Improvement of Electromagnetic Wave Propagation Using Novel Finite Element Methodology

Transcription

1 Improvm of Elcromgc Wv ropgo Usg Novl F Elm Mhodolog Npo Jsumroum d Somsk kmgool Fcul of Tchcl Educo Kg Mogku s Uvrs of Tcholog Norh Bgkok Thld po89@gml.com src - Ths rsrch prsd w umrcl lss pproch o mprov smulo sofwr pplg h f lm srg for lcromgc prolm. W prs h lzd prs of lcromgc wv d propgo vrous mdum. Ths wll l o dcrs duco d rsrch rld udgs. Nowds h commrcl sofwr s cosl d co dusl h sourc cod so h s o suffc o smulo rsrch works. Th smulo progrm s shszd d dsgd o solv h compl oudr codo for lcromgc wv propgo. Th smulo rflcs h ffcv umrcl lss pproch prsd usg MTLB. I c ppld grg duco s wll s c usd o solv complcd lcromgc ssus. Kwords - F Elm Mhod Smulo rogrm Elcromgc Wv ropgo I. INTODUCTION cl h cholog dvlopm s ssl commuco ssm. Usull h hgh frquc ssms commuco cholog r dvlopd oh duco d rsrch. Thr r svrl compuol mhods usd o solv lcromgc wv prolms such s h Mhod of Mom (MoM) [] h F Dffrc Tm Dom (FDTD) [-5] F Dffrc Mhod (FDM) [6] d h F Elm Mhod (FEM) [7-8]. Thrfor h dvlopm of vrous umrcl mhods s cssr for cosruco of ffc lcromgc smulo ool [9]. I sc MoM mhod s rcordd cds would log w mor ssod ovr hs for hs h v gog ck o h h cur d h vrol chqus ll porrd Lord lgh. I s lso wdl ulzd s pr of srucur mchcs owds d ddoll o compuol flud dmcs compuol hrmodmcs h umrcl rrgm of Schrödgr's quo fld ssus grl d of cours lcromgc. Wh h foudo w rg prsl od wh h FDTD lso MoM o lookr wll dsgush umrous chrcrscs smlr mr s oh of hs chqus h rm o k fr rl h wll lkl o soshd o rlz vr o of h hr h c pld sd of wghd rmg sg up how o do hs for h FDTD s o sl ovous. I smlr mr s h of h MoM h m cocp s o dsplc som oscur cpc o dom ghrg of lms wh rfrrd o shp howvr oscur plful. Dffr from h dvduls crucl FDTD h plc h clos smo of h lcrc d mgc flds wll cslssl do wh dmro o rcgulr sggrd grd h FEM prms grl ll gomrcl sgms oc chc o usd lso (usull) m ulzo o grd. Th mos grll ulzd lms r kow s smplfs hs us ms l Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp

2 Npo Jsumroum d Somsk kmgool lms D rgulr D d rhdrl D. No h lss rcgulr kldoscopc d v curvlr lms lkws fd cross h ord pplco. Susqu o h hcd gomrcl modlg md cocvl prculrl rgulr or rhdrl mshs s o of h rl chrcrscs sprg h FEM from h FDTD. Our vsgo of h FEM wll o gr cofd o hs lms. Irgud pruss mgh dscovr rms of ohr lm shps h rfrcs. Whl s smlr o h FDTD d prll lk h MOM h FEM dpds o locl dscrpo of h fld qus drmd from h dffrl quo porrl of h Mwll s quos d dos o cosqul o h Somrfld rdo codo. O prcc hs ds fw srucur of msh rmo schm s rqurd. Ths ppr prss h mhod of usg h F Elm Mhod (FEM) o solv h lcromgc wv propgo prolms hgh frquc crcus. Th lss modl sd o F Elm Mhod ws mplmd usg h Grphc Usr Irfc (GUI) fuco of MTLB sofwr. Usrs r l o df h dmsos of h coducg pl d slc h shp of pch coducor lso cv dmso d umr of mod for lss of h lcromgc wv h spcrl dom vrous mdums. Thrfor h dvlopm of umrcl mhods s mpor for ffc lcromgc smulo ool. II. THEOY. Wv ropgo Compuo for h lcromgc wv propgo cluds mplud drco of h cd rflcd d rsmd wvs h propg oh coducor d mdum. Th wvs c clculd h rl dom coducg pl d spcrum dom scrg wvgud cocr ou frquc of wv TE d TM mod h coducv show Fg.. For F Elm Mhod h coducg pl c lzd m shps of coducor hs s h dvg of hs mhod. Shp of coducor hs sud c rplcd shp Fg.. Fg. Th Coducor Bo Fg. Shp of Coducor Elcrc flds for rsvrs lcrc (TE) mod followg quo s: E E TE TE m m m m m m cos s m s cos () Elcrc flds for rsvrs mgc (TM) mod followg quo s: E E TM TM Whl m m m m m cos s m m s cos If m d r o qul o zro. m If m d r qul o zro. m Crculr cgulr Dpol Ellpcl Dsscor Trgulr () Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp

3 Improvm of Elcromgc Wv ropgo Usg Novl F Elm Mhodolog Th oudr vlu prolm of coducg pl h coducor mdum c compud d lzd usg oudr prolm of c soluo for hlf coc o h spc d hlf coc o h coducg pl. I h opro c lzd wvgud quo s show Fg.. Th sm mhod of compuo d lss usg wvgud quo s lso ppld o h coducg cv Fg. 5 Msh d Nod of Irsg go Fg. Th Coducor lcd Coducg Cv Th Eg vlus; d cuoff wvumrs; c clculos wr crrd ou Eg vlu show () m () B. F Elm Mhod (FEM) Th F Elm Mhod c solv h prolm soluo m dmsos such s h lm show Fg.. Th F Elm Mhod hs oprg procss followg.. r-rocssg Sp Th prprocssg sp rqurs h uomc msh gror. I dvds h rgo r udr lr o s of lms mosl rgls h r f grc wo dmsol shp. Th msh gror crs followg formo ou h msh s show Fg. 5. Fg. () O-Dmso () Two-Dmso d (c) Thr-Dmso Th msh d mus compud h LLCE o solv h prolm proprl. Ths r cod Tl I II d III. Tl I dspls lss of h od coords d Tl II dspls lss of h ods h r drl oudr codos d Tl III dspls lss of h r lm d dscrd ods.. Buldg h Mr Th ukow fuco s ppromd ch lm usd h poloml prsso. c c () Th ppromd Crs coord us fuco pol ssums h rgl od vlu. TBLE I NODE COODINTE Nod Nod X Y X Y Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp. 98-5

4 Npo Jsumroum d Somsk kmgool Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp c c c (5) Th quo mr form c rwr s: c (6) Whl s h r of lm. (7) Iroducg quo (7) o () lds (8) s show Fg. 6 h wo proprs r prsd s (9) Whr; Th fucol lm c prssd s (). d () I c rwr quo of mr form. () TBLE II NODE COODINTE Nod L. rscrd ol Nod L. rscrd ol Fg. 6 Shp Fucos d Lr ppromo for Trgulr Elm Wh () Whr;

5 Improvm of Elcromgc Wv ropgo Usg Novl F Elm Mhodolog Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp lso TBLE III CONNECTION BETWEEN GLOBL ND LOCL NUMBEING SCHEMES Locl Nod Locl Nod El. Locl Nod El. Numr El. Numr Numr L. L. L ssmlg h Glol Mrcs I cos h ukow prolm whch c wr quo s g g g g () Whr r h glol mrcs ] [ () Th f lm msh cosss of hr lms s show Fg. 7. Th glol coffc mr c fd vlus s show (5). (5)

6 Npo Jsumroum d Somsk kmgool 5 () () () Fg. 7 Thr-Trgl Mshs wh Locl d Glol Nod Numrg.. Mmzg h Fuco W vod ucssrl compl od o h mr of lr quo (6) 5. os-rocssg Sp s mod ov h mmum vlu whch c ssum s rprss h sord rg h FEM compuo s show (8). Fg. 9 Flowchr of Elcromgc Smulo S (7) C. Elcromgc Smulo Dsg Th lcromgc smulo ws crd hrough grphcl usr rfc (GUI) fuco of MTLB progrm s show Fg. 8 d compug procss of lcromgc smulo usg ovl FEM mhod for lss of coducg pch plcd cv ws show Fg. 9 d Fg.. Fg. 8 Elcromgc Smulo rogrm Fg. Th Coducor lcd Coducg Cv III. ESULTS ND DISCUSSION Th dvlopd lcromgc smulo progrm c compu d show ccurc lcrc d mgc fld propgd o h coducg pch grv s show Fg. cludg grph pr of TE d TM mod o coss o lcromgc hor s show Fg. d d h gvlus wr show l IV d V. Th dvg of hs rsrch c lz vrous coducg shp mdum. Thus h prso of pprochd F Elm Mhod c ppld o dsg d lz hgh frquc crcus furhrmor lcommuco grg. Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp. 98-5

