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大家帮忙看看我这个UPML有耗介质的迭代方程 ..
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大家帮忙看看我这个UPML有耗介质的迭代方程写的对吗（代码已贴出）？
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xiaoyuan
UID ：53338
注册：
2010-02-28
登录：
2015-12-05
发帖：
156
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仿真二级
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发表于: 2010-08-29 06:12:32
小弟初学者，我基于论坛里Program author: Keely J. Willis, Graduate Student UW Computational Electromagnetics Laboratory
u ij^tN %
Director: Susan C. Hagness编的真空UPML代码的基础上改编成UPML连接有耗介质的代码，但是一旦我把sigma赋值后，比如让sigma=0.5，结果就不对，非常小（10的负一百多次方），而且幅值是一直增大的趋势。但当把sigma赋成0时，结果看上去似乎就合理。不知道为什么，想请各位有经验的高手给点建议或找找原因。 谢谢大家！！
:\His{%
sAL ]N][Y
下面是我的迭代方程。其中磁场迭代方程我没有动它，和源代码一样。电场迭代方程我是基于talflove的书第二版第七章7.10节的公式。
31G0 B_T
"W(Ae="60
%
Update magnetic field
S\&3t}_
<TRhn z
bstore=bx;
3+>n!8x ;A
bx(2:ie_tot,:,:)=D1hx(2:ie_tot,:,:).* bx(2:ie_tot,:,:)-...
qclc--fsE
D2hx(2:ie_tot,:,:).*((ez(2:ie_tot,2:jh_tot,:)-ez(2:ie_tot,1:je_tot,:))-...
IyyBW2
(ey(2:ie_tot,:,2:kh_tot)-ey(2:ie_tot,:,1:ke_tot)))./delta;
U"p</Q
&gY) x{
hx(2:ie_tot,:,:)= D3hx(2:ie_tot,:,:).*hx(2:ie_tot,:,:)+...
&EQhk9j
D4hx(2:ie_tot,:,:).*(D5hx(2:ie_tot,:,:).*bx(2:ie_tot,:,:)-...
Z}dK6h5+'
D6hx(2:ie_tot,:,:).*bstore(2:ie_tot,:,:));
#H>{>0q
)&7. E
bstore=by;
qVE0[ve
by(:,2:je_tot,:)=D1hy(:,2:je_tot,:).* by(:,2:je_tot,:)-...
~RuX2u-2&u
D2hy(:,2:je_tot,:).*((ex(:,2:je_tot,2:kh_tot)-ex(:,2:je_tot,1:ke_tot))-...
Kh(`6 f
(ez(2:ih_tot,2:je_tot,:)-ez(1:ie_tot,2:je_tot,:)))./delta;
6,3o_"J !
d)Yl D]I
hy(:,2:je_tot,:)= D3hy(:,2:je_tot,:).*hy(:,2:je_tot,:)+...
f;zNNx< ;
D4hy(:,2:je_tot,:).*(D5hy(:,2:je_tot,:).*by(:,2:je_tot,:)-...
M[YFyM(
D6hy(:,2:je_tot,:).*bstore(:,2:je_tot,:));
gK[;"R)4o@
qEST[S V
bstore=bz;
Zg(Y$ h\
bz(:,:,2:ke_tot)=D1hz(:,:,2:ke_tot).* bz(:,:,2:ke_tot)-...
&9#m] Mz
D2hz(:,:,2:ke_tot).*((ey(2:ih_tot,:,2:ke_tot)-ey(1:ie_tot,:,2:ke_tot))-...
?s^3 o{!<W
(ex(:,2:jh_tot,2:ke_tot)-ex(:,1:je_tot,2:ke_tot)))./delta;
3$k #bC
C PP~ ,E_
hz(:,:,2:ke_tot)= D3hz(:,:,2:ke_tot).*hz(:,:,2:ke_tot)+...
H,X|-B
D4hz(:,:,2:ke_tot).*(D5hz(:,:,2:ke_tot).*bz(:,:,2:ke_tot)-...
_q27 3QG/"
D6hz(:,:,2:ke_tot).*bstore(:,:,2:ke_tot));
Wx GD*%
EaO@I. [
% Update electric field
Kg$RT?q-C6
qMNW w\k
p1store=px1;
!`Rh2g*o9
:V)jm`)#+
px1(:,2:je_tot,2:ke_tot)=C1ex(:,2:je_tot,2:ke_tot).* px1(:,2:je_tot,2:ke_tot)+...
@9gZH_ur>E
C2ex(:,2:je_tot,2:ke_tot).*((hz(:,2:je_tot,2:ke_tot)-hz(:,1:je_tot-1,2:ke_tot))-...
;X,u
( hy(:,2:je_tot,2:ke_tot)-hy(:,2:je_tot,1:ke_tot-1)))./delta;
V ;XKvH
\7/yWd{N$
p2store=px2;
0d9z8y
:BF ? r
px2(:,2:je_tot,2:ke_tot)=C3ex(:,2:je_tot,2:ke_tot).* px2(:,2:je_tot,2:ke_tot)+...
== 5F[U X
C4ex(:,2:je_tot,2:ke_tot).*( px1(:,2:je_tot,2:ke_tot)-...
%7)=k}4
p1store(:,2:je_tot,2:ke_tot));
Pj-INc 96
{G:y?q'z
ex(:,2:je_tot,2:ke_tot)=C5ex(:,2:je_tot,2:ke_tot).* ex(:,2:je_tot,2:ke_tot)+...
! = ,4tg`
C6ex(:,2:je_tot,2:ke_tot).*(C7ex(:,2:je_tot,2:ke_tot).* px2(:,2:je_tot,2:ke_tot)-...
cj8cV|8@
C8ex(:,2:je_tot,2:ke_tot).*p2store(:,2:je_tot,2:ke_tot));
k k3^m1
K}R+~<bIY
p1store=py1;
D%YgS$p[M$
.9qK88fU R
py1(2:ie_tot,:,2:ke_tot)=C1ey(2:ie_tot,:,2:ke_tot).* py1(2:ie_tot,:,2:ke_tot)+...
fo@^=-4A-
C2ey(2:ie_tot,:,2:ke_tot).*((hx(2:ie_tot,:,2:ke_tot)-hx(2:ie_tot,:,1:ke_tot-1))-...
M`Er&nQs
( hz(2:ie_tot,:,2:ke_tot)-hz(1:ie_tot-1,:,2:ke_tot)))./delta;
5XZ! yYB?
s 3Vb2C*
p2store=py2;
'+cI W(F?
~hLa n&T
py2(2:ie_tot,:,2:ke_tot)=C3ey(2:ie_tot,:,2:ke_tot).* py2(2:ie_tot,:,2:ke_tot)+...
ijF_ KP'
C4ey(2:ie_tot,:,2:ke_tot).*( py1(2:ie_tot,:,2:ke_tot)-...
E MW6'
p1store(2:ie_tot,:,2:ke_tot));
~ y!'\d>q<
LSJ?;Zg(=z
ey(2:ie_tot,:,2:ke_tot)=C5ey(2:ie_tot,:,2:ke_tot).* ey(2:ie_tot,:,2:ke_tot)+...
)S)L9('IxT
C6ey(2:ie_tot,:,2:ke_tot).*(C7ey(2:ie_tot,:,2:ke_tot).* py2(2:ie_tot,:,2:ke_tot)-...
~t`s& t'c|
C8ey(2:ie_tot,:,2:ke_tot).*p2store(2:ie_tot,:,2:ke_tot));
3`H K^((o
-Ks>s
p1store=pz1;
LmF ,en5
aKbmj
pz1(2:ie_tot,2:je_tot,:)=C1ez(2:ie_tot,2:je_tot,:).* pz1(2:ie_tot,2:je_tot,:)+...
C|$q Vh>
C2ez(2:ie_tot,2:je_tot,:).*((hy(2:ie_tot,2:je_tot,:)-hy(1:ie_tot-1,2:je_tot,:))-...
\WCQ>c?~
( hx(2:ie_tot,2:je_tot,:)-hx(2:ie_tot,1:je_tot-1,:)))./delta;
!.] JiT'o
p2store=pz2;
)#}>,,S
Z .6dL
pz2(2:ie_tot,2:je_tot,:)=C3ez(2:ie_tot,2:je_tot,:).* pz2(2:ie_tot,2:je_tot,:)+...
Dsg>~J'
C4ez(2:ie_tot,2:je_tot,:).*( pz1(2:ie_tot,2:je_tot,:)-...
8-#%l~dr
p1store(2:ie_tot,2:je_tot,:));
_8VP'S=
dw bR,K
pz2(is,js,ks:ks+1)=pz2(is,js,ks:ks+1)+exp(-((n-4.5*tau/dt)^2/(tau/dt)^2));
@LKQ-<dZG
BPba3G9H
ez(2:ie_tot,2:je_tot,:)=C5ez(2:ie_tot,2:je_tot,:).* ez(2:ie_tot,2:je_tot,:)+...
;<AcW.jx
C6ez(2:ie_tot,2:je_tot,:).*(C7ez(2:ie_tot,2:je_tot,:).* pz2(2:ie_tot,2:je_tot,:)-...
2@D`^]]
C8ez(2:ie_tot,2:je_tot,:).*p2store(2:ie_tot,2:je_tot,:));
QOF@Dv Q
*glZb;_
以下是全部代码：希望各位能帮忙看看哪里不对。
DZ8|20b
（注明：我在给迭代系数赋值时是一部分一部分慢慢赋值，并没有像原代码那样一起赋值，所以有点冗长，但是我目前是想找出这个代码哪里有毛病。所以优化问题先放一边，希望大家能理解，如果对代码有不清楚的地方，回复我。我会每天都上论坛给予解释。谢谢！）
*x"80UX L
% t9C
（说明：（其实大家不用在意这个）为了方便大家理解，我的UPML层，想象中是整体向内缩减了0.25个网格长度。如果把网格坐标定为1，2，3...一直到61（60个格子)，那pml层的坐标就是从1.25，2.25，3.25.... 一直到11.25和 从50.75，51.75....一直到60.75。大家可以想象一下。 （原来可能是从1，2，3...到11，51,52，53.....到61 我就是将每个方向的pml的范围将两头向中间压缩了0.25个网格长。）
'-;[8:y.
n{ ;j
_>; W z7
%***********************************************************************
KQdIG9O+6
% Fundamental constants
p~qe/
%***********************************************************************
9Eyx Ob
g>@JGzMLP
cc=2.99792458e8;
pN%&`]Wev
muz=4.0*pi*1.0e-7;
0 M_oFx
epsz=1.0/(cc*cc*muz);
!+T1kMP+l
etaz=sqrt(muz/epsz);
0m Y Y:?v
sigma_e=0.0; %大家run一下程序就知道当将此处sigma_e的值改为比如0.5，结果就不太对。为什么？？
zH8E,)
K9lgDk"i
&_ekA44 E
%***********************************************************************
<\aeC2~M
% Material parameters
,^#Jw`w^
%***********************************************************************
Eah6"j!B8n
Sjpx G@k
mur=1.0;
,fVD`RR(W?
epsr=80;
_!\d?]Ya
freq=20000;
u/zBz*zh
eta=etaz*sqrt(mur/epsr); %
H GDrH
du3f'=q6|
c=1/sqrt(epsr*epsz*muz*mur);
#< im?
%***********************************************************************
X W) TI
% Grid parameters
!_<6}:ZB
%
IHl q27O
% Each grid size variable name describes the number of sampled points
)h!cOEt
% for a particular field component in the direction of that component.
d8j1L /e
% Additionally, the variable names indicate the region of the grid
}htjT/Nm
% for which the dimension is relevant. For example, ie_tot is the
g` 7XE
% number of sample points of Ex along the x-axis in the total
"s*-dZO
% computational grid, and jh_bc is the number of sample points of Hy
#o.e (C
% along the y-axis in the y-normal UPML regions.
