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时域有限差分法 FDTD
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帮忙看看我的编程思路有没有问题(附程序)
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帮忙看看我的编程思路有没有问题(附程序)
离线
yuyeliuxu
UID :21110
注册:
2008-11-10
登录:
2009-10-09
发帖:
31
等级:
仿真一级
0楼
发表于: 2009-07-10 10:02:08
得到的结果pml不吸收
q pCI[[
tic;
C,An\lsT
clear; clc;
W7^[W.
N_iteration=1;
5BJE
%***********************************************************************
7~SwNt,
% Fundamental constants
0^lWy+
%***********************************************************************
$P=C7;
< cvh1~>(
cc=2.99792458e8; %speed of light in free space
1h&`mqY)L.
muz=4.0*pi*1.0e-7; %permeability of free space
V&w2pp0
epsz=1.0/(cc*cc*muz); %permittivity of free space
|@vkQ
{uj_4Ft
freq=5e+9; %frequency of source excitation
51SmoFbMz
Tc=0.2e-9 %Time shift, i.e. time for the center position of the pulse
b,Oh8O;>
Tau=1/freq; %impulse width parameter, e.g.: 0.2ns pulse width here
<.Ws; HN}
% corresponds frequency of 1/Tau Hz, i.e.
-}#HaL#'K
% 0.2ns---5GHz, 0.5ns---2GHz
>> zd
lambda=cc/freq; %center wavelength of source excitation
xSm;~')g
omega=2.0*pi*freq;
q0iJy@?A
N% 4"9K
M_factor=1;%1 % refine the mesh to get higher quality M_factor times meshed on 1e-3
Ttt'X<9
{%f{U"m
ZEAUoC1E1
$@D a|d4
nmax=500*M_factor; %total number of calculating time steps nmax=2200*M_factor;
{drc}BL_
nstep=10; % =250 every nstep give a display
} o%^ Mu B
TIWR[r1!
r- <O'^C
X H-_tvB
);$99t
%***********************************************************************
[ QiG0D_'=
% Grid parameters
j,.\QwpU
%***********************************************************************
gcU*rml
ie=100*M_factor; %100 %number of grid cells in x-direction
5&ku]l+
je=100*M_factor; %100 %number of grid cells in y-direction
O$<>v\NC?
E5w;75,
ib=ie+1;
T.4&P#a1
jb=je+1;
c-sjYJXKM*
imp_x=50*M_factor; %imp_x=5*M_factor; %imp_x=10*M_factor;
KwuucY
imp_y=50*M_factor; %(imp_x ,imp_y) is the location of the point source impulse
7;s#QqG`I
CIjc5^Y2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
qhEv6Yxfw6
1^!SuAA@
%%%%% fine meshed %%%%
p+CUYo(
dx=1e-3/M_factor ;% dx=0.25e-3; %dx=1e-3 %dx=0.25e-3; %dx=1e-3/M_factor; %space increment of square lattice
[d: u(
dt=dx/(2.0*cc); %time step dt=dx/(2.0*cc);
V)j[`,M:
>?, Zn
iebc=8*M_factor; %thickness of left and right PML region
/|IPBU 5
jebc=8*M_factor; %thickness of front and back PML region
~SnUnNDm `
rmax=0.000001; %reflection factor ?x?? concerning PML issue
+(W1x C0
orderbc=2;
FEaT}/h;
ibbc=iebc+1;
`Mnu<)v
jbbc=jebc+1;
*yu}e)(0
iefbc=ie+2*iebc;
!sb r!Qt
jefbc=je+2*jebc;
u^1#9bAW8
ibfbc=iefbc+1;
CMXF[X)%
jbfbc=jefbc+1;
{KG 6#/%;
# ]7Lieh[5
%***********************************************************************
CkT(\6B-
% Material parameters
;-+q*@sa]
%***********************************************************************
8]ZzO(=@{
epss=10;
Z0F~?
eps=7;
G0E5Y;YIN$
tau0=7e-12;
^7-zwl(>?N
sigdisp=(epss-eps)*epsz/tau0;
A&Y5z[p
sig=0.15+sigdisp;
Oynb"T&8
mur=1.0;
*MP.YI:h
sim=0;
fpD$%.y'J
%***********************************************************************
[nTI\17iA
% Wave excitation
qt@L&v}~j
%***********************************************************************
IS2cU'
source=zeros(1,nmax);
!%iHJwS#
% for n=1:nmax
6l#x1o;
% t(n)=dt*n;
m`/Nl<
% source(n)=-sqrt(exp(1))*(2*pi/Tau)*(t(n)-Tc)*exp(-(1/2)*(2*pi*(t(n)-Tc)/Tau)^2); % normalized
O>~,RI!
% end
ZK5nN9`
for n=1:nmax % n=n1:n2
:DD<0
t(n)=dt*n;
/wV|;D^ )
source(n)=-sin(omega*(t(n)-Tc)); % %Eq.(6) of Monocycle shapes paper
=V^-@ji)b
end
g!'R}y
%***********************************************************************
J ^'El^F
% Field arrays
t|aV:x
%***********************************************************************
mj~:MCC
@(3F4Z.i%.
ex=zeros(ie,jb); %fields in main grid
6b2UPI7m~
px=zeros(ie,jb);
CXa[%{[n
ey=zeros(ib,je);
M]x>u@JH
py=zeros(ib,je);
0j.K?]f)h
hz=zeros(ie,je);
{.p.?