7 Improvm of Elcromgc Wv ropgo Usg Novl F Elm Mhodolog covol umrcl mhod. IV. CONCLUSIONS Fg. Elcrc d Elcrc Fld TE Mod Fg. Mgc d Mgc Fld TM Mod TBLE IV NLYTICL ND NUMEICL VLUES FO TE MODE Mod lcl sul FEM sul TE.. TE TE TE TE TE TBLE V NLYTICL ND NUMEICL VLUES FO TM MODE Mod lcl sul FEM sul TM TM TM.. TM TM.5. TM Tl IV d V show h rsuls comprd wh lcl d F Elm Mhod (FEM) cuoff frquc or gvlus of rsvrs lcrc (TE) d rsvrs mgc (TM) flds. Th rsul c show FEM prfrmc coss wh I hs ppr h smpl lcromgc fld prolms wr prsd m d frquc dom d dsg of compl lcromgc wv o solv mor complcd soluos. Th horcl summr of h wv quos prssd o h lcrc d mgc fld usg h F Elm Mhod (FEM) ws pprochd s wll h h drvg of h ppld wk forms m d frquc dom d hr pplco mhods ws dscussd d crd o lcromgc smulo o rprs h phscl hvor of flds grv. s s s h f lm m dom (FDTD) solvg h Mwll s quos grl usrucurd msh hs prsd ls m. Th FDTD lgorhm drcl solvs rs lcrc flds pplg Glrk s mhod wh homogous drchl oudr codos o h lcrc fld dffuso quo. To compu l lcrc flds ovr rrr coducv rh modl for sp-off sourc wvform h scodr pol mhod s usd o solv osso s quo. Th mhod ds h succssful us of dg lms h frquc dom o h m dom couco wh fc lms schm for h m dscrzo. Cosdrg lmo of rc prolm ssu hs ppr h F Elm Mhod (FEM) wll usd o solvg homogous wvgud prolms ppromd rmos of fucol o hghr ccurc h umrcl mhods prsl mplod d rll o produc compl umrcl ss ll compuol cos. Is usfulss for solvg prolms oh cov d o-cov rgos hs dmosrd comprg compud rsuls wh lcll kow soluos. I s show how h FEM c roducd o lcrcl grg usg ol fw commd of MTLB progrm rld drcl o h FEM oprg cods. Th rsuls of Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp. 98-5

8 Npo Jsumroum d Somsk kmgool dvlopd smulo show h our progrm mplmd usg h Grphc Usr Irfc (GUI) gvs h propr rsuls h c usd duco d solv mor complcd lcromgc prolms. Ths rsrch llusrd h dvgs of FEM comprd o lcl mhod d show how h cocps cqurd c rdl dd o ohr prolm ssus. Howvr h prsd progrmmg chqus c mplod for smlr compl prolms. EFEENCES (rrgd h ordr of co h sm fsho s h cs of Fooos.) [] Ev L. d Dvdso D.B. (). GU-cclrd mhod of moms mpl: Moosc scrg. IEEE s d ropgo Mgz 5(6) pp. -5. [] odsup K. d Kulworwchpog T. (). Smulo of Lghg Surg ropgo Trsmsso Ls Usg h FDTD Mhod. World cdm of Scc Egrg d Tcholog. [] Ckr G. Svg L. d Ufmsv.Y. (). FDTD modlg of lcromgc wv scrg from wdg wh prfcl rflcg oudrs: Comprsos gs lcl modls d clro. IEEE Trscos o s d ropgo 6(7) pp. 6-. [] Frcés J. érz-mol M. Bld S. Frádz E. Npp C. d Blédz. (). Educol Sofwr for Irfrc d Opcl Dffrco lss Frsl d Fruhofr gos Bsd o MTLB GUIs d h FDTD Mhod. Educo IEEE Trscos o 55() pp [5] Gffr M. d Jo D. (). plc d ucodoll sl FDTD mhod for lcromgc lss. IEEE Trscos o Mcrowv Thor d Tchqus 6() pp [6] Choocd S. d kmgool S. (). Dvlopm of ffcc m smulo ool for cpcv d ducv oscl lss. Elcrcl Egrg/Elcrocs Compur Tlcommucos d Iformo Tcholog (ECTI-CON) Irol Cofrc. [7] Zmmrm d Wllm B.J. (6). Mulphscs modlg wh f lm mhods. Vol. 8 World Scfc ulshg Co. Ic. [8] Zhog L. d l. (). Covrgc d opml of dpv dg f lm mhods for mhrmoc Mwll quos. Mhmcs of Compuo 8(78) pp [9] Um E.S. Hrrs J.M. d lumugh D.L. (). rv f lm m-dom mhod for smulg hr-dmsol lcromgc dffuso rh. Gophscl Jourl Irol 9() pp Irol Jourl of h Compur h Ir d Mgm Vol.5 (M-ugus 7) pp