EE75 Avan Engnrng Eltromagnt Ltur 7
D EM W onr a D ffrntal quaton of th form α α β f ut to p on Γ α α. n γ q on Γ whr Γ Γ Γ th ontour nlong th oman an n th unt outwar normal ot that th ounar onton ma a Drhlt uman or m Drhlt an uman. α α an β ar funton aoat wth th phal paramtr an f th taton EE75 Dr. Moham Bakr
EE75 Dr. Moham Bakr D EM Cont Γ Γ.5 q f - γ β α α Th funtonal aoat wth th prolm Prov t!
D EM Anal Th omputatonal oman v nto trangl lmnt Eah no ha oth a loal an a gloal n 5 5 A onntvt arra n an M tor th gloal n of th no 5 5 6 5 6 EE75 Dr. Moham Bakr
D EM Anal Cont Γ W aum that thr ar M ln gmnt on Γ W tor th n arra n an M of gloal n of no on Γ EE75 Dr. Moham Bakr 5
Input Data to th D EM Anal Th oornat of th no r whr th total numr of no Th valu of α α β an f for ah lmnt Th valu of p for ah no rng on Γ Th valu of γ an q for ah gmnt wth no on Γ Th two arra n an M an n an M EE75 Dr. Moham Bakr 6
7 EE75 Dr. Moham Bakr Elmntal Intrpolaton Ovr th th lmnt w utlz th lnar appromaton a Th thr no of th th lmnt mut atf th lnar ntrpolaton rlaton a a a Solvng for a an w otan whr a A a a a
8 EE75 Dr. Moham Bakr Elmntal Intrpolaton Cont A th ara of th th lmnt an gvn A Th ntrpolaton funton atf δ
9 EE75 Dr. Moham Bakr Th Homognou uman BC a W frt onr th a γ q Th funtonal pr a a um of lmntal ufunton M whr f - β α α.5 Suttutng wth th lnar ntrpolaton pron w wrt
EE75 Dr. Moham Bakr Th Homognou uman BC a f.5 β α α f - β α α [ ] [ ] [ ]
Th Homognou uman BC a Cont α α β f EE75 Dr. Moham Bakr an If α α β an f ar takn a ontant ovr ah lmnt an utlzng th proprt l! m! n! l m n A l! m! n! w gt A α α δ A A f β
Th Pro of Aml Th pro of aml nvolv torng th loal lmntal omponnt nto thr propr loaton n th gloal tm of quaton [ ] [ ] [] Th lmnt Th lmnt a to n a to n n EE75 Dr. Moham Bakr
An Aml Eampl 5 5 5 5 6 5 6 Thr ar no W ntalz an wth zro 6 6 6 R an R Evaluat an an a thm to th propr loaton to gt EE75 Dr. Moham Bakr
An Aml Eampl Cont Evaluat an an a thm to th propr loaton Rpat th am tp for all lmnt EE75 Dr. Moham Bakr
Inorporatng a Bounar Conton of th r n In th a γ an q ar not zro γ Th tra ufuntonal q Γ a to Γ th funtonal Bau Γ ompr of M ln gmnt w ma wrt M W appromat th funton ovr th gmnt th lnar pron ξ ξ Γ ξ ξ ξ th normalz tan from no to no EE75 Dr. Moham Bakr 5
6 EE75 Dr. Moham Bakr Inorporatng a r n BC Cont Γ q γ U th panon Γ q - γ Dffrntat an u Γl ξ l q - l ξ ξ γ [ ] [ ] [ ] n matr form an l q l ξ ξ γ Aml thn appl to tor th offnt
Th Drhlt Bounar Conton Th Drhlt ounar onton ar mpo lmnatng th known no uttutng for thr valu pp up pu uu p u p u Orgnal tm uu u u up p Ru tm EE75 Dr. Moham Bakr 7
An Eampl: A Shl Mrotrp Ln ε o ε o /n ε r ε r Th mrotrp kpt at potntal whl th trnal hlng o kpt at potntal Smmtr ma mplo to ru th omputatonal oman on half Th govrnng BVP EE75 Dr. Moham Bakr 8
9 EE75 Dr. Moham Bakr An Eampl: A Shl Mrotrp Ln Cont ε ρ ε ε o r r wth on th outr onutor on th mrotrp an / nonthplanofmmtr It follow that w hav α α ε r β f Th ltr fl otan through E-. But ovr ah lmnt appromat a A A E Ovr th th lmnt
An Eampl: A Shl Mrotrp Ln Cont Th nt Elmnt Mtho n Eltromagnt Janmng Jn EE75 Dr. Moham Bakr
An Eampl: A Shl Mrotrp Ln Cont Th nt Elmnt Mtho n Eltromagnt Janmng Jn Th qu-potntal ln EE75 Dr. Moham Bakr