I//=C6
exbcf=zeros(iefbc,jebc); %fields in front PML region
A,}M ^$@
pxbcf=zeros(iefbc,jebc);
J2YQdCL
eybcf=zeros(ibfbc,jebc);
eS`VI+=@0
pybcf=zeros(ibfbc,jebc);
3JCo!n0
hzxbcf=zeros(iefbc,jebc);
%6UF%dbYH`
hzybcf=zeros(iefbc,jebc);
v}G^+-?
fB+L%+mr8
exbcb=zeros(iefbc,jbbc); %fields in back PML region
. %RM8
pxbcb=zeros(iefbc,jbbc);
H iyg1
eybcb=zeros(ibfbc,jebc);
D(!^$9e9b
pybcb=zeros(ibfbc,jebc);
L, JQ\!c
hzxbcb=zeros(iefbc,jebc);
D|]BFu)F
hzybcb=zeros(iefbc,jebc);
LdPLC':}x|
w!.@64-
exbcl=zeros(iebc,jb); %fields in left PML region
#9vC]Gm
pxbcl=zeros(iebc,jb);
s]arNaaA
eybcl=zeros(iebc,je);
MdHm%Vx
pybcl=zeros(iebc,je);
@60D@Y
hzxbcl=zeros(iebc,je);
KZm&sk=QM-
hzybcl=zeros(iebc,je);
Dw-d`8*
j[>cv;h ;
exbcr=zeros(iebc,jb); %fields in right PML region
t]/eCsR
pxbcr=zeros(iebc,jb);
2jsbg{QS#_
eybcr=zeros(ibbc,je);
YR%iZ"`*+O
pybcr=zeros(ibbc,je);
jvzioFCt
hzxbcr=zeros(iebc,je);
,,H "?VO
hzybcr=zeros(iebc,je);
p"g|]@m
)t6]F6!_
%***********************************************************************
N[%u>!
% Updating coefficients
]<;,HGO
%***********************************************************************
J2UQq 7-y
rQ;w{8J\t
U{U"%XdO
Syk)S<
haf=dt*sim/(2.0*muz*mur);
NYm"I`5w
da=(1.0-haf)/(1.0+haf);
ZN[<=w&(cB
db=dt/muz/mur/dx/(1.0+haf);
L P<A q
dapm=(2*tau0-dt)/(2*tau0+dt);
ys[Li.s:
dbpm=2*tau0*dt/(2*tau0+dt)*sigdisp;
nxLuzf4U5
sX>u.
bO '\QtW9
%***********************************************************************
e#"h@kZP
% Geometry specification (main grid)
9!FX*}dC
%***********************************************************************
YOCEEh?
haf=dt*sim/(2.0*muz*mur);
><V*`{bD9)
dahz(1:ie,1:je)=(1.0-haf)/(1.0+haf);
|VfEp
dbhz(1:ie,1:je)=dt/muz/mur/dx/(1.0+haf);
1!#85SMx
for i=1:ie
d2k-MZuT6
for j=1:jb
x7j#@C
gQ1obT"|
eaf=dt*sig/(2.0*epsz*eps);
(O.%Xbx3
caex(i,j)=(1.0-eaf)/(1.0+eaf); % parameters refer to page 6 from
+H)'(<
cpex(i,j)=dt/epsz/eps/tau0/(1.0+eaf);
jLVJ+mu
cbex(i,j)=dt/epsz/eps/dx/(1.0+eaf); % p.6 from the book of Yun Wenhua
r*X,]\V0x
dapx(i,j)=(2*tau0-dt)/(2*tau0+dt);
7T~M`$h
dbpx(i,j)=2*tau0*dt/(2*tau0+dt)*sigdisp;
B9v>="F
vOQ%f?%G\
end
f5jl$H.
end
)2}R1K>
_z\/{
for i=1: ib
Dk1& <} I
for j=1: je
;b~ S/
eaf=dt*sig/(2.0*epsz*eps);
rzjVUPdnh
caey(i,j)=(1.0-eaf)/(1.0+eaf); % parameters refer to page 6 from
bJ^JK
cpey(i,j)=dt/epsz/eps/tau0/(1.0+eaf);
G7Nw}cVJ)
cbey(i,j)=dt/epsz/eps/dx/(1.0+eaf); % p.6 from the book of Yun Wenhua
0-2|(9 Kc
dapy(i,j)=(2*tau0-dt)/(2*tau0+dt);
U|^xr~q!f-
dbpy(i,j)=2*tau0*dt/(2*tau0+dt)*sigdisp;
v4$/LUJZp
n 8cA8<
end
Y\|#Lu>B
end
$a(-r-_Fi]
%***********************************************************************
3h:j.8Z
% Fill the PML regions
mU'<:gL+
%***********************************************************************
60D36b(
delbc=iebc*dx;
mxc)Wm<4
sigmam=-log(rmax/100.0)*epsz*cc*(orderbc+1)/(2*delbc);
u9lZHh#V-
ys_2?uv
eaf=dt*sig/(epsz*eps);
7[m?\/K~
capml=exp(-eaf);
h Yu6PWK
cbpml=(1.0-capml)*dt/(eaf*epsz*eps*dx);
.l}Ap7@
cppml=(1.0-capml)*dt/(eaf*epsz*eps*tau0); % p.6 from the book of Yun Wenhua
iD^,O)b
dap=exp(-dt/tau0);
U&?hG>
dbp=(1-dap)*sigdisp*tau0;
c9(3z0!F?
