Electromagnetic solvers for medium-size objects. Time-Domain - FDTD. The Finite-Difference. (Yee 1966) G. Marrocco, University of Roma, Tor Vergata
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1 lecomagec solves fo medum-se obecs The e-dffeece Tme-Doma - DTD Yee 966 G. Maocco Uves of Roma To Vegaa
2 e-dffeece Tme-Doma - Scope G. Maocco Uves of Roma To Vegaa
3 G. Maocco Uves of Roma To Vegaa Tme Tme-Doma Maell quaos Doma Maell quaos J B D J M m # ' & # ' & # ' & ' * µ * ' aada Law Ampee Law Gauss Law Magec-flu cosevao Chage cosevao law B D µ Cosuve quaos Causal me-vaa meda Tesos fo asoopc meda plasma fee M J lecc souce eal o equvale Magec souce equvale ˆ ˆ ˆ µ
4 Tme-Doma Maell quaos -cod Cul-equaos gve a ssem of s coupled scala dffeeal equaos of fs ode. - Space ad me devaves - Bouda codos G. Maocco Uves of Roma To Vegaa
![Tme-Doma Maell quaos J -Bouda codos M ˆ Radao owad f lecc bouda Magec Bouda lm - [ * ˆ ]](/docs-images/92/109091334/images/5-6.jpg "0 µ ˆ * ˆ 0 ˆ * ˆ 0 Impedace bouda ˆ * * ˆ Z s * ˆ Z s. s G.")
5 Tme-Doma Maell quaos J -Bouda codos M ˆ Radao owad f lecc bouda Magec Bouda lm - [ * ˆ ] 0 µ ˆ * ˆ 0 ˆ * ˆ 0 Impedace bouda ˆ * * ˆ Z s * ˆ Z s. s G. Maocco Uves of Roma To Vegaa
6 DTD Appomao Paal dffeeal equaos wll be appomaed b eplacg he mespace devaves wh fe dffeeces Couous ssem! Dscee ssem G. Maocco Uves of Roma To Vegaa
7 DTD Appomao - basc dea The devaves ca be appomaed b he cemeal ao ' owad dffeece Bacwad dffeece Ceal dffeece G. Maocco Uves of Roma To Vegaa
8 Talo epaso ' 0 ' ' 0 ' ''! DTD Appomao 6! 4[ 0 0 ] - accuac ' 0 ' ' 0 ' ''! 6! 4[ 0 0 ] Bacwadowad dffeece: 0 0 ' 0 '' 0 '''! 6 O Ceal dffeece: 0 0 ' 0 ' ''! 3 6! O 3 4[ 0 0 ] Ceal-Dffeece appomao s secod-ode accuae G. Maocco Uves of Roma To Vegaa
9 G. Maocco Uves of Roma To Vegaa DTD Appomao DTD Appomao - basc dea basc dea 5 A fuco ad s fs devave ae defed sampled a dffee pos : ' 6 - ' I fou dmesos: Doma spaceme samplg
10 Space samplg gd -wo-dmesoal case Yee cell eld samples ae shfed he elemea Y cell Cell-se:! #0 G. Maocco Uves of Roma To Vegaa
11 G. Maocco Uves of Roma To Vegaa Space samplg gd Space samplg gd -D homogeeous case D homogeeous case µ 6
12 G. Maocco Uves of Roma To Vegaa Tme samplg scheme Tme samplg scheme Sabl Codo Coua # c 8 D D 3D 3 µ µ 9 & 9 & 9 & lecc ad magec felds ae sampled a aleae mes
13 G. Maocco Uves of Roma To Vegaa Complee D equaos Complee D equaos J : : ; < >? : : ; < >? : : ; < >? J Couous case DTD appomao
![f [ J 0.5 ] lowcha 0.5 g[ 0.](/docs-images/92/109091334/images/14-4.jpg "5 05 plc equaos Ieave soluo updag No ma veso Compuaoal ad memo comple popooal o")
14 f [ J 0.5 ] lowcha 0.5 g[ plc equaos Ieave soluo updag No ma veso Compuaoal ad memo comple popooal o he umbe of cells uows ] G. Maocco Uves of Roma To Vegaa
15 G. Maocco Uves of Roma To Vegaa Thee Thee-dmesoal scheme dmesoal scheme lecc compoes ae ageal o he cell edges Magec compoes ae ohogoal o he cell sdes
16 A e.m. souce could have he followg epesso J L & cao wavefoms wdebad moochomac Susod f f 0 Gaussa pulse 0 < f < f ma Devaed Gaussa pulse f < f < m f ma Modulaed Gaussa pulse 0 f f < f G. Maocco Uves of Roma To Vegaa
17 Gd ucao To be compuaoal affodable he smulao ego should be ucaed he suoudg of he scaees Absobg Bouda Codos eed o be efoced o he ucao sdes o smulae he ope space ad avod eflecos - Oe wa equaos MUR - Pefecl mached laes PML G. Maocco Uves of Roma To Vegaa
18 Absobg Bouda Codos - Oe wa equao Oe Wa quao gqus & Mada 970 A paal dffeeal equao ha pems wave popagao ol some decos. Whe appled o he oue bouda of a DTD gd a oewave equao umecall absobs mpgg scaeed waves. pohess: he feld mpgg he bouda s supposed o be as a plae wave U U c U 0 D wave equao U: feld compoe paallel o he bouda L D D D c Paal 5 5 c dffeeal opeao ± D L L L L D ± S acoao c fo 0 bouda D S Appled o 0 wos as a eac D c L aalcal ABC fo wave moo U 0 ogag fom he eo of spaal doma a a G. Maocco Uves of Roma To Vegaa
19 Absobg Bouda Codos - Pefecl Mached Laes G. Maocco Uves of Roma To Vegaa
20 Absobg Bouda Codos - oe-wa eq.. vs. PML µsp GND Mached load Oe-wa MUR Refleco coeffce a he souce po G. Maocco Uves of Roma To Vegaa
21 Absobg Bouda Codos - oe-wa eq.. Mu Mu vs. PML Oe wa MUR s ode efoced ol o he bouda ageal feld compoes las cell compuaoall lgh lowe accuac useful fo a fs me fas aalss PML efoced o a hc bouda shell 6- cells compuaoal had 0 ume ovehead hgh accuac A <-70dB useful fo efeme aalss G. Maocco Uves of Roma To Vegaa
22 Tme Tucao Tme eaos pogesses ul he elecomagec ssem ehbs he sead-sae. Moochomac egme Afe a ase each feld sample oscllaes a a same fequec Tes ove he mamummmum wh successve peods ma m < Pulsed egme The whole sgal eeg afe boucg ad absopo wll leave he compuao doma Tes ove global eeg G. Maocco Uves of Roma To Vegaa
23 G. Maocco Uves of Roma To Vegaa amples
24 Avalable Solves XDTD Remcom MPIR IMST Gmbh Mcowave Sudo CST SMCAD Speag BST Uv Roma To Vegaa G. Maocco Uves of Roma To Vegaa
25 Refeeces M. N. O. Sadu Numecal Techques lecomagecs CRC Pess Boca Rao L 99 A. S. Ku R. J. Lubbes The e-dffeece Tme-Doma mehod fo lecomagecs CRC Pess Boca Rao L 993 A. Taflove Compuaoal elecomagecs: The e-dffeece Tme-Doma mehod Aech ouse Nowood MA 995 A. Taflove Advaces Compuaoal elecomagecs: The e-dffeece Tme-Doma mehod Aech ouse Nowood MA 998 G. Maocco Uves of Roma To Vegaa
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