric, optical and optoelectronic circuits</topic><topic>Electronics</topic><topic>Exact sciences and technology</topic><topic>Finite difference method</topic><topic>Finite difference methods</topic><topic>Finite difference time domain method</topic><topic>finite-difference time-domain (FDTD) method</topic><topic>Geometry</topic><topic>Magnetoelectric, magnetostrictive, magnetoacoustic, magnetooptic and magnetothermal devices. Spintronics</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Matrix decomposition</topic><topic>Maxwell's equations</topic><topic>Microwave filters</topic><topic>Microwaves</topic><topic>numerical anisotropy</topic><topic>numerical dispersion</topic><topic>Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices</topic><topic>Sparse matrices</topic><topic>Sun</topic><topic>Theoretical study. Circuits analysis and design</topic><topic>Time domain analysis</topic><topic>Transmission line matrix methods</topic><topic>unconditionally stable method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guilin Sun</creatorcontrib><creatorcontrib>Trueman, C.W.</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>Guilin Sun</au><au>Trueman, C.W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method</atitle><jtitle>IEEE transactions on microwave theory and techniques</jtitle><stitle>TMTT</stitle><date>2006-05-01</date><risdate>2006</risdate><volume>54</volume><issue>5</issue><spage>2275</spage><epage>2284</epage><pages>2275-2284</pages><issn>0018-9480</issn><eissn>1557-9670</eissn><coden>IETMAB</coden><abstract>When a finite-difference time-domain (FDTD) method is constructed by applying the Crank-Nicolson (CN) scheme to discretize Maxwell's equations, a huge sparse irreducible matrix results, which cannot be solved efficiently. This paper proposes a factorization-splitting scheme using two substeps to decompose the generalized CN matrix into two simple matrices with the terms not factored confined to one sub-step. Two unconditionally stable methods are developed: one has the same numerical dispersion relation as the alternating-direction implicit FDTD method, and the other has a much more isotropic numerical velocity. The limit on the time-step size to avoid numerical attenuation is investigated, and is shown to be below the Nyquist sampling rate. The intrinsic temporal numerical dispersion is discussed, which is the fundamental accuracy limit of the methods.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TMTT.2006.873639</doi><tpages>10</tpages></addata></record> |
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| subjects | Anisotropic magnetoresistance Applied sciences Attenuation Computational electromagnetics Crank-Nicolson (CN) scheme Dispersions Electric, optical and optoelectronic circuits Electronics Exact sciences and technology Finite difference method Finite difference methods Finite difference time domain method finite-difference time-domain (FDTD) method Geometry Magnetoelectric, magnetostrictive, magnetoacoustic, magnetooptic and magnetothermal devices. Spintronics Mathematical analysis Mathematical models Matrix decomposition Maxwell's equations Microwave filters Microwaves numerical anisotropy numerical dispersion Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices Sparse matrices Sun Theoretical study. Circuits analysis and design Time domain analysis Transmission line matrix methods unconditionally stable method |
| title | Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method |
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