|Uh8b %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-m@o\9Ic
% FRONT region
c-Lz luWi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+pofN-*%
/y$Omc^
caexbcf(1:iefbc,1)=1.0; %0.0 %1.0;
@d75X Y Ku
cbexbcf(1:iefbc,1)=0.0;
.RD<]BxJ
cpexbcf(1:iefbc,1)=0.0;
f?3-C8hU
dapxbcf(1:iefbc,1)=1.0;
wxN)dB
dbpxbcf(1:iefbc,1)=0.0;
q+P@2FL
bcfactor=eps*sigmam/(dx*(delbc^orderbc)*(orderbc+1));
J<)qw
for j=2:jebc
z;OYPGvkw
y1=(jebc-j+1.5)*dx;
eUPa5{P
y2=(jebc-j+0.5)*dx;
)SV.|
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
]#!uke Q
eaf1=dt*(sigmay+sigdisp)/(epsz*eps);
`lf_wB+I
ca1=exp(-eaf1);
mHD_cgKN
cb1=(1.0-ca1)/((sigmay+sigdisp)*dx);
9zaNfs
cp1=(1.0-ca1)/((sigmay+sigdisp)*tau0);
Fs+tcr/\[
caexbcf(1:iefbc,j)=ca1;
X.]I4O&_
cbexbcf(1:iefbc,j)=cb1;
8K%N7RL|
cpexbcf(1:iefbc,j)=cp1;
kZ]H[\Fs
dapxbcf(1:iefbc,j)=dap;
@gUp9ZwtH
dbpxbcf(1:iefbc,j)=dbp;
BK$y>= `
end
'yo@5*x7
sigmay = bcfactor*(0.5*dx)^(orderbc+1);
t,/ G
eaf1=dt*(sigmay+sigdisp)/(epsz*eps);
FD=% 4#|
ca1=exp(-eaf1);
c*USA eP
cb1=(1.0-ca1)/((sigmay+sigdisp)*dx);
W!Tx%
cp1=(1.0-ca1)/((sigmay+sigdisp)*tau0);
K)Y& I
$vn6%M[
caex(1:ie,1)=ca1;
Vl^(K_`(
cbex(1:ie,1)=cb1;
rd <m:r
cpex(1:ie,1)=cp1;
,Oo`*'a[o7
dapx(1:ie,1)=dap;
(vXr2Z<l
dbpx(1:ie,1)=dbp;
K<JzIuf&
caexbcl(1:iebc,1)=ca1;
F(")ga$r
cbexbcl(1:iebc,1)=cb1;
iP:i6U]
cpexbcl(1:iebc,1)=cp1;
lExQp2E
dapxbcl(1:iebc,1)=dap;
PKm|?kn{0(
dbpxbcl(1:iebc,1)=dbp;
]a3$hAcj6"
caexbcr(1:iebc,1)=ca1;
05UN <l]
cbexbcr(1:iebc,1)=cb1;
$8EEtr,!
cpexbcr(1:iebc,1)=cp1;
r]B8\5|<d
dapxbcr(1:iebc,1)=dap;
{UiSa'TR1b
dbpxbcr(1:iebc,1)=dbp;
JWVV?~1
for j=1:jebc
*TOd Iq&z
y1=(jebc-j+1)*dx;
W4$o\yA]
y2=(jebc-j)*dx;
5Xy(za
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
{Jr1K,
sigmays=sigmay*(muz/(epsz*eps));
_]:b@gXUw
da1=exp(-sigmays*dt/muz);
=H95?\}T[
db1=(1-da1)/(sigmays*dx);
dQ:,pe7A
dahzybcf(1:iefbc,j)=da1;
XF`2*:7
dbhzybcf(1:iefbc,j)=db1;
O\}C`CiC
caeybcf(1:ibfbc,j)=capml;
VRo&1:
cbeybcf(1:ibfbc,j)=cbpml;
Q*M# e
cpeybcf(1:ibfbc,j)=cppml;
Dy08.Sss
h>Kx
dahzxbcf(1:iefbc,j)=da;
kHM Jh~
dbhzxbcf(1:iefbc,j)=db;
6 2xOh\(
4.A^5J'W
dapybcf(1:ibfbc,j)=dap;
':4cQ4Z
dbpybcf(1:ibfbc,j)=dbp;
B|`?hw@g+
end
GwWK'F'2
/2^L;#
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3:nhZN/95T
% BACK region
X9>fE{)!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(leX` SN0u
caexbcb(1:iefbc,jbbc)=1.0; % 0.0 %1.0;
L!f~Am:#
cbexbcb(1:iefbc,jbbc)=0.0;
'|yx B')
cpexbcb(1:iefbc,jbbc)=0.0;
_[:6.oNjIe
dapxbcb(1:iefbc,1)=1.0;
\PX4>/d@y
dbpxbcb(1:iefbc,1)=0.0;
ct+F\:e
bcfactor=eps*sigmam/(dx*(delbc^orderbc)*(orderbc+1));
.1QGNW
for j=2:jebc
6)[moR{N1
y1=(j-0.5)*dx;
5"%.8P
y2=(j-1.5)*dx;
j cd<'\;
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
gC7!cn
eaf1=dt*(sigmay+sigdisp)/(epsz*eps);
@2(u=E: ^
ca1=exp(-eaf1);
PgtLyzc
cb1=(1.0-ca1)/((sigmay+sigdisp)*dx);
5(;Y&?k
cp1=(1.0-ca1)/((sigmay+sigdisp)*tau0);
5Ds[?
