fdtd with mur abc

1

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DTDF -1

: 2(

volfaT 6 .

:0=x @

=y=x htiW dnA

2

@ x=h ,y=0, y=h the way is similar to x=0 , and by using 6.28b 6.28c 6.28d ,equations similar to 6.34 can be obtained

MATLAB : a=2; %length b=2; %width c=3e8 ; %Light Speed % Simulation parameter s=0.5; %Courant Stability Factor d=.01; %Delta x,delta y dt=s*d/3e8; %Delta t N=floor(a/d); %Intrvals on length M=floor(b/d); %Intrvals on width Nt=1200; %Total number of simulation time xn1=floor(0.7/d)+1; %Field Point Location yn1=floor(0.5*a/d)+1; %Field Point Location xn2=floor(0.5*a/d)+1; %Field Point Location yn2=floor(1.3/d)+1; %Field Point Location xn3=floor(0.2/d)+1; %Field Point Location yn3=floor(1.3/d)+1; %Field Point Location xnp=floor(0.5*a/d); %Source Point Location ynp=floor(0.5*b/d); %Source Point Location % Initial fields Ez2=zeros(M+1,N+1,3); Hx2=zeros(M,N+1,3); Hy2=zeros(M+1,N,3); Es1=zeros(1,Nt); Es2=zeros(1,Nt); Es3=zeros(1,Nt); Ez=zeros(M+1,N+1); Hx=zeros(M,N+1); Hy=zeros(M+1,N); % FDTD nx=N;ny=M; %%% To Determine Mur Absorbing Boundery Condition We need Fields at 3 Time

3

%%% Steps,And For This I Write This 'for' Here for n=3:Nt %Apply Source % Ez(xnp,ynp)=sin(1e9*2*pi*dt*n); Ez(xnp,ynp)=exp(-(((n-2)*dt-2e-9)/(.5e-9))^2); % Yee Cubic Field Calculation Hx=Hx-dt/(4*pi*1e-7*d)*(Ez(2:end,:)-Ez(1:end-1,:)); Hy=Hy+dt/(4*pi*1e-7*d)*(Ez(:,2:end)-Ez(:,1:end-1)); Ez(2:end-1,2:end-1)=Ez(2:end-1,2:end-1)+dt/(8.854e-12*d)*(Hy(2:end-1,2:end)-Hy(2:end-1,1:end-1)-(Hx(2:end,2:end-1)-Hx(1:end-1,2:end-1))); % First time Step if n-3*floor(n/3)==0 m11=1;%next m10=2;%before m=3;%curent Hx2(:,:,1)=Hx; Hy2(:,:,1)=Hy; Ez2(:,:,1)=Ez; % Second time Step elseif n-3*floor(n/3)==1 m11=2;%next m10=3;%before m=1;%curent Hx2(:,:,2)=Hx; Hy2(:,:,2)=Hy; Ez2(:,:,2)=Ez; % Third time Step elseif n-3*floor(n/3)==2 m11=3;%next m10=1;%before m=2;%curent Hx2(:,:,3)=Hx; Hy2(:,:,3)=Hy; Ez2(:,:,3)=Ez; end %Apply Boundary Condition for i=1:N for j=1:M % For Corners Ez2(1,1,m11)=Ez2(2,2,m10); Ez2(1,M,m11)=Ez2(2,M-1,m10); Ez2(N,M,m11)=Ez2(N-1,M-1,m10); Ez2(N,1,m11)=Ez2(N-1,2,m10); %@x=0 if i==1

4

if j>1 && j1 && j

5

dne ;)11m,:,:(2zE=zE ))m,:,:(2zE(csegami ))m,:,:(2zE(frus % ;)02,'eziStnoF',acg(tes rabroloc )]1.0 0[(sixac % )]4 4-[(milz % % % % % % % % ;emarfteg ;)1+n,:,:(xH=xH % ;)1+n,:,:(yH=yH % ;)1+n,:,:(zE=zE % tniop dleif ta atad niamod emit evaS% ;)1ny,1nx(2zE=)n(1sE tniop dleif ta atad niamod emit evaS% ;)2ny,2nx(2zE=)n(2sE tniop dleif ta atad niamod emit evaS% ;)3ny,3nx(2zE=)n(3sE dnE ;)'3sE','2sE','1sE','tam.5_1c_laciremuN_tseT'(evas

: rof ty x

. draH . eeY

zE ruM zE rof n

. m 11m 01m m 321

1=01m 2=m . 3=11m

0=y 0=x h=y h=x

. 0=y 0=x

6

frus csegami .

zE . eeY

3sE 2sE 1sE . )3.0,3.0( )0,3.0( )3.0,0(

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s . 5.1=s 1=s .

.

: baltaM ;)'3sE','2sE','1sE','tam.5_1c_2laciremuN_tseT'(daol ;1sE=sE ;3.0=nx ;3.0=ny emit noitalumis fo rebmun latoT% ;002=tN rotcaF ytilibatS tnaruoC% ;5.0=s y atled,x atleD% ;10.=d t atleD% ;8e3/d*s=td ;9e3=sF ;)sE(htgnel=L y fo htgnel morf 2 fo rewop txeN % ;)L(2woptxen^2 = TFFN ;)TFFN,sE(tff = Y ;)1+2/TFFN,1,0(ecapsnil*2/sF = f ;))1+2/TFFN:1(Y(sba=lpmA_sE ;)Y(gami=gami_Y ;)Y(laer=laer_Y ;))1+2/TFFN:1(laer_Y/.)1+2/TFFN:1(gami_Y(dnata=esahp %%%%%%%%%%%% ;td*tN:td:0=x ;)2^.))9-e5.0(/)9-e2-x((-(pxe = gis ;9e3=sF

7

;)gis(htgnel=L ;T*)1-L:0( = t % y fo htgnel morf 2 fo rewop txeN % ;)L(2woptxen^2 = TFFN ;)TFFN,gis(tff = AY ;)1+2/TFFN,1,0(ecapsnil*2/sF =f ;)2^ny+2^nx(trqs=p ;8e3/f*ip*2=evaw_k ;21-e458.8=spe ;)1+2/TFFN:1(AY=I ;)p*evaw_k,2,0(hlesseb*.)spe*f*.ip*2*4(/)2^.)evaw_k(*.I-(=p_AzE

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evas ) daol.

sE ( . ) ny , nx(

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: td

y x d 8e3/d*s=td t .

10.0 d . 11-e7666.1=td

8

:

DTDF zE .

: 5.0=C )3.0,0(

zE .

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DTDF .1

51

: 0,3.0

12

5.0=c 3.0,3.0

72

DTDF 1=c .

: 3.0,0

33

: 0,3.0

93

: 3.0,3.0

44

: 5.1=c

. DTDF

3.0,0

15

0,3.0

75

3.03.0

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DTDF ( .

DTDF .

41.0 5.0=c 3.0,3.0 . 1.0

36

:

5.0=C

3.0,0

96

0,3.0

57

3.03.0

08

1=c

3.0,0

68

0,3.0

29

3.03.0

89

5.1=c

3.0,0

401

0,3.0

011

3.0,3.0

fdtd with mur abc

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