An SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components for TM Analysis
A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method is proposed to model geometrically fine structures in this article. Compared with other works, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or...
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| Veröffentlicht in: | IEEE transactions on microwave theory and techniques 2023-02, Vol.71 (2), p.579-592 |
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| creator | Wang, Yuhui Cheng, Yu Wang, Xiang-Hua Yang, Shunchuan Chen, Zhizhang |
| description | A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method is proposed to model geometrically fine structures in this article. Compared with other works, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or modifying any field components through field extrapolation on the boundaries to make the discrete operators satisfy the SBP property. The accuracy of extrapolation keeps consistency with that of the second-order finite-difference scheme near the boundaries. In addition, the SATs are used to weakly enforce the tangential boundary conditions between multiple mesh blocks with different mesh sizes. With carefully designed interpolation matrices and selected free parameters of the SATs, no dissipation occurs in the whole computational domain. Therefore, its long-time stability is theoretically guaranteed. Four numerical examples are carried out to validate its effectiveness. Results show that the proposed SBP-SAT FDTD subgridding method is stable, accurate, efficient, and easy to implement based on the existing FDTD codes with only a few modifications. |
| doi_str_mv | 10.1109/TMTT.2022.3205633 |
| format | Article |
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Compared with other works, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or modifying any field components through field extrapolation on the boundaries to make the discrete operators satisfy the SBP property. The accuracy of extrapolation keeps consistency with that of the second-order finite-difference scheme near the boundaries. In addition, the SATs are used to weakly enforce the tangential boundary conditions between multiple mesh blocks with different mesh sizes. With carefully designed interpolation matrices and selected free parameters of the SATs, no dissipation occurs in the whole computational domain. Therefore, its long-time stability is theoretically guaranteed. Four numerical examples are carried out to validate its effectiveness. Results show that the proposed SBP-SAT FDTD subgridding method is stable, accurate, efficient, and easy to implement based on the existing FDTD codes with only a few modifications.</description><identifier>ISSN: 0018-9480</identifier><identifier>EISSN: 1557-9670</identifier><identifier>DOI: 10.1109/TMTT.2022.3205633</identifier><identifier>CODEN: IETMAB</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Boundary conditions ; Extrapolation ; Finite difference method ; Finite difference methods ; Finite difference time domain method ; Finite element method ; Finite-difference time-domain (FDTD) ; Interpolation ; Mathematical models ; Microwave theory and techniques ; Numerical stability ; Operators (mathematics) ; Power system stability ; projection operator ; stability ; Stability criteria ; subgridding ; summation-by-parts simultaneous approximation term (SBP-SAT) ; Time-domain analysis</subject><ispartof>IEEE transactions on microwave theory and techniques, 2023-02, Vol.71 (2), p.579-592</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2023</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c293t-d9d7aaac4c3b3ee904cfa90e0ebe7ea94797352cf97cdc270d41c7be8150ad403</citedby><cites>FETCH-LOGICAL-c293t-d9d7aaac4c3b3ee904cfa90e0ebe7ea94797352cf97cdc270d41c7be8150ad403</cites><orcidid>0000-0003-1208-7329 ; 0000-0002-4190-3885 ; 0000-0001-5346-2514</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9897090$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/9897090$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Wang, Yuhui</creatorcontrib><creatorcontrib>Cheng, Yu</creatorcontrib><creatorcontrib>Wang, Xiang-Hua</creatorcontrib><creatorcontrib>Yang, Shunchuan</creatorcontrib><creatorcontrib>Chen, Zhizhang</creatorcontrib><title>An SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components for TM Analysis</title><title>IEEE transactions on microwave theory and techniques</title><addtitle>TMTT</addtitle><description>A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method