~Iu! B Y
%
!>8~ R2
%***********************************************************************
*T|B'80
k_al*iM>H
`2s!%/
%是一个三维立方体空间，60*60*60（已经包括了厚度为10的upml层）
`FP?9R6Y
6o 3 bq|
0B NLTRv
ie=40; % Size of main grid
CLb6XnkcA\
je=40;
\N>-+r
ke=40;
'y8{, R4C
ih=ie+1;
'X `Z1L/
jh=je+1;
/0h *(nL
kh=ke+1;
*z=_s D?1
3FEJ 9ZyG
upml=10; % Thickness of PML boundaries
l>?c AB[
ih_bc=upml+1;
_FLEz|%~
jh_bc=upml+1;
d2 ^}ooE
kh_bc=upml+1;
}'X=& 3m
c?p^!zG
ie_tot=ie+2*upml; % Size of total computational domain
\oQ]=dDCd%
je_tot=je+2*upml;
U2oCSo5:3N
ke_tot=ke+2*upml;
i e}O ZM
ih_tot=ie_tot+1;
Y?T{>"_W
jh_tot=je_tot+1;
^URCnJ67Se
kh_tot=ke_tot+1;
^u /%zL
GF'wDi}
pxs = 11;
y7R#Pk Q ~
pys = 11;
(!os &/",
pzs = 11;
Hd|l6/[xz
(B7G'h.?
pxe = 51;
$`=p]
pye = 51;
5gszAvOO
pze = 51;
--$o$ EP`
m7 =$*1k
is=round(ih_tot/2); % Location of z-directed current source
fV(3RG
js=round(jh_tot/2);
sGvbL-S-f:
ks=round(ke_tot/2);
I$n= >s
S2~cAhR|M
%***********************************************************************
jcH@*c=%e
% Fundamental grid parameters
)xGAe #E~j
%***********************************************************************
8sG3<$Z^
V|7Y Ra@
delta= 83.794539403718844;
FqKJids-
dt=0.9./sqrt(3.0./delta./delta)./c;
pMc6p0
%dt=delta*sqrt(epsr*mur)/(2.0*cc);
^E !v D
%dt=delta*0.5/c;
A KNx~!%2
nmax=200;
`+J Fvn!
v0^9 "V:y
%***********************************************************************
&J[a.:..
% Differentiated Gaussian pulse excitation
\u3\ T J
%***********************************************************************
::L2zVq5V
wucdXj{%
rtau=50.0e-12;
=BsV`p7rU
%tau=rtau/dt;
4JSPD#%f
tau = 20*delta/2/c;
KaGUp Hw
ndelay=3*tau;
|m19fg3u
J0=-1.0*epsz;
7p&jSOY
^ k^y|\UtZ
%***********************************************************************
?0tg}0|
% Initialize field arrays
^ ?69|,
%***********************************************************************
bdUPo+
-+9[X*VCc
ex =zeros(ie_tot,jh_tot,kh_tot);
s:`i~hjq
px1=zeros(ie_tot,jh_tot,kh_tot);
2E Y"[xK|
px2=zeros(ie_tot,jh_tot,kh_tot);
_B4&Fb.
?Cq7_rq
ey= zeros(ih_tot,je_tot,kh_tot);
I-7LT?r
py1=zeros(ih_tot,je_tot,kh_tot);
A]1Nm3@
py2=zeros(ih_tot,je_tot,kh_tot);
o<2GtF1"o
7\u+%i;YZ
ez= zeros(ih_tot,jh_tot,ke_tot);
l?Y^3x}j
pz1=zeros(ih_tot,jh_tot,ke_tot);
/Y Kd [RQ
pz2=zeros(ih_tot,jh_tot,ke_tot);
ZS Med(//b
@u3`lhUcT
hx=zeros(ih_tot,je_tot,ke_tot);
'[F:uA
hy=zeros(ie_tot,jh_tot,ke_tot);
+)Te)^&v%
hz=zeros(ie_tot,je_tot,kh_tot);
k_=SDm a
bx=zeros(ih_tot,je_tot,ke_tot);
&4'< {
by=zeros(ie_tot,jh_tot,ke_tot);
tiK?VwaKI
bz=zeros(ie_tot,je_tot,kh_tot);
<G"cgN#]
)n/%P4l
%***********************************************************************
E$d3+``
% Initialize update coefficient arrays
CU$kh z"
%***********************************************************************
4 p_C +4
% 系数矩阵
bIKg>U'5d
C1ex=zeros(size(ex));
3JoY-
C2ex=zeros(size(ex));
gU9{~-9}
C3ex=zeros(size(ex));
:fRXLe1=
C4ex=zeros(size(ex));
r@r%qkh(.@
C5ex=zeros(size(ex));
_Fb}zPU!
C6ex=zeros(size(ex));
kH!Z|P s?R
C7ex=zeros(size(ex));
b ^Hr zn
C8ex=zeros(size(ex));
Zw]`z*,yRA
Er~ 17$b
C1ey=zeros(size(ey));
?5|;3N/zt
C2ey=zeros(size(ey));
B( [x8A]
C3ey=zeros(size(ey));
F c[KIG3@
C4ey=zeros(size(ey));
V la,avON
C5ey=zeros(size(ey));
N,ht< l\
C6ey=zeros(size(ey));
^}3^| jF
C7ey=zeros(size(ey));
QWmE:F[M~
C8ey=zeros(size(ey));
a(Y'C`x
[+#m THX
C1ez=zeros(size(ez));
- F[8 ZiZ
C2ez=zeros(size(ez));
rvA>khu0/
C3ez=zeros(size(ez));
?M2(8 0
C4ez=zeros(size(ez));
wZrFu(_
C5ez=zeros(size(ez));
r^9l/H~ $
C6ez=zeros(size(ez));
U%{GLO
C7ez=zeros(size(ez));
[)H 6`w
C8ez=zeros(size(ez));
!Jg;%%E3:i
D+8d^-:
D1hx=zeros(size(hx));
1CtUf7 `/Q
D2hx=zeros(size(hx));
2Fc L-?
D3hx=zeros(size(hx));
jA? #!lx_
D4hx=zeros(size(hx));
`i{d"H0E
D5hx=zeros(size(hx));
?0b-fL^^+l
D6hx=zeros(size(hx));
^ Fk;t
?}||?2=P
D1hy=zeros(size(hy));
fV:15!S[
D2hy=zeros(size(hy));
Wj{lb_Rj
D3hy=zeros(size(hy));
e~h>b.~
D4hy=zeros(size(hy));
ia6 jiW x
D5hy=zeros(size(hy));
^df wWP
D6hy=zeros(size(hy));
t2&kGf"
9#LMK 1ge
D1hz=zeros(size(hz));
^ 5 >e
D2hz=zeros(size(hz));
*7Dba5B
D3hz=zeros(size(hz));
bT,:eA
D4hz=zeros(size(hz));
|@ mz@
D5hz=zeros(size(hz));
_sjS'*]
D6hz=zeros(size(hz));
5Z=4%P*I
f^%3zWp|-
%***********************************************************************
PSr x !
% Update coefficients, as described in Section 7.8.2.
570Xk\R@M
%
W? 7l-k=S
% In order to simplify the update equations used in the time-stepping
~C-Sr@ a?/
% loop, we implement UPML update equations throughout the entire
FOaA}D `]
% grid. In the main grid, the electric-field update coefficients of
%zavSm"
% Equations 7.91a-f and the correponding magnetic field update
9O[IR)O~
% coefficients extracted from Equations 7.89 and 7.90 are simplified
6fwNlC/9
% for the main grid (free space) and calculated below.
01bC P
%
4^_6~ YP7
%***********************************************************************
2Gyq40
H7O~So*N5
%以下是主区域的迭代系数，即非pml参数时的系数
x" r0<RK
C1=(2*epsz*epsr-sigma_e*dt)/(2*epsz*epsr+sigma_e*dt);
rOIb9:
C2=2*dt/(2*epsz*epsr+sigma_e*dt);
D(cD8fn,J
C3=1.0;
l\U Q2i
C4=1.0;
j:9M${~
C5=1.0;
g/?Vl2W
C6=1/2/epsz/epsr;
"tCI_ Zi;
C7=2*epsz*epsr;
6iFlz9XiI
C8=2*epsz*epsr;
-oD,F $Rb
_h%Jf{nu
D1=1.0;
ktu?-?#0,
D2=dt;
&lc@]y8
D3=1.0;
>OG189O
D4=1.0/2.0/epsr/epsz/mur/muz;
mY|c7}>V;
D5=2.0*epsr*epsz;
(qcFGM22U
D6=2.0*epsr*epsz;
;W |kc</R*
AR"2?2<mJ7
%***********************************************************************
<J%qzt}
% Initialize main grid update coefficients
KbJ6U75|f
%***********************************************************************
E4# { &sRT
% 给主计算区域系数赋值。
xBHf~:!
C1ex(:,:,:)=C1;
_K5<)( )
C2ex(:,:,:)=C2;
LUbhTc
C3ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C3; %11 51
ZvY"yl ?e
C4ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C4;
glAS$<
C5ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C5; %11 51
ci,( ]T +!
C6ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C6;
.[= {Yx0!I
C7ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C7; %11 50
vrn4yHoZ
C8ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C8;
0 _!0\d#c
S)CsH1Q
C1ey(:,:,:)=C1;
t@KTiJI ]
C2ey(:,:,:)=C2;
tX*@r
C3ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C3; %11 51
/4{WT ?j
C4ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C4;
SH*'<
C5ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C5; %11 51
h*%p%t<
C6ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C6;
5!0iK9O
C7ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C7; %11 50
Zy0M\-Mn
C8ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C8;
f5}afPk
HOW<IZ^
C1ez(:,:,:)=C1;
H`[FC|RYyE
C2ez(:,:,:)=C2;
" <bjS
C3ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C3; %11 51
K'OG-fn;
C4ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C4;
&9jJ\+:7
C5ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C5; %11 51
(}#&HE<
C6ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C6;
LpHGt]|D
C7ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C7; %11 50
H4i}gdR
C8ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C8;
~z^l~Vyg?
ODJ"3 J
D1hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D1; %11 50
=^"Sx? ?V
D2hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D2;
Urni JB]
D3hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D3; %11 50
3=S |U,
D4hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D4;
r #-
D5hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D5; %11 51
N'1I6e "
D6hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D6;
&o L"AJU
cGot0' mB
D1hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D1; %11 50
b"g^Jm! j
D2hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D2;
(>`_N%_
D3hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D3; %11 50
=lNW1J\SW
D4hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D4;
Nr4Fp`b8
D5hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D5; %11 51
>=k7#av
D6hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D6;
3 s\UU2yr
s>9I#_4]
D1hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D1; %11 50
:?f<tNU$
D2hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D2;
-e_fn&2,Y
D3hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D3; %11 50
b:1B >
D4hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D4;
q NGR6i
D5hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D5; %11 51
I0-1Hr
D6hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D6;
>N3X/8KL%
;NP-tA)
rmax=exp(-16); % R(0) desired reflection error, designated as R(0) in Equation 7.62
? Fqh i
z$<=8ox8e
orderbc=4; % m order of the polynomial grading, designated as m in Equation 7.60a,b
<3Ftq=
l&& i`
% 以下是给pml层的系数赋值，我完全是用的talflove书上的公式，没有用原来代码中的公式
H UJqB0D ?
% x-varying material properties
1$Up7=Dr=
delbc=upml*delta; % d
eDd& vf
sigmam=-log(rmax)*(orderbc+1.0)/(2.0*eta*delbc);
288mP]a(v_
%sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0));
D ksYKv
kmax=1;
QW..=}pL
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc;
_ep&`K
cMK|t;" 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
97c0bgI!+
% xp xn
oKGH|iVEe
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\Y x G
? [Yn<|
% Coefficients for field components in the center of the grid cell
-J]?M
V .K jcy
% x1=(upml-i+1)*delta;x1;
)St0}?I~
% x2=(upml-i)*delta;x2;
\mF-L,yu
r_center = ([1:upml] - 0.25)/upml;
HoBx0N9\2
t/i*.>7
%按照场分量在网格中的位置，我每一个方向有两个循环，分别对应分量在网格中间和在网格边上
o sc8;B/
Z@Rqm:e
for i=1:upml
M]8>5Zx.
%sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1));
x1 =`Z@^
%ki=1+kfactor*(x1^(orderbc+1)-x2^(orderbc+1));
S iNgV\('U
sigma(i) = sigmam * r_center(i)^orderbc;
74_ ?@Z(
ki = 1;
LM<*VhX
facm=(2*epsr*epsz*ki-sigma(i)*dt);
RqROl!6
facp=(2*epsr*epsz*ki+sigma(i)*dt);
sBlq)h;G?6
%ie_tot-upml+i;
cGE{dWz
%upml-i+1;
`JI p$
%/eG{ oh-
C7ex(upml-i+1,:,:)=facp;
q\tr&@4iC
C7ex(ie_tot-upml+i,:,:)=facp;
TF%n1H-sF
C8ex(upml-i+1,:,:)=facm;
u7!gF&tA
C8ex(ie_tot-upml+i,:,:)=facm;
4Q+ ,_iP
D1hz(upml-i+1,:,:)=facm/facp;
su0K#*P&I
D1hz(ie_tot-upml+i,:,:)=facm/facp;
(4Db%Iw
D2hz(upml-i+1,:,:)=2.0*epsr*epsz*dt/facp;
|\bNFnn(
D2hz(ie_tot-upml+i,:,:)=2.0*epsr*epsz*dt/facp;
j ,rc9
D3hy(upml-i+1,:,:)=facm/facp;
9^^\Z5
D3hy(ie_tot-upml+i,:,:)=facm/facp;
hl]d99Lc
D4hy(upml-i+1,:,:)=1.0/facp/mur/muz;
M:O*_>KF
D4hy(ie_tot-upml+i,:,:)=1.0/facp/mur/muz;
MpKXC
5|0}bv O
end
CI+)0=`<1B
lG6&uMvo
% Coefficients for field components on the grid cell boundary
G-CL \G\n
~'*23]j
r_boundary = ([1:upml] - 0.75)/upml;
zDg* ds\
z B m~ J%
W *0!Z:?
for i=1:upml
S 1k*"><
% x1=(upml-i+1.5)*delta;
CfOyHhhKX
% x2=(upml-i+0.5)*delta;
Iq|h1ie m+
% sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1));
TJ)Nr*U3_
% ki=1.0+kfactor*(x1^(orderbc+1)-x2^(orderbc+1));
]n=z(2Z9lD
sigma(i) = sigmam * r_boundary(i)^orderbc;
THl: >s
ki = 1;
%>&~?zrq
facm=(2.0*epsr*epsz*ki-sigma(i)*dt);
]xf89[ ;0
facp=(2.0*epsr*epsz*ki+sigma(i)*dt);
.p{lzI9
Y1o[|yt W
C3ez(upml-i+2,:,:)=facm/facp;
TT/=0 ^"
C3ez(ie_tot-upml+i,:,:)=facm/facp;
' !huU
C4ez(upml-i+2,:,:)=2*epsr*epsz/facp;
[KUkv
C4ez(ie_tot-upml+i,:,:)=2*epsr*epsz/facp;
Eq@sU ?j
C5ey(upml-i+2,:,:)=facm/facp;
r6j[C"@
C5ey(ie_tot-upml+i,:,:)=facm/facp;
2NFk#_9e~
C6ey(upml-i+2,:,:)=1.0/facp;
j1Ys8k%$l
C6ey(ie_tot-upml+i,:,:)=1.0/facp;
58?WO}
D5hx(upml-i+2,:,:)=facp;
iBWzxPv:z
D5hx(ie_tot-upml+i,:,:)=facp;
JP!e'oWxi
D6hx(upml-i+2,:,:)=facm;
*wAX&+);
D6hx(ie_tot-upml+i,:,:)=facm;
$%U}k=-
4=MVn
end
fe\'N4
czw:xG!&
% 以下可能大家看了有点迷惑，是在xp(x的正方向的pml层）中除了和sigmax有关的系数之外，
-raK
% 其他不含sigmax的系数赋值。
UXZ3~/L5 O
%xp
. (&6gB
C3ex(pxe:ie_tot,pys+1:pye-1,2:ke_tot)=C3;
QeY+imM
C4ex(pxe:ie_tot,pys+1:pye-1,2:ke_tot)=C4;
0ytAn+/"x
C5ex(pxe:ie_tot,2:je_tot,pzs+1:pze-1)=C5;
oVqx)@$K
C6ex(pxe:ie_tot,2:je_tot,pzs+1:pze-1)=C6;
^uX"04>;
QAI=nrlp
C3ey(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=C3;
:qS~"@ ?<
C4ey(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=C4;
yS)k"XNb
C7ey(pxe:ie_tot,pys:pye-1,2:ke_tot)=C7;
dLQp"vs $
C8ey(pxe:ie_tot,pys:pye-1,2:ke_tot)=C8;
M5[#YG'FlQ
hW~% :v
C5ez(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=C5;
'"Cqq{*
C6ez(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=C6;
/XG7M=A$o
C7ez(pxe:ie_tot,2:je_tot,pzs:pze-1)=C7;
=$}`B{(H
C8ez(pxe:ie_tot,2:je_tot,pzs:pze-1)=C8;
Cpzd k~+H
02 FLe*zQ
D1hx(pxe:ie_tot,pys:pye-1,1:ke_tot)=D1;
E.yFCaL
D2hx(pxe:ie_tot,pys:pye-1,1:ke_tot)=D2;
:Gz$(!j1.'
D3hx(pxe:ie_tot,1:je_tot,pzs:pze-1)=D3;
+;H=_~b
D4hx(pxe:ie_tot,1:je_tot,pzs:pze-1)=D4;
.KYs5Qu
| {zka.sJ
D1hy(pxe:ie_tot,2:je_tot,pzs:pze-1)=D1;
#WA7}tHb
D2hy(pxe:ie_tot,2:je_tot,pzs:pze-1)=D2;
kW+>"3
D5hy(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=D5;
E QnU:a
D6hy(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=D6;
y**L^uvr
6n:X p_yO
D3hz(pxe:ie_tot,pys:pye-1,2:ke_tot)=D3;
VK9E{~0=
D4hz(pxe:ie_tot,pys:pye-1,2:ke_tot)=D4;
/&?ei*z
D5hz(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=D5;
!'\(OFv9Im
D6hz(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=D6;
+VIEDV+
e?\Od}Hbw
% 以下可能大家看了有点迷惑，是在xn(x的负方向的pml层）中除了和sigmax有关的系数之外，
gISA13
% 其他不含sigmax的系数赋值。
3 {H!B&sb
%xn
&2@"zD
C3ex(1:pxs-1,pys+1:pye-1,2:ke_tot)=C3;
,> g( %3C
C4ex(1:pxs-1,pys+1:pye-1,2:ke_tot)=C4;
AU*]D@H
C5ex(1:pxs-1,2:je_tot,pzs+1:pze-1)=C5;
ldG 8hK
C6ex(1:pxs-1,2:je_tot,pzs+1:pze-1)=C6;
jKP75jm
&WCVdZK:
C3ey(2:pxs,1:je_tot,pzs+1:pze-1)=C3;
=5:vKL j
C4ey(2:pxs,1:je_tot,pzs+1:pze-1)=C4;
L9[m/(:y
C7ey(2:pxs,pys:pye-1,2:ke_tot)=C7;
FpttH?^
C8ey(2:pxs,pys:pye-1,2:ke_tot)=C8;
X W '7
_2k<MiqCD[
C5ez(2:pxs,pys+1:pye-1,1:ke_tot)=C5;
E.'6p \
C6ez(2:pxs,pys+1:pye-1,1:ke_tot)=C6;
5m;pHgkb
C7ez(2:pxs,2:je_tot,pzs:pze-1)=C7;
}+ W5Snx
C8ez(2:pxs,2:je_tot,pzs:pze-1)=C8;
9U9ghWH8
;J?fK69%
D1hx(2:pxs,pys:pye-1,1:ke_tot)=D1;
&x j40IZ
D2hx(2:pxs,pys:pye-1,1:ke_tot)=D2;
AB!({EIi
D3hx(2:pxs,1:je_tot,pzs:pze-1)=D3;
zv1,DnkqF
D4hx(2:pxs,1:je_tot,pzs:pze-1)=D4;
<q MX,h2
vr>J$(F
D1hy(1:pxs-1,2:je_tot,pzs:pze-1)=D1;
{3Gj rE
D2hy(1:pxs-1,2:je_tot,pzs:pze-1)=D2;
WnQ'I=E#~
D5hy(1:pxs-1,pys+1:pye-1,1:ke_tot)=D5;
F 0m[ls$
D6hy(1:pxs-1,pys+1:pye-1,1:ke_tot)=D6;
Q2|6W E
Z(E .F,k
D3hz(1:pxs-1,pys:pye-1,2:ke_tot)=D3;
hAi'|;g
D4hz(1:pxs-1,pys:pye-1,2:ke_tot)=D4;
u`L *
D5hz(1:pxs-1,1:je_tot,pzs+1:pze-1)=D5;
,g P;XRe1
D6hz(1:pxs-1,1:je_tot,pzs+1:pze-1)=D6;
VQ~eg wJL
^wIP`dn
% PEC walls
O[ans_8
% C3ez(1,:,:)=-1.0;
^ ' )4RU
% C3ez(ih_tot,:,:)=-1.0;
N9c#N%cu
% C4ez(1,:,:)=0.0;
4pDZ +}p
% C4ez(ih_tot,:,:)=0.0;
54JI/!a
% C5ey(1,:,:)=-1.0;
*n M.`7g*[
% C5ey(ih_tot,:,:)=-1.0;
b9f5
% C6ey(1,:,:)=0.0;
<!u(_Bxw/
% C6ey(ih_tot,:,:)=0.0;
v&^N +>p
DL_M#c`<
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
r|jBKq~
% y-varying material properties
ZZL%5{ w_
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
z_C7=ga<
delbc=upml*delta;
I t n?''~;
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1.0)/(2.0*delbc);
Y 5>' (A>
% sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0));
,! ~U5~
kmax=1.0;
Mi!ak
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc;
F7p`zf@O]
IxP$ lx
% Coefficients for field components in the center of the grid cell
yC }x6xG
r_center = ([1:upml] - 0.25)/upml;
/[3!kW
d{^ K8T3
for j=1:upml
0O q5;5
@S012} xH
wS2N,X/Y
% y1=(upml-j+1)*delta;
H]lD*3b
% y2=(upml-j)*delta;
or` "{wop
% sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1));
v|kL7t)}
% ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1));
F fzY3r+
sigma(j) = sigmam * r_center(j)^orderbc;
|qk%UN<
ki = 1;
yEr vgf
facm=(2*epsr*epsz*ki-sigma(j)*dt);
`Q^Vm3h
facp=(2*epsr*epsz*ki+sigma(j)*dt);
~fA H6FdZ\
t/"9LMKs?
C7ey(:,upml-j+1,:)=facp;
_*(:6,8
C7ey(:,je_tot-upml+j,:)=facp;
Yh %
C8ey(:,upml-j+1,:)=facm;
Z} O0DfT ;
C8ey(:,je_tot-upml+j,:)=facm;
I>3G"[t
D1hx(:,upml-j+1,:)=facm/facp;
{ *|$@%y!