caexbcb(1:iefbc,j)=ca1;
A|biOz
cbexbcb(1:iefbc,j)=cb1;
]4~Yi1]
cpexbcb(1:iefbc,j)=cp1;
uHbg&eW
dapxbcb(1:iefbc,j)=dap;
pyEQb#
dbpxbcb(1:iefbc,j)=dbp;
q~`hn(S
end
~E}kwF
sigmay = bcfactor*(0.5*dx)^(orderbc+1);
e02Hf{eOfw
|3$Ew.
eaf1=dt*(sigmay+sigdisp)/(epsz*eps);
Bc>j5^)8w
ca1=exp(-eaf1);
dCx63rF`G
cb1=(1.0-ca1)/((sigmay+sigdisp)*dx);
O>`k@X@9/
cp1=(1.0-ca1)/((sigmay+sigdisp)*tau0);
44CZl{pt
caex(1:ie,jb)=ca1;
Omd;
cbex(1:ie,jb)=cb1;
l5z//E}W
cpex(1:ie,jb)=cp1;
q ` S ~w
dapx(1:ie,jb)=dap;
ammi4k/
dbpx(1:ie,jb)=dbp;
~DH9iB
caexbcl(1:iebc,jb)=ca1;
M1jT+
cbexbcl(1:iebc,jb)=cb1;
+%5 L2/n7
cpexbcl(1:iebc,jb)=cp1;
+.cpZqWn3
dapxbcl(1:iebc,jb)=dap;
If'q8G3]-
dbpxbcl(1:iebc,jb)=dbp;
R~<N*En~
caexbcr(1:iebc,jb)=ca1;
74e=zW?
cbexbcr(1:iebc,jb)=cb1;
g-3^</_fZ
cpexbcr(1:iebc,jb)=cp1;
>N&{DJmD
dapxbcr(1:iebc,jb)=dap;
(g6e5Sgi>
dbpxbcr(1:iebc,jb)=dbp;
\p^V~fy7rU
for j=1:jebc
KXKT5E$
y1=j*dx;
)x-b+SC
y2=(j-1)*dx;
?XKX&ws
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
QO@86{u#Y
sigmays=sigmay*(muz/(epsz*eps));
u%-]-:c
da1=exp(-sigmays*dt/muz);
=OufafZb
db1=(1-da1)/(sigmays*dx);
(Y py}
dahzybcb(1:iefbc,j)=da1;
|n_N.Z
dbhzybcb(1:iefbc,j)=db1;
(Cr
caeybcb(1:ibfbc,j)=capml;
hqRC:p#9
cbeybcb(1:ibfbc,j)=cbpml;
b'4a;k!rS
cpeybcb(1:ibfbc,j)=cppml;
N:G]wsh
dahzxbcb(1:iefbc,j)=da;
.zb
dbhzxbcb(1:iefbc,j)=db;
wd:Yy
lpi"@3
dapybcb(1:ibfbc,j)=dap;
*QK) 1Y1W
dbpybcb(1:ibfbc,j)=dbp;
[^!SkQ
end
WZa6*pF
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
, ['}9:f9
% LEFT region
RO3LZBL
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[$3+5K#
k?=1q[RQH
caeybcl(1,1:je)=1.0; %0.0%1.0;
$S>'0mL
cbeybcl(1,1:je)=0.0;
n7> |$2Y
cpeybcl(1,1:je)=0.0;
TX)W.2u=
dapybcl(1,1:je)=1.0;
@Y0ZW't
dbpybcl(1,1:je)=0.0;
}6Pbjm *
bcfactor=eps*sigmam/(dx*(delbc^orderbc)*(orderbc+1));
" {<X! ^u>
for i=2:iebc
V x#M!os0
x1=(iebc-i+1.5)*dx;
3ynkf77cn
x2=(iebc-i+0.5)*dx;
X5owAc6
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
F:/x7]7??Z
eaf1=dt*(sigmax+sigdisp)/(epsz*eps);
`2>p#`
ca1=exp(-eaf1);
bvD}N<>3N
cb1=(1.0-ca1)/((sigmax+sigdisp)*dx);
6R :hs C$
cp1=(1.0-ca1)/((sigmax+sigdisp)*tau0);
mG)5xD
caeybcl(i,1:je)=ca1;
MlTC?Rp#
cbeybcl(i,1:je)=cb1;
"#)|WVa=BM
cpeybcl(i,1:je)=cp1;
coCT]<
dapybcl(i,1:je)=dap;
Jm!,=}oP'
dbpybcl(i,1:je)=dbp;
stiF`l
caeybcf(i,1:jebc)=ca1;
'Agw~ &$
cbeybcf(i,1:jebc)=cb1;
jCY~Wc
cpeybcf(i,1:jebc)=cp1;
[aSuEu?mC
dapybcf(i,1:jebc)=dap;
NQD5=/o
dbpybcf(i,1:jebc)=dbp;
(wj:Gc
caeybcb(i,1:jebc)=ca1;
e&sH<hWR
cbeybcb(i,1:jebc)=cb1;
cvcZ\y
cpeybcb(i,1:jebc)=cp1;
^%!{qAp}Z
dapybcb(i,1:jebc)=dap;
2n.HmS
dbpybcb(i,1:jebc)=dbp;
~\=D@G,9
end
%P}H3;2
sigmax=bcfactor*(0.5*dx)^(orderbc+1);
~d7t\S
eaf1=dt*(sigmax+sigdisp)/(epsz*eps);
l/3=o}8q
ca1=exp(-eaf1);
$SQ$2\iC
cb1=(1.0-ca1)/((sigmax+sigdisp)*dx);
97Dq;
cp1=(1.0-ca1)/((sigmax+sigdisp)*tau0);
G#[A'tbKk
caey(1,1:je)=ca1;
v4e4,Nt
cbey(1,1:je)=cb1;
KHx2$*E_
cpey(1,1:je)=cp1;
,^bgk -x-
dapy(1,1:je)=dap;
3cHYe
dbpy(1,1:je)=dbp;
20I`F>-*
caeybcf(iebc+1,1:jebc)=ca1;
L#SW!