is proposed to model geometrically fine structures in this article. Compared with other works, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or modifying any field components through field extrapolation on the boundaries to make the discrete operators satisfy the SBP property. The accuracy of extrapolation keeps consistency with that of the second-order finite-difference scheme near the boundaries. In addition, the SATs are used to weakly enforce the tangential boundary conditions between multiple mesh blocks with different mesh sizes. With carefully designed interpolation matrices and selected free parameters of the SATs, no dissipation occurs in the whole computational domain. Therefore, its long-time stability is theoretically guaranteed. Four numerical examples are carried out to validate its effectiveness. Results show that the proposed SBP-SAT FDTD subgridding method is stable, accurate, efficient, and easy to implement based on the existing FDTD codes with only a few modifications.</description><subject>Boundary conditions</subject><subject>Extrapolation</subject><subject>Finite difference method</subject><subject>Finite difference methods</subject><subject>Finite difference time domain method</subject><subject>Finite element method</subject><subject>Finite-difference time-domain (FDTD)</subject><subject>Interpolation</subject><subject>Mathematical models</subject><subject>Microwave theory and techniques</subject><subject>Numerical stability</subject><subject>Operators (mathematics)</subject><subject>Power system stability</subject><subject>projection operator</subject><subject>stability</subject><subject>Stability criteria</subject><subject>subgridding</subject><subject>summation-by-parts simultaneous approximation term (SBP-SAT)</subject><subject>Time-domain analysis</subject><issn>0018-9480</issn><issn>1557-9670</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1Lw0AURQdRsFZ_gLgZcOEq9c1HOpllbW0VWhSaIq7CdOalprRJnUkW_fcmtLh6XDj38jiE3DMYMAb6OV2k6YAD5wPBIR4KcUF6LI5VpIcKLkkPgCWRlglck5sQtm2UMSQ98jsq6fLlM1qOUjqdpBO6bNYbXzhXlBu6wPqncnQVurCszWaDHh39RnwKdNZSgX4VLdLUdFG5Ij923LTAnaPjan-oSizrQPPK03RBR6XZHUMRbslVbnYB7863T1bT13T8Fs0_Zu_j0TyyXIs6ctopY4yVVqwFogZpc6MBAdeo0GiptBIxt7lW1lmuwElm1RoTFoNxEkSfPJ52D776bTDU2bZqfPtEyLhSUnCWSNlS7ERZX4XgMc8Ovtgbf8wYZJ3ZrDObdWazs9m283DqFIj4z-tEK9Ag_gAdN3SY</recordid><startdate>20230201</startdate><enddate>20230201</enddate><creator>Wang, Yuhui</creator><creator>Cheng, Yu</creator><creator>Wang, Xiang-Hua</creator><creator>Yang, Shunchuan</creator><creator>Chen, Zhizhang</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Compared with other works, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or modifying any field components through field extrapolation on the boundaries to make the discrete operators satisfy the SBP property. The accuracy of extrapolation keeps consistency with that of the second-order finite-difference scheme near the boundaries. In addition, the SATs are used to weakly enforce the tangential boundary conditions between multiple mesh blocks with different mesh sizes. With carefully designed interpolation matrices and selected free parameters of the SATs, no dissipation occurs in the whole computational domain. Therefore, its long-time stability is theoretically guaranteed. Four numerical examples are carried out to validate its effectiveness. Results show that the proposed SBP-SAT FDTD subgridding method is stable, accurate, efficient, and easy to implement based on the existing FDTD codes with only a few modifications.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TMTT.2022.3205633</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0003-1208-7329</orcidid><orcidid>https://orcid.org/0000-0002-4190-3885</orcidid><orcidid>https://orcid.org/0000-0001-5346-2514</orcidid></addata></record> |
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| subjects | Boundary conditions Extrapolation Finite difference method Finite difference methods Finite difference time domain method Finite element method Finite-difference time-domain (FDTD) Interpolation Mathematical models Microwave theory and techniques Numerical stability Operators (mathematics) Power system stability projection operator stability Stability criteria subgridding summation-by-parts simultaneous approximation term (SBP-SAT) Time-domain analysis |
| title | An SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components for TM Analysis |
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