D1hx(:,je_tot-upml+j,:)=facm/facp;
x(zW<J 5X"
D2hx(:,upml-j+1,:)=2*epsr*epsz*dt/facp;
ku5g`h o
D2hx(:,je_tot-upml+j,:)=2*epsr*epsz*dt/facp;
FLl L0Gu
D3hz(:,upml-j+1,:)=facm/facp;
v C R\lR+
D3hz(:,je_tot-upml+j,:)=facm/facp;
Bsz;GnD|r
D4hz(:,upml-j+1,:)=1/facp/mur/muz;
:;x#qtv~Iz
D4hz(:,je_tot-upml+j,:)=1/facp/mur/muz;
q r/N ?,
end
7"_g X
c_2kHT
% Coefficients for field components on the grid cell boundary
k.0pPl
iu,Bmf^oD
r_boundary = ([1:upml] - 0.75)/upml;
r,Pu-bhF
LZ9IE>sj
for j=1:upml
RA62Z&W3
%y1=(upml-j+1.5)*delta;
XG6UV('
%y2=(upml-j+0.5)*delta;
PI" )^`
%sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1));
?@_,_gTQ
%ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1));
PJcz] <
sigma(j) = sigmam * r_boundary(j)^orderbc;
T|nN.
ki = 1;
f1VA61z{)
facm=(2*epsr*epsz*ki-sigma(j)*dt);
fI( H :N
facp=(2*epsr*epsz*ki+sigma(j)*dt);
E?f*Z {~,
7W#9ki1
C3ex(:,upml-j+2,:)=facm/facp;
}Sb&ux
C3ex(:,je_tot-upml+j,:)=facm/facp;
hmd, g>J:<
C4ex(:,upml-j+2,:)=2*epsr*epsz/facp;
u`X}AKC
C4ex(:,je_tot-upml+j,:)=2*epsr*epsz/facp;
)2,\Y
C5ez(:,upml-j+2,:)=facm/facp;
=HvLuVc
C5ez(:,je_tot-upml+j,:)=facm/facp;
LYiz:cQh
C6ez(:,upml-j+2,:)=1/facp;
Yc'7F7.<6
C6ez(:,je_tot-upml+j,:)=1/facp;
`!T6#6 h
D5hy(:,upml-j+2,:)=facp;
|c>A3 P$=B
D5hy(:,je_tot-upml+j,:)=facp;
B UKh5L
D6hy(:,upml-j+2,:)=facm;
5h(] S[Zf3
D6hy(:,je_tot-upml+j,:)=facm;
d3C*]|gQ
/9yA.W;
end
$VJ=A<
cXokq
%yp y的正方向
k@R)_,2HH
C5ex(1:ie_tot,pye:je_tot,pzs+1:pze-1)=C5;
esEOV$s}
C6ex(1:ie_tot,pye:je_tot,pzs+1:pze-1)=C6;
? Kn~fs8
C7ex(pxs:pxe-1,pye:je_tot,2:ke_tot)=C7;
0 g(hY:
C8ex(pxs:pxe-1,pye:je_tot,2:ke_tot)=C8;
0:L m=9 o
?3i-wpzMp
C3ey(2:ie_tot,pye:je_tot,pzs+1:pze-1)=C3;
4B8{\ "6
C4ey(2:ie_tot,pye:je_tot,pzs+1:pze-1)=C4;
K31rt-IIt
C5ey(pxs+1:pxe-1,pye:je_tot,2:ke_tot)=C5;
7" cgj#
C6ey(pxs+1:pxe-1,pye:je_tot,2:ke_tot)=C6;
I1(, J
#P6;-d@a
C3ez(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=C3;
<tTn$<b
C4ez(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=C4;
T+/Gz'
C7ez(2:ie_tot,pye:je_tot,pzs:pze-1)=C7;
kR-5RaW
C8ez(2:ie_tot,pye:je_tot,pzs:pze-1)=C8;
2 ? 7a\s
dTP$7nfe
D3hx(2:ie_tot,pye:je_tot,pzs:pze-1)=D3;
e{9(9qE"
D4hx(2:ie_tot,pye:je_tot,pzs:pze-1)=D4;
86@@j*c(@k
D5hx(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=D5;
}F R yG%
D6hx(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=D6;
P 3YG:*
iyhB;s5Rgw
D1hy(1:ie_tot,pye:je_tot,pzs:pze-1)=D1;
G#0 4h{
D2hy(1:ie_tot,pye:je_tot,pzs:pze-1)=D2;
= %7 :[#n
D3hy(pxs:pxe-1,pye:je_tot,1:ke_tot)=D3;
(iiyptJ
D4hy(pxs:pxe-1,pye:je_tot,1:ke_tot)=D4;
71w $i 4
4d3PF`,H`
D1hz(pxs:pxe-1,pye:je_tot,2:ke_tot)=D1;
\bb,gRfP
D2hz(pxs:pxe-1,pye:je_tot,2:ke_tot)=D2;
{ Z|.-~W
D5hz(1:ie_tot,pye:je_tot,pzs+1:pze-1)=D5;
,G,T&W
D6hz(1:ie_tot,pye:je_tot,pzs+1:pze-1)=D6;
N|1k6g= 0
# 6JCm!s
%yn y的负方向
m[u 6<C
C5ex(1:ie_tot,2:pys,pzs+1:pze-1)=C5;
[w)6OT
C6ex(1:ie_tot,2:pys,pzs+1:pze-1)=C6;
Hw/1~O$T
C7ex(pxs:pxe-1,2:pys,2:ke_tot)=C7;
3C 8'@-U
C8ex(pxs:pxe-1,2:pys,2:ke_tot)=C8;
IV:Knh+ ?
P z +8u&~p
C3ey(2:ie_tot,1:pys-1,pzs+1:pze-1)=C3;
C`x>)wm:
C4ey(2:ie_tot,1:pys-1,pzs+1:pze-1)=C4;
[XQoag;!
C5ey(pxs+1:pxe-1,1:pys-1,2:ke_tot)=C5;
Rf\>bI<.
C6ey(pxs+1:pxe-1,1:pys-1,2:ke_tot)=C6;
cj<j *(ZZ
'bg%9}
C3ez(pxs+1:pxe-1,2:pys,1:ke_tot)=C3;
Wcn^IQ
C4ez(pxs+1:pxe-1,2:pys,1:ke_tot)=C4;
]Ikj Z=
C7ez(2:ie_tot,2:pys,pzs:pze-1)=C7;
Efw/bTEg
C8ez(2:ie_tot,2:pys,pzs:pze-1)=C8;
T ~t%3 G
S* CR Vs
D3hx(2:ie_tot,1:pys-1,pzs:pze-1)=D3;
;comL29l2`
D4hx(2:ie_tot,1:pys-1,pzs:pze-1)=D4;
fD|ox
D5hx(pxs+1:pxe-1,1:pys-1,1:ke_tot)=D5;
XH2g: $
D6hx(pxs+1:pxe-1,1:pys-1,1:ke_tot)=D6;
HW GlC <
T , gMc
D1hy(1:ie_tot,2:pys,pzs:pze-1)=D1;
fe mAVx}go
D2hy(1:ie_tot,2:pys,pzs:pze-1)=D2;
4 ITSDx
D3hy(pxs:pxe-1,2:pys,1:ke_tot)=D3;
,[^P
D4hy(pxs:pxe-1,2:pys,1:ke_tot)=D4;
4S.%y7d\
FUm- Fp
D1hz(pxs:pxe-1,1:pys-1,2:ke_tot)=D1;
=RUK N 38
D2hz(pxs:pxe-1,1:pys-1,2:ke_tot)=D2;
s 4}}MV3X
D5hz(1:ie_tot,1:pys-1,pzs+1:pze-1)=D5;
_ Oq (& I
D6hz(1:ie_tot,1:pys-1,pzs+1:pze-1)=D6;
M ~!*PCd5
u Bs[[9je(
% PEC walls
Ph.$]yQCc]
% C3ex(:,1,:)=-1;
R m *"SG
% C3ex(:,jh_tot,:)=-1;
n4CzReG
% C4ex(:,1,:)=0;
{{=7 mbc
% C4ex(:,jh_tot,:)=0;
4aZsz,=
% C5ez(:,1,:)=-1;
+Mv0X% (N
% C5ez(:,jh_tot,:)=-1;
x<=+RYz#^:
% C6ez(:,1,:)=0;
w>rglm&
% C6ez(:,jh_tot,:)=0;
O` m W,
9!FV. yp%F
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2Sb~tTGz79
% z-varying material properties
)mZ` j .
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
P*(lc:
t L;;Yt
delbc=upml*delta;
f=J#mmH w$
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1)/(2*delbc);
t/S~CIA
%sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1));
jvm "7)h
kmax=1;
ScfW;
kfactor=(kmax-1)/delta/(orderbc+1)/delbc^orderbc;
T.W/S0#j3
/{1 xpR
% Coefficients for field components in the center of the grid cell
^ tm,gh
P5vM y'1X
r_center = ([1:upml] - 0.25)/upml;
R{6.O+j`
for k=1:upml
WohK,<Or
oc-7gz )
%z1=(upml-k+1)*delta;
Jb {m
%z2=(upml-k)*delta;
<<&:BK
%sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1));
#ZGWU_l}
%ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1));
m.EWYO0XQ
sigma(k) = sigmam * r_center(k)^orderbc;
K=Fcy #, f
ki = 1;
"v~w#\pz7
facm=(2*epsr*epsz*ki-sigma(k)*dt);
Kh w!+!(H
facp=(2*epsr*epsz*ki+sigma(k)*dt);
k2*^W&Z
;Z.}~d6>!
C7ez(:,:,upml-k+1)=facp;
x _(B7ob
C7ez(:,:,ke_tot-upml+k)=facp;
'(u [
C8ez(:,:,upml-k+1)=facm;
/5r[M=_ihr
C8ez(:,:,ke_tot-upml+k)=facm;
|vWx[ =`o
D1hy(:,:,upml-k+1)=facm/facp;
.6OE8w 1
D1hy(:,:,ke_tot-upml+k)=facm/facp;
zYSXG -k
D2hy(:,:,upml-k+1)=2*epsr*epsz*dt/facp;
8X*6i-j5E
D2hy(:,:,ke_tot-upml+k)=2*epsr*epsz*dt/facp;
]Wv\$JXI
D3hx(:,:,upml-k+1)=facm/facp;
X'[S Cs
D3hx(:,:,ke_tot-upml+k)=facm/facp;
P RX:*0
D4hx(:,:,upml-k+1)=1/facp/mur/muz;
XX}RbE#4
D4hx(:,:,ke_tot-upml+k)=1/facp/mur/muz;
} "y{d@
j|HOry1E &
end
v =SC*
^O[q C X
m=NX;t
% Coefficients for field components on the grid cell boundary
)Hlr 09t=]
r_boundary = ([1:upml] - 0.75)/upml;
0t*q5pAG".
for k=1:upml
HcQ{ok9u
%z1=(upml-k+1.5)*delta;
S] {K^Q),
%z2=(upml-k+0.5)*delta;
-oe&1RrdVg
%sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1));
`t ZvIy*
%ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1));
R^_/ iy
sigma(k) = sigmam * r_boundary(k)^orderbc;
$o1G xz
ki = 1;
>48zRi\N
facm=(2*epsr*epsz*ki-sigma(k)*dt);
&sWq SS
facp=(2*epsr*epsz*ki+sigma(k)*dt);
R4QXX7h!
p#J}@a
C3ey(:,:,upml-k+2)=facm/facp;
@Z K|k
C3ey(:,:,ke_tot-upml+k)=facm/facp;
t]" 3vE>
C4ey(:,:,upml-k+2)=2*epsr*epsz/facp;
le|e 4f*+
C4ey(:,:,ke_tot-upml+k)=2*epsr*epsz/facp;
-@L*i|A
C5ex(:,:,upml-k+2)=facm/facp;
i':< Ro
C5ex(:,:,ke_tot-upml+k)=facm/facp;
,1F3";`n[
C6ex(:,:,upml-k+2)=1/facp;
Z: 9" 7^+
C6ex(:,:,ke_tot-upml+k)=1/facp;
M*+_E8Lh
D5hz(:,:,upml-k+2)=facp;
b\ VY)=U
D5hz(:,:,ke_tot-upml+k)=facp;
^i#q{@g
D6hz(:,:,upml-k+2)=facm;
+l&ZN\@0X
D6hz(:,:,ke_tot-upml+k)=facm;
't^OIil
Y@^M U->+
end
{b+!0[
q^goi 1
A*~zdZ p
)0RH"#, 2L
Alp9] 0(
%zp z的正方向
/o![%&-l
C7ex(pxs:pxe-1,2:je_tot,pze:ke_tot)=C7;
c<-_Vh.:5
C8ex(pxs:pxe-1,2:je_tot,pze:ke_tot)=C8;
`;4zIBJ
C3ex(1:ie_tot,pys+1:pye-1,pze:ke_tot)=C3;
*]O[ZjyOY
C4ex(1:ie_tot,pys+1:pye-1,pze:ke_tot)=C4;
~XQN4Tv-
LYavth`@h
C5ey(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=C5;
A'6>"=ziP
C6ey(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=C6;
CQzJ_aSJ (
C7ey(2:ie_tot,pys:pye-1,pze:ke_tot)=C7;
s'fHh G6
C8ey(2:ie_tot,pys:pye-1,pze:ke_tot)=C8;
A^ t[PKM"
g;eMsoJ G
C5ez(2:ie_tot,pys+1:pye-1,pze:ke_tot)=C5;
`2d ,=.X
C6ez(2:ie_tot,pys+1:pye-1,pze:ke_tot)=C6;
) <^9`
C3ez(pxs+1:pxe-1,2:je_tot,pze:ke_tot)=C3;
o XV
C4ez(pxs+1:pxe-1,2:je_tot,pze:ke_tot)=C4;
z+NXD4
0 j4bu}@
D1hx(2:ie_tot,pys:pye-1,pze:ke_tot)=D1;
eA#J7=eC
D2hx(2:ie_tot,pys:pye-1,pze:ke_tot)=D2;
xC!, v 0&
D5hx(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=D5;
f#/v^Ql*
D6hx(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=D6;
&kR kOjuk
d5+ (@HSR
D3hy(pxs:pxe-1,2:je_tot,pze:ke_tot)=D3;
07# ~cV I
D4hy(pxs:pxe-1,2:je_tot,pze:ke_tot)=D4;
i4v7 x;m_p
D5hy(1:ie_tot,pys+1:pye-1,pze:ke_tot)=D5;
SAc}5.