cbeybcf(iebc+1,1:jebc)=cb1;
2hV -h
cpeybcf(iebc+1,1:jebc)=cp1;
'p5M|h\:T
dapybcf(iebc+1,1:jebc)=dap;
J0V m&TY
dbpybcf(iebc+1,1:jebc)=dbp;
/<_!Gz.@uG
caeybcb(iebc+1,1:jebc)=ca1;
fXWy9 #M
cbeybcb(iebc+1,1:jebc)=cb1;
4dixHpq'
cpeybcb(iebc+1,1:jebc)=cp1;
Cl'$*h
dapybcb(iebc+1,1:jebc)=dap;
8SpG/gl"
dbpybcb(iebc+1,1:jebc)=dbp;
x[mz`0
for i=1:iebc
{.Qv1oOa
x1=(iebc-i+1)*dx;
Mbc&))A
x2=(iebc-i)*dx;
G:*vV#K
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
U/'l "N[
sigmaxs=sigmax*(muz/(epsz*eps));
`h'+4
da1=exp(-sigmaxs*dt/muz);
ZtZ3I?%U3
db1=(1-da1)/(sigmaxs*dx);
9(t(sP_
dahzxbcl(i,1:je)=da1;
k, N{
dbhzxbcl(i,1:je)=db1;
bci]"uzB
YPx+9^)
dahzxbcf(i,1:jebc)=da1;
B*_K}5UO
dbhzxbcf(i,1:jebc)=db1;
Tdh(J",d
np2&W'C/i
dahzxbcb(i,1:jebc)=da1;
LZ wCe$1
dbhzxbcb(i,1:jebc)=db1;
'( I0VJJ
]Ea-MeH
caexbcl(i,2:je)=capml;
\me5"ZU
cbexbcl(i,2:je)=cbpml;
D>k(#vYKB
cpexbcl(i,2:je)=cppml;
6y!U68L;B
dapxbcl(i,2:je)=dap;
(:8a6=xQ
dbpxbcl(i,2:je)=dbp;
Q z(n41@`
dahzybcl(i,1:je)=da;
OPN\{<`*d
dbhzybcl(i,1:je)=db;
lU 62$2
D?#l8
end
uZ8-?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Ma!
% RIGHT region
n*"r!&Dg
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
c:7V..
/"J 6``MV
caeybcr(ibbc,1:je)=1.0; %0.0%1.0;
5r)8MklZ
cbeybcr(ibbc,1:je)=0.0;
UYxn?W.g
cpeybcr(ibbc,1:je)=0.0;
N!ihj:,
dapybcr(ibbc,1:je)=1.0;
mrr]{K
dbpybcr(ibbc,1:je)=0.0;
L\UPM+tE
bcfactor=eps*sigmam/(dx*(delbc^orderbc)*(orderbc+1));
aX1b(h2
for i=2:iebc
=4` wYh
x1=(i-0.5)*dx;
]AQ}_dRi=
x2=(i-1.5)*dx;
%}(`?
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
GXxI=,L8F
eaf1=dt*(sigmax+sigdisp)/(epsz*eps);
#czTX%+9(e
ca1=exp(-eaf1);
U;/2\Ii
cb1=(1.0-ca1)/((sigmax+sigdisp)*dx);
3w)r"" C&
cp1=(1.0-ca1)/((sigmax+sigdisp)*tau0);
n UmyPQ~
caeybcr(i,1:je)=ca1;
O?g;Ny
cbeybcr(i,1:je)=cb1;
%|e)s_%XE
cpeybcr(i,1:je)=cp1;
?L\"qz%gP
^?RH<z
dapybcr(i,1:je)=dap;
WzstO}?P(
dbpybcr(i,1:je)=dbp;
lrZ]c:%k
"dP-e
caeybcf(i+iebc+ie,1:jebc)=ca1;
8#;=>m%
cbeybcf(i+iebc+ie,1:jebc)=cb1;
46]BRL2 G
cpeybcf(i+iebc+ie,1:jebc)=cp1;
)!v"(i.5Xo
)Xqjl
dapybcf(i+iebc+ie,1:jebc)=dap;
U',C-56z
dbpybcf(i+iebc+ie,1:jebc)=dbp;
|!] "y<
^R:&c;&,
caeybcb(i+iebc+ie,1:jebc)=ca1;
S3/%;=|
cbeybcb(i+iebc+ie,1:jebc)=cb1;
{@CQ (
cpeybcb(i+iebc+ie,1:jebc)=cp1;
pl%!AY'oE>
\(Oc3+n6
dapybcb(i+iebc+ie,1:jebc)=dap;
x</4/d
dbpybcb(i+iebc+ie,1:jebc)=dbp;
Q>D//_TF
end
sJKr%2nVV
sigmax=bcfactor*(0.5*dx)^(orderbc+1);
Ho&:Zs
eaf1=dt*(sigmay+sigdisp)/(epsz*eps);
WP*}X7IS
ca1=exp(-eaf1);
Zb2pZhkW
cb1=(1.0-ca1)/((sigmax+sigdisp)*dx);
?fH1?Z\'K
cp1=(1.0-ca1)/((sigmax+sigdisp)*tau0);
M?YNK]
caey(ib,1:je)=ca1;
7LU^Xm8
cbey(ib,1:je)=cb1;
RWv4/=}(G
cpey(ib,1:je)=cp1;
"LTw;& y
dapy(ib,1:je)=dap;
hlL$3.]
dbpy(ib,1:je)=dbp;
Eu' ;f_s
;[;WEA
caeybcf(iebc+ib,1:jebc)=ca1;
,r*Kxy
cbeybcf(iebc+ib,1:jebc)=cb1;
UhqTn$=fb
cpeybcf(iebc+ib,1:jebc)=cp1;
oc)`hg2=
dapybcf(iebc+ib,1:jebc)=dap;
mDK*LL5]W
dbpybcf(iebc+ib,1:jebc)=dbp;
lIS`_H}
L9O;K$[s
caeybcb(iebc+ib,1:jebc)=ca1;
(1|wM+)"
cbeybcb(iebc+ib,1:jebc)=cb1;
#&T O(bk
cpeybcb(iebc+ib,1:jebc)=cp1;
Hrpz4E%\Aw
dapybcb(iebc+ib,1:jebc)=dap;
IQU1 JVkZ
dbpybcb(iebc+ib,1:jebc)=dbp;
Hy4;i^Ik <
for i=1:iebc
/i8OyRpSyk
x1=i*dx;
VOD-< "|
x2=(i-1)*dx;
iO?AY
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
Eo2`Vr9g
sigmaxs=sigmax*(muz/(epsz*eps));
t3<8n;'y:
da1=exp(-sigmaxs*dt/muz);
FWJ**J
db1=(1-da1)/(sigmaxs*dx);
/%g9g_rt#
dahzxbcr(i,1:je) = da1;
nEu:& 4
dbhzxbcr(i,1:je) = db1;
%JrZMs>
0e<>2AL
dahzxbcf(i+ie+iebc,1:jebc)=da1;
w^Y/J4 I0
dbhzxbcf(i+ie+iebc,1:jebc)=db1;
%IBT85{
Z@1kx3Wx$
dahzxbcb(i+ie+iebc,1:jebc)=da1;
keLeD1
dbhzxbcb(i+ie+iebc,1:jebc)=db1;
ZeuL*c \
aC`>~uX##V
dapxbcb(i,2:je)=dap;
27fLW&b2
dbpxbcb(i,2:je)=dbp;
f$QkzWvr
caexbcr(i,2:je)=capml;
msgR"T3'
cbexbcr(i,2:je)=cbpml;
pC:YT/J
cpexbcr(i,2:je)=cppml;
jUM'f24
)Xg5=zn$
dahzybcr(i,1:je)=da;
xgMh@@e
dbhzybcr(i,1:je)=db;
( jU $
end
;Tnid7:S
ya1 aWs~
%***********************************************************************
Fc@R,9
% BEGIN TIME-STEPPING LOOP
lXTE#,XVf
%***********************************************************************
]?+i6 [6U
for n=1:nmax
,93Uji[l
s1Acl\l-uF
%***********************************************************************
"x9yb0
% Update electric fields (EX and EY) in main grid
QNOdt 2NN
%***********************************************************************
;+XrCy!.)L
ex(:,2:je)=caex(:,2:je).*ex(:,2:je)+...
Xi%Og\vm5
cbex(:,2:je).*(hz(:,2:je)-hz(:,1:je-1))+cpex(:,2:je).*px(:,2:je);
h_?`ESI~
pk9Ics;y
ey(2:ie,:)=caey(2:ie,:).*ey(2:ie,:)+...
~D3S01ecM
cbey(2:ie,:).*(hz(1:ie-1,:)-hz(2:ie,:))+cpey(2:ie,:).*py(2:ie,:);
}(8>&
[-*&ZYp
%***********************************************************************
SbGdcCB
% Update EX in PML regions
@U8u6JNK'
%***********************************************************************
b]b>i]n
4*qBu}(
% FRONT
u ,3B[
0Qa0
exbcf(:,2:jebc)=caexbcf(:,2:jebc).*exbcf(:,2:jebc)-...
dscah0T
cbexbcf(:,2:jebc).*(hzxbcf(:,1:jebc-1)+hzybcf(:,1:jebc-1)-...
iV/I909*''
hzxbcf(:,2:jebc)-hzybcf(:,2:jebc))+...