D6hy(1:ie_tot,pys+1:pye-1,pze:ke_tot)=D6;
O\B_=KWDO
)5)S8~Oc
D1hz(pxs:pxe-1,1:je_tot,pze:ke_tot)=D1;
3(}HD*{E[@
D2hz(pxs:pxe-1,1:je_tot,pze:ke_tot)=D2;
K )1K ]
D3hz(1:ie_tot,pys:pye-1,pze:ke_tot)=D3;
p^7ZF UP
D4hz(1:ie_tot,pys:pye-1,pze:ke_tot)=D4;
;&^S-+
@+:S'mAQC
%zn z的负方向
LYkW2h`JQ
C7ex(pxs:pxe-1,2:je_tot,2:pzs)=C7;
" F}a nPY
C8ex(pxs:pxe-1,2:je_tot,2:pzs)=C8;
do7 [Nj
C3ex(1:ie_tot,pys+1:pye-1,2:pzs)=C3;
KDwjck"5;
C4ex(1:ie_tot,pys+1:pye-1,2:pzs)=C4;
SpjL\ p0
L&Bc-kMH
C5ey(pxs+1:pxe-1,1:je_tot,2:pzs)=C5;
q9yY%
C6ey(pxs+1:pxe-1,1:je_tot,2:pzs)=C6;
qnv9?Xh
C7ey(2:ie_tot,pys:pye-1,2:pzs)=C7;
4vW:xK
C8ey(2:ie_tot,pys:pye-1,2:pzs)=C8;
\BbemCPAm
W<u63P
C5ez(2:ie_tot,pys+1:pye-1,1:pzs-1)=C5;
b 9F=}.4
C6ez(2:ie_tot,pys+1:pye-1,1:pzs-1)=C6;
l)HF4#Bs
C3ez(pxs+1:pxe-1,2:je_tot,1:pzs-1)=C3;
q A#!3<
C4ez(pxs+1:pxe-1,2:je_tot,1:pzs-1)=C4;
!ZD[ $lt+
\ d+&&ns
D1hx(2:ie_tot,pys:pye-1,1:pzs-1)=D1;
4=>/x90y
D2hx(2:ie_tot,pys:pye-1,1:pzs-1)=D2;
6}n>Nb;L"
D5hx(pxs+1:pxe-1,1:je_tot,1:pzs-1)=D5;
=MRg
D6hx(pxs+1:pxe-1,1:je_tot,1:pzs-1)=D6;
'X"@C;q
rM< c;iQ
D3hy(pxs:pxe-1,2:je_tot,1:pzs-1)=D3;
C8DZ:3E$c
D4hy(pxs:pxe-1,2:je_tot,1:pzs-1)=D4;
Bj;Fy9[yb
D5hy(1:ie_tot,pys+1:pye-1,1:pzs-1)=D5;
$2 ~RZpS
D6hy(1:ie_tot,pys+1:pye-1,1:pzs-1)=D6;
* pyi;
-? &wD["y
D1hz(pxs:pxe-1,1:je_tot,2:pzs)=D1;
iAbtv^fn
D2hz(pxs:pxe-1,1:je_tot,2:pzs)=D2;
%#yCp2
D3hz(1:ie_tot,pys:pye-1,2:pzs)=D3;
,c Y U
D4hz(1:ie_tot,pys:pye-1,2:pzs)=D4;
S3`zB?7,
?msx
2r,K/ '
,X)0+DNsq
\ :1MM
% PEC walls
=Qp~@k=2
% C3ey(:,:,1)=-1;
[>oq~[e)?
% C3ey(:,:,kh_tot)=-1;
c*9Rz D#Zj
% C4ey(:,:,1)=0;
/ \!hW-+]W
% C4ey(:,:,kh_tot)=0;
&M*&oi (
% C5ex(:,:,1)=-1;
h~u rZXD<
% C5ex(:,:,kh_tot)=-1;
yfnqu4Cn
% C6ex(:,:,1)=0;
p Z uYmMP
% C6ex(:,:,kh_tot)=0;
|\*7J!Liv
RN]4 Is:
%figure
,/C<GFae
%set(gcf,'DoubleBuffer','on')
|Xlc2?e
OTl\^ !
%***********************************************************************
Nf%jLK~
% Begin time stepping loop
IO/2iSbW
%***********************************************************************
="P 3TP
12~zS
for n=1:nmax
;KWR/?ec
1K"``EvNB
% Update magnetic field
LwZBM#_g
bstore=bx;
T""X~+{Z@
bx(2:ie_tot,:,:)=D1hx(2:ie_tot,:,:).* bx(2:ie_tot,:,:)-...
%XMrS lSOp
D2hx(2:ie_tot,:,:).*((ez(2:ie_tot,2:jh_tot,:)-ez(2:ie_tot,1:je_tot,:))-...
< }pqj3
(ey(2:ie_tot,:,2:kh_tot)-ey(2:ie_tot,:,1:ke_tot)))./delta;
^g$k4
hx(2:ie_tot,:,:)= D3hx(2:ie_tot,:,:).*hx(2:ie_tot,:,:)+...
,i;kAy)
D4hx(2:ie_tot,:,:).*(D5hx(2:ie_tot,:,:).*bx(2:ie_tot,:,:)-...
5Q^ L"&0
D6hx(2:ie_tot,:,:).*bstore(2:ie_tot,:,:));
L/1?PM
bstore=by;
-z-58FLlO
by(:,2:je_tot,:)=D1hy(:,2:je_tot,:).* by(:,2:je_tot,:)-...
nG1 m x/w
D2hy(:,2:je_tot,:).*((ex(:,2:je_tot,2:kh_tot)-ex(:,2:je_tot,1:ke_tot))-...
&-470Z%/
(ez(2:ih_tot,2:je_tot,:)-ez(1:ie_tot,2:je_tot,:)))./delta;
'bN\bbR
hy(:,2:je_tot,:)= D3hy(:,2:je_tot,:).*hy(:,2:je_tot,:)+...
yrs![ u
D4hy(:,2:je_tot,:).*(D5hy(:,2:je_tot,:).*by(:,2:je_tot,:)-...
6I.N:)=
D6hy(:,2:je_tot,:).*bstore(:,2:je_tot,:));
@c,}\"(
bstore=bz;
7,d^?.~S
bz(:,:,2:ke_tot)=D1hz(:,:,2:ke_tot).* bz(:,:,2:ke_tot)-...
&^8 >Kd8
D2hz(:,:,2:ke_tot).*((ey(2:ih_tot,:,2:ke_tot)-ey(1:ie_tot,:,2:ke_tot))-...
sT?Qlj 'Zd
(ex(:,2:jh_tot,2:ke_tot)-ex(:,1:je_tot,2:ke_tot)))./delta;
xYtY}?!"
hz(:,:,2:ke_tot)= D3hz(:,:,2:ke_tot).*hz(:,:,2:ke_tot)+...
=4/LixsV|
D4hz(:,:,2:ke_tot).*(D5hz(:,:,2:ke_tot).*bz(:,:,2:ke_tot)-...
z T6ng#
D6hz(:,:,2:ke_tot).*bstore(:,:,2:ke_tot));
KIps {_J[<
C=t:0.:PJ
% PEC on the PML outer boundary
<fC gU&
4~53% =+
% tangential ex=0 on front-back plane
E tWpB g
ex(:,1,:)=0.0;
@f{yx\u/
ex(:,jh_tot,:)=0.0;
jX$Ti G
ZsirX~W<
% tangential ex=0 on down-up plane
o) `zb?
ex(:,:,1)=0.0;
[#fXmW>N/
ex(:,:,kh_tot)=0.0;
no?TEXp*
) **k3u t4
U#gHc:$
% tangential ey=0 on left-right plane
\5BI!<
ey(1,:,:)=0.0;
A=o p R
ey(ih_tot,:,:)=0.0;
Z=_p
1uG?R
(9CB&LZ(+E
% tangential ey=0 on down-up plane
'""qMRCm
ey(:,:,1)=0.0;
.Kv>*__-Q
ey(:,:,kh_tot)=0.0;
2^Tj7@
?g&6l0 n`
5H1SC8+B,
% tangential ez=0 on left-right plane
LS{g=3P0
ez(1,:,:)=0.0;
%qcBM~efT
ez(ih_tot,:,:)=0.0;
y/K% F,WMf
L ,!Z
=3?t%l;n
% tangential ez=0 on front-back plane
Is` S
ez(:,1,:)=0.0;
C0[Rf.*
ez(:,jh_tot,:)=0.0;
1 M7=*w,
N'+d1
% Update electric field
N{IY \/;\
jJg9M'@2!
p1store=px1;
6]Q ~c"+5
px1(:,2:je_tot,2:ke_tot)=C1ex(:,2:je_tot,2:ke_tot).* px1(:,2:je_tot,2:ke_tot)+...
D9B?9Qt2[
C2ex(:,2:je_tot,2:ke_tot).*((hz(:,2:je_tot,2:ke_tot)-hz(:,1:je_tot-1,2:ke_tot))-...
"!i7U2M'
( hy(:,2:je_tot,2:ke_tot)-hy(:,2:je_tot,1:ke_tot-1)))./delta;
J6;^: ()
p2store=px2;
pM9Hav@iWU
px2(:,2:je_tot,2:ke_tot)=C3ex(:,2:je_tot,2:ke_tot).* px2(:,2:je_tot,2:ke_tot)+...
N#Bg`:!
C4ex(:,2:je_tot,2:ke_tot).*( px1(:,2:je_tot,2:ke_tot)-...
Z~F% K~(
p1store(:,2:je_tot,2:ke_tot));
YES! ?^}
{ c<MB xk
ex(:,2:je_tot,2:ke_tot)=C5ex(:,2:je_tot,2:ke_tot).* ex(:,2:je_tot,2:ke_tot)+...
$g$~TuA w
C6ex(:,2:je_tot,2:ke_tot).*(C7ex(:,2:je_tot,2:ke_tot).* px2(:,2:je_tot,2:ke_tot)-...
f&bY=$iff
C8ex(:,2:je_tot,2:ke_tot).*p2store(:,2:je_tot,2:ke_tot));
[3>l^ Q|#
LyhLPU0^q
p1store=py1;
/7De .O~H
py1(2:ie_tot,:,2:ke_tot)=C1ey(2:ie_tot,:,2:ke_tot).* py1(2:ie_tot,:,2:ke_tot)+...
Xw!eB?A
C2ey(2:ie_tot,:,2:ke_tot).*((hx(2:ie_tot,:,2:ke_tot)-hx(2:ie_tot,:,1:ke_tot-1))-...
S3PW [R@=
( hz(2:ie_tot,:,2:ke_tot)-hz(1:ie_tot-1,:,2:ke_tot)))./delta;
;Z:z'';Lm
p2store=py2;
! s/ij' T
py2(2:ie_tot,:,2:ke_tot)=C3ey(2:ie_tot,:,2:ke_tot).* py2(2:ie_tot,:,2:ke_tot)+...
5m&{ f>]T
C4ey(2:ie_tot,:,2:ke_tot).*( py1(2:ie_tot,:,2:ke_tot)-...
Un c;@=c
p1store(2:ie_tot,:,2:ke_tot));
.J#xlOa-
41>Bm*if
ey(2:ie_tot,:,2:ke_tot)=C5ey(2:ie_tot,:,2:ke_tot).* ey(2:ie_tot,:,2:ke_tot)+...
lY[>}L*H8
C6ey(2:ie_tot,:,2:ke_tot).*(C7ey(2:ie_tot,:,2:ke_tot).* py2(2:ie_tot,:,2:ke_tot)-...
- o$S=
C8ey(2:ie_tot,:,2:ke_tot).*p2store(2:ie_tot,:,2:ke_tot));
ICo_O] Ke
y4$UPLm
p1store=pz1;
<1.].A@b*
pz1(2:ie_tot,2:je_tot,:)=C1ez(2:ie_tot,2:je_tot,:).* pz1(2:ie_tot,2:je_tot,:)+...