?D.+D(
cpexbcf(:,2:jebc).*pxbcf(:,2:jebc);
#dae^UjM
ex(1:ie,1)=caex(1:ie,1).*ex(1:ie,1)-...
>\[]z^J
cbex(1:ie,1).*(hzxbcf(ibbc:iebc+ie,jebc)+...
d~qQ_2M[G
hzybcf(ibbc:iebc+ie,jebc)-hz(1:ie,1))+...
z.8 nYL5^}
cpex(1:ie,1).*px(1:ie,1);
I+H~ 5zq.
g8uqW1E^
% BACK
U4=l`{5on
>fWGiFmlk
exbcb(:,2:jebc-1)=caexbcb(:,2:jebc-1).*exbcb(:,2:jebc-1)-...
\"(?k>]E
cbexbcb(:,2:jebc-1).*(hzxbcb(:,1:jebc-2)+hzybcb(:,1:jebc-2)-...
3bWGWI
hzxbcb(:,2:jebc-1)-hzybcb(:,2:jebc-1))+...
fY9+m}$S$
cpexbcb(:,2:jebc-1).*pxbcb(:,2:jebc-1);
Op-z"inw
ex(1:ie,jb)=caex(1:ie,jb).*ex(1:ie,jb)-...
=( |%%,3
cbex(1:ie,jb).*(hz(1:ie,jb-1)-hzxbcb(ibbc:iebc+ie,1)-...
x7/Vf,N
hzybcb(ibbc:iebc+ie,1))+...
]TT >3"Dw7
cpex(1:ie,jb).*px(1:ie,jb);
_l9fNf!@
I;NW!"pU
% LEFT
y/\b0&
*"WP*A\1
exbcl(:,2:je)=caexbcl(:,2:je).*exbcl(:,2:je)-...
j5/pVXO
cbexbcl(:,2:je).*(hzxbcl(:,1:je-1)+hzybcl(:,1:je-1)-...
P4Pc;8T@!
hzxbcl(:,2:je)-hzybcl(:,2:je))+...
Q~nVbj?c2v
cpexbcl(:,2:je).*pxbcl(:,2:je);
g6%]uCFB
exbcl(:,1)=caexbcl(:,1).*exbcl(:,1)-...
IMwV9rF
cbexbcl(:,1).*(hzxbcf(1:iebc,jebc)+hzybcf(1:iebc,jebc)-...
,Tr&`2w
hzxbcl(:,1)-hzybcl(:,1))+cpexbcl(:,1).*pxbcl(:,1);
'Wnh1|z
exbcl(:,jb)=caexbcl(:,jb).*exbcl(:,jb)-...
N_bgW QY
cbexbcl(:,jb).*(hzxbcl(:,je)+hzybcl(:,je)-...
nRc\!4
hzxbcb(1:iebc,1)-hzybcb(1:iebc,1))+...
+]cf/_8+s
cpexbcl(:,jb).*pxbcl(:,je);
*|Vf1R]
lo>9 \ Po
% RIGHT
7*uN[g#p
7 2JwG7qh
exbcr(:,2:je)=caexbcr(:,2:je).*exbcr(:,2:je)-...
? Vd~
cbexbcr(:,2:je).*(hzxbcr(:,1:je-1)+hzybcr(:,1:je-1)-...
3S3(Gl
hzxbcr(:,2:je)-hzybcr(:,2:je))+...
neM.M)0
cpexbcr(:,2:je).*pxbcr(:,2:je);
'r 7[9[
exbcr(:,1)=caexbcr(:,1).*exbcr(:,1)-...
r%f Q$q>
cbexbcr(:,1).*(hzxbcf(1+iebc+ie:iefbc,jebc)+...
c ^ds|7i]a
hzybcf(1+iebc+ie:iefbc,jebc)-...
qm!cv;}c1
hzxbcr(:,1)-hzybcr(:,1))+cpexbcr(:,1).*pxbcr(:,1);
q6F1Rt
exbcr(:,jb)=caexbcr(:,jb).*exbcr(:,jb)-...
G^t)^iI"'
cbexbcr(:,jb).*(hzxbcr(:,je)+hzybcr(:,je)-...
GP c B(
hzxbcb(1+iebc+ie:iefbc,1)-...
T"{~mQ*
hzybcb(1+iebc+ie:iefbc,1))+cpexbcr(:,jb).*pxbcr(:,jb);
?@4Mt2Z\
7JBs7LG
%***********************************************************************
Zq8 5q
% Update EY in PML regions
AuQ|CXG-\
%***********************************************************************
3XlQ 4
XiTi3vCe
% FRONT
m@XX2l9:9
`{!A1xKZ
eybcf(2:iefbc,:)=caeybcf(2:iefbc,:).*eybcf(2:iefbc,:)-...
[@lK[7 u
cbeybcf(2:iefbc,:).*(hzxbcf(2:iefbc,:)+hzybcf(2:iefbc,:)-...
V8 8u-
hzxbcf(1:iefbc-1,:)-hzybcf(1:iefbc-1,:))+...
LHA^uuBN}
cpeybcf(2:iefbc,:).*pybcf(2:iefbc,:);
`.J)Z=o
B-N//ef}
% BACK
v_5qE
Pv5S k8
eybcb(2:iefbc,:)=caeybcb(2:iefbc,:).*eybcb(2:iefbc,:)-...
yS~Y"#F!.
cbeybcb(2:iefbc,:).*(hzxbcb(2:iefbc,:)+hzybcb(2:iefbc,:)-...