_ |D8~\y
C2ez(2:ie_tot,2:je_tot,:).*((hy(2:ie_tot,2:je_tot,:)-hy(1:ie_tot-1,2:je_tot,:))-...
WM}:%T-
( hx(2:ie_tot,2:je_tot,:)-hx(2:ie_tot,1:je_tot-1,:)))./delta;
9aD6mp
p2store=pz2;
%4Ylq|d
pz2(2:ie_tot,2:je_tot,:)=C3ez(2:ie_tot,2:je_tot,:).* pz2(2:ie_tot,2:je_tot,:)+...
6C9KT;6
C4ez(2:ie_tot,2:je_tot,:).*( pz1(2:ie_tot,2:je_tot,:)-...
k[R/RhHQ,
p1store(2:ie_tot,2:je_tot,:));
lb2m Wsg"
-wtavv,J
pz2(is,js,ks:ks+1)=pz2(is,js,ks:ks+1)+exp(-((n-4.5*tau/dt)^2/(tau/dt)^2));
]^Z7w`=%5
BhJqMK>'S
ez(2:ie_tot,2:je_tot,:)=C5ez(2:ie_tot,2:je_tot,:).* ez(2:ie_tot,2:je_tot,:)+...
Mc oHV]x
C6ez(2:ie_tot,2:je_tot,:).*(C7ez(2:ie_tot,2:je_tot,:).* pz2(2:ie_tot,2:je_tot,:)-...
oOy@X =cw
C8ez(2:ie_tot,2:je_tot,:).*p2store(2:ie_tot,2:je_tot,:));
l]Jk }.
?|Fu^eR%X
4NUCLr7Y
% pz2(is,js,ks:ks+1)=pz2(is,js,ks:ks+1)+(sin(pi*(n-ndelay)/(tau-ndelay)))^2;
fz31di9$
% pz2(is,js,ks:ks+1)=pz2(is,js,ks:ks+1)+J0*(n-ndelay)*exp(-((n-ndelay)^2/tau^2));
aD8cqVhM3&
%1 <No/
% pz2(is,js,ks:ks+1)=J0*(n-ndelay)*exp(-((n-ndelay)^2/tau^2));
r.** z j
% pz2(is,js,ks:ks+1)=pz2(is,js,ks:ks+1)+sin(2*pi*freq*n);
)5_G Jm&R9
"\Jq2vM
n;
X0^gj>GI|
%ex(15,15,15)
T D].*9
%***********************************************************************
L.$9ernVY
% Visualize fields
-v8Jn# f
%***********************************************************************
g3 6oE z~|
smooth(ex(:,15,15));
E&}r"rbI
surfl(ex(:,:,15));
z[b, :G
colorbar;
EC&t+"= R
pause(0.1);
`0 uKJF g
disp('ex()=');
{H#1wu^]O$
disp(ex(15,15,15));
&<R 8'
AA(n)=ex(15,15,15);
.*:SZ3v
EShc1KPqc
% timestep=int2str(n);
m=Y9s B
% tview(:,:)=squeeze(ez(ih_bc:upml+ie,jh_bc:upml+je,ks));
C_dsYuQ5R
% sview(:,:)=squeeze(ez(ih_bc:upml+ie,js,kh_bc:upml+ke));
LTG#nM0
%
@y[Zr6\z
% subplot('position',[0.15 0.57 0.7 0.35])
- y{*U1[
% imagesc(tview');
Ihw JYPLF
% caxis([-0.2 0.2]);
Y}7'OM
% colorbar;
9E)*X
% axis image; axis xy;
Ij( S"P@
% title(['E_z(i,j,k=k_s_o_u_r_c_e), time step = ',timestep]);
N5#qox$D
% xlabel('i coordinate');
,RKBGOz?f
% ylabel('j coordinate');
e] !Vxn3
%
YYr &Jc j
% subplot('position',[0.15 0.08 0.7 0.35])
PwQW5,,h0
% imagesc(sview');
ZD/> L/
% caxis([-0.2 0.2]);
9*GwW&M%1_
% colorbar;
Z^`& Z3s
% axis image; axis xy;
vnMt>]w-}
% title(['E_z(i,j=j_s_o_u_r_c_e,k), time step = ',timestep]);
7f8%WD)
% xlabel('i coordinate');
J:dF^3Y
% ylabel('k coordinate');
yBE1mA:x7:
%
\)eHf 7H
% pause(0.05)
fs&J%ku\
ji? 0;2Y
*#;8 mM
4*&x% ~*
end
oF,XSd
T=(1:1:nmax);
cR}}N F
figure(2);
Q 2cF++Q1
plot(T,AA);
'C+z
xlabel('Timestep');
D-9zg\\'`
ylabel('ex');
JiEcPii
7Gnslp?[U
clear
X5U_|XK6Y
}oigZI(1
%***********************************************************************
%E?:9. :NJ
% Fundamental constants
e &^BPzg
%***********************************************************************
Jy@cMq2
>/;\{IG Wn
cc=2.99792458e8;
FXV=D_G}
muz=4.0*pi*1.0e-7;
3H%R`ha
epsz=1.0/(cc*cc*muz);
bYQ h{q
etaz=sqrt(muz/epsz);
0){ %4
sigma_e=0.0; %主区域的电导率（不是upml中那个电导率）
@ ^a6^*X>
/* `BGNkYY
%***********************************************************************
R?qV FMQ
% Material parameters
y T`[9u ,
%***********************************************************************
il<D e]G
\=Af AO@
mur=1.0;
F')T:;,s
epsr=80;
6[$kEKOY=
freq=20000;
bxyEn'vNvQ
eta=etaz*sqrt(mur/epsr); %
Ev0GAc1
$^ (q0zR~l
c=1/sqrt(epsr*epsz*muz*mur);
+P/"bwv0
%***********************************************************************
7J~6J .m
% Grid parameters
yY_G;W k
%
7Ro7/PT (
% Each grid size variable name describes the number of sampled points
N#@xo) -H
% for a particular field component in the direction of that component.
2FD[D `n]f
% Additionally, the variable names indicate the region of the grid
)&1yt4 x6%
% for which the dimension is relevant. For example, ie_tot is the
& d\`=e
% number of sample points of Ex along the x-axis in the total
aO.'(kk8
% computational grid, and jh_bc is the number of sample points of Hy
z{d] ,M
% along the y-axis in the y-normal UPML regions.
m?'5*\(ST
%
6?Q&>V26Y
%***********************************************************************
C, n]9
QtJe){(z+
7U:,:=
%是一个三维立方体空间，60*60*60（已经包括了厚度为10的upml层）
[6V'UI6
1)/B V{n
$5GvF1
ie=40; % Size of main grid
pu=T pSZ
je=40;
)wP0U{7?v
ke=40;
\hdR &f5q
ih=ie+1;
^%~ztn 51
jh=je+1;
%\_I% yF
kh=ke+1;
rtvuAFiH
:{h,0w'd
upml=10; % Thickness of PML boundaries
[#V"a:8m}
ih_bc=upml+1;
twz
jh_bc=upml+1;
Oh6;o1UI
kh_bc=upml+1;
vY *p][$
k^Tu9}[W1
ie_tot=ie+2*upml; % Size of total computational domain
, M /-lW
je_tot=je+2*upml;
%2^C
ke_tot=ke+2*upml;
a w/ Y#
ih_tot=ie_tot+1;
l<PGUm:_
jh_tot=je_tot+1;
%=/Y~ml?
kh_tot=ke_tot+1;
[ P OcO
0(Y$x g
pxs = 11;
g,Kb9['
pys = 11;
@p Qv}%
pzs = 11;
v|VY5vN
-?e~dLu
pxe = 51;
|~8\{IcZ
pye = 51;
'97)c7E
pze = 51;
XtT;UBE
Xx:0Nt]
is=round(ih_tot/2); % Location of z-directed current source
$} TqBBe
js=round(jh_tot/2);
l"}W $3]u$
ks=round(ke_tot/2);
j:"+/5rV8
W2|*:<Jt
%***********************************************************************
Q}^ n
% Fundamental grid parameters
e~$MIHBY]
%***********************************************************************
}E]`ly<Z
.2Q`. o)
delta= 83.794539403718844;
`PSr64h:D
dt=0.9./sqrt(3.0./delta./delta)./c;
nuw90=qj!]
%dt=delta*sqrt(epsr*mur)/(2.0*cc);
|4-c/@D.~
%dt=delta*0.5/c;
&_,^OE}K_:
nmax=200;
{5. ,gb @6
-yg 9ug
%***********************************************************************
-}{\C]%
% Differentiated Gaussian pulse excitation
6Kh: m-E9
%***********************************************************************
= A DAMP
9V?MJZ@aG
rtau=50.0e-12;
6'(5pt
%tau=rtau/dt;
86/CA[Y-
tau = 20*delta/2/c;
si=/=h
ndelay=3*tau;
Z@ h<xo*r
J0=-1.0*epsz;
$Pzvv`f*
lcJ`OLG
%***********************************************************************
PdMx6 Ab
% Initialize field arrays
]SBv3 Q0D7
%***********************************************************************
hOfd<k\A
L45&O *%
ex =zeros(ie_tot,jh_tot,kh_tot);
S#jH2fRo
px1=zeros(ie_tot,jh_tot,kh_tot);
on*?O O'
px2=zeros(ie_tot,jh_tot,kh_tot);
]j*o&6cQf
dmP * 2
ey= zeros(ih_tot,je_tot,kh_tot);
BS*cG>T
py1=zeros(ih_tot,je_tot,kh_tot);
x?:WR*5w
py2=zeros(ih_tot,je_tot,kh_tot);
dLD"Cx
a&#Z=WK4
ez= zeros(ih_tot,jh_tot,ke_tot);
Br]VCp
pz1=zeros(ih_tot,jh_tot,ke_tot);
>G' NI?$
pz2=zeros(ih_tot,jh_tot,ke_tot);
H b]
PHDKx+$
hx=zeros(ih_tot,je_tot,ke_tot);
;Bc f~[ErM
hy=zeros(ie_tot,jh_tot,ke_tot);
9`dQ7z.8t
hz=zeros(ie_tot,je_tot,kh_tot);
'0H + 2
bx=zeros(ih_tot,je_tot,ke_tot);
cIl^5eE^Pq
by=zeros(ie_tot,jh_tot,ke_tot);
GK95=?f~8;
bz=zeros(ie_tot,je_tot,kh_tot);
!aa^kcEjnL
uz>s2I}B
%***********************************************************************
2s-f?WetbP
% Initialize update coefficient arrays
(d^p YPr{
%***********************************************************************
4 E 4o=Z|K
% 系数矩阵
zq4,%$y8|
C1ex=zeros(size(ex));
akm) X0!-}
C2ex=zeros(size(ex));
[+{ ot
C3ex=zeros(size(ex));
/Ia=/Jj7N
C4ex=zeros(size(ex));
dAEz hR[=
C5ex=zeros(size(ex));
J9/9k
C6ex=zeros(size(ex));
5PKv@Mk
C7ex=zeros(size(ex));
Zdh4CNEeFP
C8ex=zeros(size(ex));
5tP0dQYd
BTjF^&`
C1ey=zeros(size(ey));
K_]LK
C2ey=zeros(size(ey));
i A^w2 K
C3ey=zeros(size(ey));
~Ufcy{x#
C4ey=zeros(size(ey));
*2 MUG h
C5ey=zeros(size(ey));
Yr-,0${m
C6ey=zeros(size(ey));
l#:=zu
C7ey=zeros(size(ey));
TQ=\l*R(A
C8ey=zeros(size(ey));
-jC. dz
cJ!wZT`
C1ez=zeros(size(ez));
7X|&:V.s|
C2ez=zeros(size(ez));
:U ?P~HI
C3ez=zeros(size(ez));
?e3q0Lg3 |
C4ez=zeros(size(ez));
*}ay
C5ez=zeros(size(ez));
@=Ly#HuUM
C6ez=zeros(size(ez));
c1|o^ eZ
C7ez=zeros(size(ez));
{nryAXK
C8ez=zeros(size(ez));
m|24)%Vj;=
8Y5* 1E*
D1hx=zeros(size(hx));
Mk@ _uPm
D2hx=zeros(size(hx));
(4M# (I~cE
D3hx=zeros(size(hx));
Ma-^o<{
D4hx=zeros(size(hx));
H1 \ ~T
D5hx=zeros(size(hx));
`*}#B ks!
D6hx=zeros(size(hx));
.vG6\U7
mWmD H74
D1hy=zeros(size(hy));
k B2+ Tr
D2hy=zeros(size(hy));
!G\1$"T$
D3hy=zeros(size(hy));
0R_ZP12
D4hy=zeros(size(hy));
gQ?>%t ]
D5hy=zeros(size(hy));
7dPA>5"XD
D6hy=zeros(size(hy));
UY}lJHp0
w/YKWv{_ S
D1hz=zeros(size(hz));
*>_:E6)
D2hz=zeros(size(hz));
2Q9s?C
D3hz=zeros(size(hz));
rZJp>Q)s
D4hz=zeros(size(hz));
qf)]!w U9
D5hz=zeros(size(hz));
N:L<ySJ7
D6hz=zeros(size(hz));
F{ l,Tl"Jw
|8+<qgQ
%***********************************************************************
\hi{r@k>}
% Update coefficients, as described in Section 7.8.2.
%*|XN*i XC
%
v#-%_V>ph
% In order to simplify the update equations used in the time-stepping
@|-ydm0
% loop, we implement UPML update equations throughout the entire
=b`>ggw#
% grid. In the main grid, the electric-field update coefficients of
/^#} \<;
% Equations 7.91a-f and the correponding magnetic field update
3XL0Pm
% coefficients extracted from Equations 7.89 and 7.90 are simplified
QREIr |q'
% for the main grid (free space) and calculated below.
Yo7ctwzdH;
%
*ArzXhs[
%***********************************************************************
>#!n"i;
mXhr: e
%以下是主区域的迭代系数，即非pml参数时的系数
i"JF~6c<
C1=(2*epsz*epsr-sigma_e*dt)/(2*epsz*epsr+sigma_e*dt);
,{'~J @
C2=2*dt/(2*epsz*epsr+sigma_e*dt);
O,^,G<`
C3=1.0;
1-w1k ^e
C4=1.0;
z W+wtYV4
C5=1.0;
'?3Hy|}
C6=1/2/epsz/epsr;
z w5 EaY
C7=2*epsz*epsr;
+BzKO >
C8=2*epsz*epsr;
).v;~yE
B Am{Gb
D1=1.0;
)x( *T
D2=dt;
L?al2aopF
D3=1.0;
AqN(htGvx
D4=1.0/2.0/epsr/epsz/mur/muz;
Bc t>EWQ
D5=2.0*epsr*epsz;
%#7M ~RB[
D6=2.0*epsr*epsz;
` aw k@
O~ qB
%***********************************************************************
_9L2JN$R6
% Initialize main grid update coefficients
^gb2=gWZ<
%***********************************************************************
N66jFRA;x
% 给主计算区域系数赋值。
CZ]+B8Pl(x
C1ex(:,:,:)=C1;
s?0r\ cc|:
C2ex(:,:,:)=C2;
ryc scE4,
C3ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C3;
I9Z8]Q+2"
C4ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C4;
4jG@ #
C5ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C5;
3l4k2
C6ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C6;
kx'6FkZPIr
C7ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C7;
&X|z (vSJ$
C8ex(pxs:pxe-1,pys+1:pye-1,pzs+1:pze-1)=C8;
G4g },p!
/8Vh G|Wb
C1ey(:,:,:)=C1;
dZnq 96<:|
C2ey(:,:,:)=C2;
PicO3m
C3ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C3;
T*YdGIFO
C4ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C4;
:$P < e~z'
C5ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C5;
^~(bm$4r
C6ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C6;
z# ,?*v
C7ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C7;
W9eR3q
C8ey(pxs+1:pxe-1,pys:pye-1,pzs+1:pze-1)=C8;
} O o
ty-4yK#
C1ez(:,:,:)=C1;
Oh8 ;YE-%
C2ez(:,:,:)=C2;
E"V|Plf c
C3ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C3;
4=q\CK2 ^A
C4ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C4;
D.? KgOZ
C5ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C5;
{?5 EOp~
C6ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C6;
7 Kh+m@q.
C7ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C7;
Ma{|+\Q.Z
C8ez(pxs+1:pxe-1,pys+1:pye-1,pzs:pze-1)=C8;
?5/Sa
oO= 6Kd+T
D1hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D1;
+d#ZSNu/
D2hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D2;
=3 - G
D3hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D3;
B623B HwS
D4hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D4;
$]Fe9E?
D5hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D5;
jq}5(*k
D6hx(pxs+1:pxe-1,pys:pye-1,pzs:pze-1)=D6;
`0 .5aa
?dxhe7m
D1hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D1;
C #TS
D2hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D2;
>@rp]xx
D3hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D3;
y# x]?%m
D4hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D4;
%kV pW& ~
D5hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D5;
:+[q `
D6hy(pxs:pxe-1,pys+1:pye-1,pzs:pze-1)=D6;
> ]6Eb`v
rRsLl/d
D1hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D1;
Q >sq:R+'
D2hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D2;
+j`*?pPD(.
D3hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D3;
g VZ~OcB!W
D4hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D4;
Xq J@NgsY
D5hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D5;
Y9PG
D6hz(pxs:pxe-1,pys:pye-1,pzs+1:pze-1)=D6;
O"Xjv `j:
RQe#X6'h
rmax=exp(-16); % R(0) desired reflection error, designated as R(0) in Equation 7.62
Cu/w><h)
8.9S91]=
orderbc=4; % m order of the polynomial grading, designated as m in Equation 7.60a,b
C9bf1ddCW&
.^Ek1fi.
%以下是给pml层的系数赋值，我完全是用的talflove书上的公式，没有用原来代码中的公式
V$ : v~*Y9
% x-varying material properties
rJ<v1Yb
delbc=upml*delta; % d
0eUsvzz 15
sigmam=-log(rmax)*(orderbc+1.0)/(2.0*eta*delbc);
h ?$4\^/
%sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0));
YpNTq_S1,
kmax=1;
-ud!j
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc;
$e<3z6
~~yo& ]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
lT$A;7[
% xp xn
\&W~nYXq"
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Y|1kE;
#]:nQ (
% Coefficients for field components in the center of the grid cell
F;MFw2G
pLk?<y
% x1=(upml-i+1)*delta;x1;
(?J&A r0
% x2=(upml-i)*delta;x2;
l&T;G 9z
r_center = ([1:upml] - 0.25)/upml;
iLS' 47
tWc!!Hf2j
%按照场分量在网格中的位置，我每一个方向有两个循环，分别对应分量在网格中间和在网格边上
:r#FI".q x
( c[|k
for i=1:upml
gy* N)iv%
%sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1));
L TO1LAac
%ki=1+kfactor*(x1^(orderbc+1)-x2^(orderbc+1));
%X#Wc:b
sigma(i) = sigmam * r_center(i)^orderbc;
X0 %k` 3
ki = 1;
9nd'"$
facm=(2*epsr*epsz*ki-sigma(i)*dt);
~BZ A_w"`1
facp=(2*epsr*epsz*ki+sigma(i)*dt);
Ng;E]2 "
%ie_tot-upml+i;
]2Lwd@
%upml-i+1;
r[~K m5
!@*Ac$J>$
C7ex(upml-i+1,:,:)=facp;
j_ :4_zdBy
C7ex(ie_tot-upml+i,:,:)=facp;
T.&^1q WWA
C8ex(upml-i+1,:,:)=facm;
c()F%e:n
C8ex(ie_tot-upml+i,:,:)=facm;
>gVR 5o
D1hz(upml-i+1,:,:)=facm/facp;
ot ,<iE#za
D1hz(ie_tot-upml+i,:,:)=facm/facp;
x2K.5q>
D2hz(upml-i+1,:,:)=2.0*epsr*epsz*dt/facp;
>B~p[wh0
D2hz(ie_tot-upml+i,:,:)=2.0*epsr*epsz*dt/facp;
iyj&O"
D3hy(upml-i+1,:,:)=facm/facp;
gbKms ; :
D3hy(ie_tot-upml+i,:,:)=facm/facp;
h^[K= J
D4hy(upml-i+1,:,:)=1.0/facp/mur/muz;
Zx`hutCv
D4hy(ie_tot-upml+i,:,:)=1.0/facp/mur/muz;
<4( rY9
Ym!Ia& n
end
8HTV"60hTs
oYqlN6n,=6
% Coefficients for field components on the grid cell boundary
JY %c<
i<&2Ffvq
r_boundary = ([1:upml] - 0.75)/upml;
<$7*yV
_=, [5 "
zFv>'1$
for i=1:upml
x ~Pv
% x1=(upml-i+1.5)*delta;
YFsEuaV
% x2=(upml-i+0.5)*delta;
=DF7l<&km
% sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1));
L! Q&?xP
% ki=1.0+kfactor*(x1^(orderbc+1)-x2^(orderbc+1));
}HXNhv-K
sigma(i) = sigmam * r_boundary(i)^orderbc;
}{ 9E~"_[
ki = 1;
4 d6F4G4U
facm=(2.0*epsr*epsz*ki-sigma(i)*dt);
qW7S<ouh
facp=(2.0*epsr*epsz*ki+sigma(i)*dt);
v\f 41M7D
t ZF G`'/
C3ez(upml-i+2,:,:)=facm/facp;
HfmTk5|/
C3ez(ie_tot-upml+i,:,:)=facm/facp;
-*tP_=- Dg
C4ez(upml-i+2,:,:)=2*epsr*epsz/facp;
M[Ls:\1a
C4ez(ie_tot-upml+i,:,:)=2*epsr*epsz/facp;
RCgs3JIE+2
C5ey(upml-i+2,:,:)=facm/facp;
{) jQbAr(G
C5ey(ie_tot-upml+i,:,:)=facm/facp;
pspV ~9,
C6ey(upml-i+2,:,:)=1.0/facp;
RQ|!?\a=
C6ey(ie_tot-upml+i,:,:)=1.0/facp;
w{Dk,9 >w)
D5hx(upml-i+2,:,:)=facp;
HH[ ?LKd<
D5hx(ie_tot-upml+i,:,:)=facp;
^$yr-p%-
D6hx(upml-i+2,:,:)=facm;
I_eYTy-a`1
D6hx(ie_tot-upml+i,:,:)=facm;
##yi^;3Y
:IS]|3wD
end
7eh}Je8
6C) G
% 以下可能大家看了有点迷惑，是在xp(x的正方向的pml层）中除了和sigmax有关的系数之外，
q=|>r n_
% 其他不含sigmax的系数赋值。
| F: ?
%xp
#9p{Y}2#
C3ex(pxe:ie_tot,pys+1:pye-1,2:ke_tot)=C3;
w,JB`jS)/
C4ex(pxe:ie_tot,pys+1:pye-1,2:ke_tot)=C4;
rX fQ_
C5ex(pxe:ie_tot,2:je_tot,pzs+1:pze-1)=C5;
O2A Z|[*I
C6ex(pxe:ie_tot,2:je_tot,pzs+1:pze-1)=C6;
HtS:'~DYo
n_?<q{GW
C3ey(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=C3;
qb "H&)aHw
C4ey(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=C4;
A^o
C7ey(pxe:ie_tot,pys:pye-1,2:ke_tot)=C7;
I[&z#foN=w
C8ey(pxe:ie_tot,pys:pye-1,2:ke_tot)=C8;
Vk>aU3\c
iVnrv`k,
C5ez(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=C5;
.qF@ }dO
C6ez(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=C6;
3Jk; +<
C7ez(pxe:ie_tot,2:je_tot,pzs:pze-1)=C7;
30[?XVI&
C8ez(pxe:ie_tot,2:je_tot,pzs:pze-1)=C8;
8[}MXMRdb
W^al`lg+y
D1hx(pxe:ie_tot,pys:pye-1,1:ke_tot)=D1;
,?i#NN5p
D2hx(pxe:ie_tot,pys:pye-1,1:ke_tot)=D2;
{w{|y[[d~
D3hx(pxe:ie_tot,1:je_tot,pzs:pze-1)=D3;
hC5iv J
D4hx(pxe:ie_tot,1:je_tot,pzs:pze-1)=D4;
Z.VVY\
f,PFvT$5e
D1hy(pxe:ie_tot,2:je_tot,pzs:pze-1)=D1;
q6/ o.j
D2hy(pxe:ie_tot,2:je_tot,pzs:pze-1)=D2;
oREZ^pE@
D5hy(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=D5;
R-hqaEB
D6hy(pxe:ie_tot,pys+1:pye-1,1:ke_tot)=D6;
G4AX8@;U
[Y JP
D3hz(pxe:ie_tot,pys:pye-1,2:ke_tot)=D3;
/ko NcpJ
D4hz(pxe:ie_tot,pys:pye-1,2:ke_tot)=D4;
j s7J#b7
D5hz(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=D5;
1<fEz
D6hz(pxe:ie_tot,1:je_tot,pzs+1:pze-1)=D6;
hIPDJ1 a
<[[DS%(M^
% 以下可能大家看了有点迷惑，是在xn(x的负方向的pml层）中除了和sigmax有关的系数之外，
j3z&0sc2(0
% 其他不含sigmax的系数赋值。
ZK_IK)g
%xn
E%j OJA
C3ex(1:pxs-1,pys+1:pye-1,2:ke_tot)=C3;
R}Z"Y xx
C4ex(1:pxs-1,pys+1:pye-1,2:ke_tot)=C4;
r"J1C
C5ex(1:pxs-1,2:je_tot,pzs+1:pze-1)=C5;
_0^<) OSY
C6ex(1:pxs-1,2:je_tot,pzs+1:pze-1)=C6;
[4( TG<I
sDWX} NV
C3ey(2:pxs,1:je_tot,pzs+1:pze-1)=C3;
~eqX<0hf@
C4ey(2:pxs,1:je_tot,pzs+1:pze-1)=C4;
z26zl[.