<8 <P,
hzxbcb(1:iefbc-1,:)-hzybcb(1:iefbc-1,:))+...
KsOSPQDGE
cpeybcb(2:iefbc,:).*pybcb(2:iefbc,:);
S. `y%t.GP
):PN0.H8
% LEFT
LSc^3=X
s 1M-(d Q
eybcl(2:iebc,:)=caeybcl(2:iebc,:).*eybcl(2:iebc,:)-...
_MC',p&
cbeybcl(2:iebc,:).*(hzxbcl(2:iebc,:)+hzybcl(2:iebc,:)-...
O80Z7
hzxbcl(1:iebc-1,:)-hzybcl(1:iebc-1,:))+...
]Ik~TW&
cpeybcl(2:iebc,:).*pybcl(2:iebc,:);
Bbs1U
ey(1,:)=caey(1,:).*ey(1,:)-...
;GM`=M4
cbey(1,:).*(hz(1,:)-hzxbcl(iebc,:)-hzybcl(iebc,:))+cpey(1,:).*py(1,:);
+:@^nPfHy
g/.FJ-I*
% RIGHT
$a~
C{/U;Ie-b
eybcr(2:iebc,:)=caeybcr(2:iebc,:).*eybcr(2:iebc,:)-...
m+'1c}n^7
cbeybcr(2:iebc,:).*(hzxbcr(2:iebc,:)+hzybcr(2:iebc,:)-...
S|tA%2z
hzxbcr(1:iebc-1,:)-hzybcr(1:iebc-1,:))+...
*,G<X^
cpeybcr(2:iebc,:).*pybcr(2:iebc,:);
hx0 t!k(3
ey(ib,:)=caey(ib,:).*ey(ib,:)-...
c;]\$#2
cbey(ib,:).*(hzxbcr(1,:)+hzybcr(1,:)- hz(ie,:))+...
HDKF>S_S
cpey(ib,:).*py(ib,:);
M _< |n
|iUF3s|?
8J'5%$3u
%***********************************************************************
NW6;7nWb
% Update magnetic fields (HZ) in main grid
LmJjO:W}^y
%***********************************************************************
6<W^T9}v@/
2?%*UxcO
% for dispersion consideration P equation (32) 1995 IEEE tran. antennas and
!QwB8yK@
% Propagation Vol.43 No. 4, pp422 (Jeffrey L. Young)
:;Z/$M16B
px(:,2:je)=dapx(:,2:je).*px(:,2:je)+...
<~uzHg%Y
dbpx(:,2:je).*ex(:,2:je);
\2 DED
>bV3~m$a+
py(2:ie,:)=dapy(2:ie,:).*py(2:ie,:)+...
C'[4jz0xF
dbpy(2:ie,:).*ey(2:ie,:);
L-E &m* %
5/P. 4<c7
?VotIruR
hz(1:ie,1:je)=dahz(1:ie,1:je).*hz(1:ie,1:je)+...
t`Bk2Cc)+
dbhz(1:ie,1:je).*(ex(1:ie,2:jb)-ex(1:ie,1:je)+...
_DSDY$Ec
ey(1:ie,1:je)-ey(2:ib,1:je));
ThX3@o
;g?PK5rB(
hz(imp_x,imp_y)=source(n); %(imp_x ,imp_y) are the location of the point source
u_WUJ_
3y.+03 W
%hz(imp_x,imp_y+25)=source(n);
xMk>r1Ud
Jf2JGTcm
%***********************************************************************
dHx4yFS
% Update HZX ,px in PML regions
i}8OaX3x
%***********************************************************************
^Ak?2,xB#+
wp }Q4I
% FRONT
,Dv*<La`\
O:GP uVb\
.>;??BG}
pxbcf(:,2:jebc)=dapxbcf(:,2:jebc).*pxbcf(:,2:jebc)+...
t8RtJ2;
dbpxbcf(:,2:jebc).*exbcf(:,2:jebc);
$Mg O)bH
px(1:ie,1)=dapx(1:ie,1).*px(1:ie,1)+...
DtBvfYO8)>
dbpx(1:ie,1).*ex(1:ie,1);
t }4
EgG3XhfS
hzxbcf(1:iefbc,:)=dahzxbcf(1:iefbc,:).*hzxbcf(1:iefbc,:)-...
!:\0}w$-
dbhzxbcf(1:iefbc,:).*(eybcf(2:ibfbc,:)-eybcf(1:iefbc,:));
c=tbl|Cq
GCYXDovh
% BACK
UucX1%
pxbcb(:,2:jebc-1)=dapxbcb(:,2:jebc-1).*pxbcb(:,2:jebc-1)+...
} OIe!
dbpxbcb(:,2:jebc-1).*exbcb(:,2:jebc-1);
| t:UpP
px(1:ie,jb)=dapx(1:ie,jb).*px(1:ie,jb)+...
t"Du
dbpx(1:ie,jb).*ex(1:ie,jb);
r jn:E
[O\)R[J
hzxbcb(1:iefbc,:)=dahzxbcb(1:iefbc,:).*hzxbcb(1:iefbc,:)-...
392(N(
dbhzxbcb(1:iefbc,:).*(eybcb(2:ibfbc,:)-eybcb(1:iefbc,:));
tb?TPd-OY
&