C7ey(2:pxs,pys:pye-1,2:ke_tot)=C7;
--.: eFE/
C8ey(2:pxs,pys:pye-1,2:ke_tot)=C8;
>iWl-hI-
jw# 'f% *
C5ez(2:pxs,pys+1:pye-1,1:ke_tot)=C5;
S 8h/AW6l
C6ez(2:pxs,pys+1:pye-1,1:ke_tot)=C6;
$eRxCX?b2
C7ez(2:pxs,2:je_tot,pzs:pze-1)=C7;
Q)H Vh[4
C8ez(2:pxs,2:je_tot,pzs:pze-1)=C8;
3}n=o d=
u`K+0^)T`
D1hx(2:pxs,pys:pye-1,1:ke_tot)=D1;
w.J2pvyB
D2hx(2:pxs,pys:pye-1,1:ke_tot)=D2;
4d 9i AN
D3hx(2:pxs,1:je_tot,pzs:pze-1)=D3;
JT l 37j
D4hx(2:pxs,1:je_tot,pzs:pze-1)=D4;
K'n^, t
Qe]@` Vg
D1hy(1:pxs-1,2:je_tot,pzs:pze-1)=D1;
N$?mul a
D2hy(1:pxs-1,2:je_tot,pzs:pze-1)=D2;
t'0r4&\
D5hy(1:pxs-1,pys+1:pye-1,1:ke_tot)=D5;
In=3#u ,M
D6hy(1:pxs-1,pys+1:pye-1,1:ke_tot)=D6;
QoI@/ jLj
:]e:-JbT4z
D3hz(1:pxs-1,pys:pye-1,2:ke_tot)=D3;
8R8J./i.K
D4hz(1:pxs-1,pys:pye-1,2:ke_tot)=D4;
xzIs,i} U
D5hz(1:pxs-1,1:je_tot,pzs+1:pze-1)=D5;
R7Hn8;..
D6hz(1:pxs-1,1:je_tot,pzs+1:pze-1)=D6;
A 3yVT8
~"br fjd|
% PEC walls
D OPOzh
% C3ez(1,:,:)=-1.0;
LK/gG6n5M0
% C3ez(ih_tot,:,:)=-1.0;
rb&^ ei9B
% C4ez(1,:,:)=0.0;
<k/'mBDk
% C4ez(ih_tot,:,:)=0.0;
\L6U}ZQ2V
% C5ey(1,:,:)=-1.0;
kB"S h_:m
% C5ey(ih_tot,:,:)=-1.0;
# `v`e"
% C6ey(1,:,:)=0.0;
L=4?vs
% C6ey(ih_tot,:,:)=0.0;
Og"50 -
d *8 c ,x
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1wqC oDgkp
% y-varying material properties
+JBhw4et;.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
)^g}'V=vIr
delbc=upml*delta;
d<(1^Rt o
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1.0)/(2.0*delbc);
c3i|q@ k
% sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0));
k`2 K?9\
kmax=1.0;
M _$pqVm
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc;
$9Y2\'w<h6
+;U}SR<
% Coefficients for field components in the center of the grid cell
7D om[f
r_center = ([1:upml] - 0.25)/upml;
g|e^}voRM
+6uu n
for j=1:upml
DQH _@-q
Yca9G?^\v
J'^BxN&
% y1=(upml-j+1)*delta;
n4(w?,w }
% y2=(upml-j)*delta;
S1E2E 3
% sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1));
G:A ~nv9
% ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1));
09%q/-$
sigma(j) = sigmam * r_center(j)^orderbc;
9j$ OU@N 8
ki = 1;
8p> %}LX/
facm=(2*epsr*epsz*ki-sigma(j)*dt);
%w6> 3#e
facp=(2*epsr*epsz*ki+sigma(j)*dt);
-:cS}I
c*MjBAq
C7ey(:,upml-j+1,:)=facp;
v?n`kw
C7ey(:,je_tot-upml+j,:)=facp;
)Qb1$%r.
C8ey(:,upml-j+1,:)=facm;
ZEUd?"gaR
C8ey(:,je_tot-upml+j,:)=facm;
hFj. d]S
D1hx(:,upml-j+1,:)=facm/facp;
]Fl +^aLS
D1hx(:,je_tot-upml+j,:)=facm/facp;
fZxZ):7i
D2hx(:,upml-j+1,:)=2*epsr*epsz*dt/facp;
4 lJ@qhV
D2hx(:,je_tot-upml+j,:)=2*epsr*epsz*dt/facp;
?2_ u/ x
D3hz(:,upml-j+1,:)=facm/facp;
!0 *=z~
D3hz(:,je_tot-upml+j,:)=facm/facp;
mcS/-DaN?
D4hz(:,upml-j+1,:)=1/facp/mur/muz;
T?^AllUZQR
D4hz(:,je_tot-upml+j,:)=1/facp/mur/muz;
p5c'gziR
end
"`C|; \w
VlXIM,
% Coefficients for field components on the grid cell boundary
z=BX-)
./J.OU1
r_boundary = ([1:upml] - 0.75)/upml;
xgsD<3
N, ;'oL +
for j=1:upml
G\Toi98d*
%y1=(upml-j+1.5)*delta;
v#YO3nD
%y2=(upml-j+0.5)*delta;
u%VO'}Gz
%sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1));
)0fQ(3oOg
%ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1));
`S{< $:D
sigma(j) = sigmam * r_boundary(j)^orderbc;
0MrtJNF]_O
ki = 1;
:[|`&_D9J
facm=(2*epsr*epsz*ki-sigma(j)*dt);
p^ 9QYR
facp=(2*epsr*epsz*ki+sigma(j)*dt);
zUIh8cAoE
REnRpp$
C3ex(:,upml-j+2,:)=facm/facp;
_6^ vxlF
C3ex(:,je_tot-upml+j,:)=facm/facp;
qC.jXU?rO
C4ex(:,upml-j+2,:)=2*epsr*epsz/facp;
0ydAdgD
C4ex(:,je_tot-upml+j,:)=2*epsr*epsz/facp;
eey <:n/Z
C5ez(:,upml-j+2,:)=facm/facp;
?ti7iBz?
C5ez(:,je_tot-upml+j,:)=facm/facp;
8y~ Jn~t
C6ez(:,upml-j+2,:)=1/facp;
d7$H})[^
C6ez(:,je_tot-upml+j,:)=1/facp;
m$pXe<
D5hy(:,upml-j+2,:)=facp;
Qj[4gN ?}=
D5hy(:,je_tot-upml+j,:)=facp;
4# ;rv$ {
D6hy(:,upml-j+2,:)=facm;
`H+ 7Hj
D6hy(:,je_tot-upml+j,:)=facm;
@Eqc&v!O
/PQg>Pa85
end
h_* =_ 2|}
!*?&V3!
%yp y的正方向
Xdq2 .:\
C5ex(1:ie_tot,pye:je_tot,pzs+1:pze-1)=C5;
Nz*qz"T
C6ex(1:ie_tot,pye:je_tot,pzs+1:pze-1)=C6;
;=*b:y Y
C7ex(pxs:pxe-1,pye:je_tot,2:ke_tot)=C7;
Y@M=6G
C8ex(pxs:pxe-1,pye:je_tot,2:ke_tot)=C8;
6:Z qS~-
Rj+}L ~"
C3ey(2:ie_tot,pye:je_tot,pzs+1:pze-1)=C3;
5}e-\:J >B
C4ey(2:ie_tot,pye:je_tot,pzs+1:pze-1)=C4;
.y+>-[j?B
C5ey(pxs+1:pxe-1,pye:je_tot,2:ke_tot)=C5;
~9h6"0K!
C6ey(pxs+1:pxe-1,pye:je_tot,2:ke_tot)=C6;
A<y3Tc?Q
8T$:^HW
C3ez(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=C3;
V:Q fI
C4ez(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=C4;
JWlH(-U4|
C7ez(2:ie_tot,pye:je_tot,pzs:pze-1)=C7;
D : 8-f3
C8ez(2:ie_tot,pye:je_tot,pzs:pze-1)=C8;
pWbzBgM?nU
ZV_mP'1*
D3hx(2:ie_tot,pye:je_tot,pzs:pze-1)=D3;
xm/v :hl=
D4hx(2:ie_tot,pye:je_tot,pzs:pze-1)=D4;
pb_mW;JVu
D5hx(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=D5;
"MM7qV
D6hx(pxs+1:pxe-1,pye:je_tot,1:ke_tot)=D6;
@bfaAh~
dH#S69>
D1hy(1:ie_tot,pye:je_tot,pzs:pze-1)=D1;
- NiFO
D2hy(1:ie_tot,pye:je_tot,pzs:pze-1)=D2;
`: i|y
D3hy(pxs:pxe-1,pye:je_tot,1:ke_tot)=D3;
nH NMoA
D4hy(pxs:pxe-1,pye:je_tot,1:ke_tot)=D4;
X O J/$y
mr E ^D|
D1hz(pxs:pxe-1,pye:je_tot,2:ke_tot)=D1;
Qn[4 &nUD
D2hz(pxs:pxe-1,pye:je_tot,2:ke_tot)=D2;
SO]x^+[
D5hz(1:ie_tot,pye:je_tot,pzs+1:pze-1)=D5;
2Z7smDJ
D6hz(1:ie_tot,pye:je_tot,pzs+1:pze-1)=D6;
s-k~_C>Fw
7{v0K"E{
%yn y的负方向
dm)V \?b
C5ex(1:ie_tot,2:pys,pzs+1:pze-1)=C5;
k[A=:H1"
C6ex(1:ie_tot,2:pys,pzs+1:pze-1)=C6;
C.%iQ x`
C7ex(pxs:pxe-1,2:pys,2:ke_tot)=C7;
%q2dpzNW
C8ex(pxs:pxe-1,2:pys,2:ke_tot)=C8;
;# {XNq<1
vb{&T<
C3ey(2:ie_tot,1:pys-1,pzs+1:pze-1)=C3;
]$y "|xqR
C4ey(2:ie_tot,1:pys-1,pzs+1:pze-1)=C4;
\dbpC Z
C5ey(pxs+1:pxe-1,1:pys-1,2:ke_tot)=C5;
= fuF]yL%
C6ey(pxs+1:pxe-1,1:pys-1,2:ke_tot)=C6;
]/JE#
XMa(XOnX
C3ez(pxs+1:pxe-1,2:pys,1:ke_tot)=C3;
o PR^Z pt
C4ez(pxs+1:pxe-1,2:pys,1:ke_tot)=C4;
1PjSa4
C7ez(2:ie_tot,2:pys,pzs:pze-1)=C7;
_o' jy^
C8ez(2:ie_tot,2:pys,pzs:pze-1)=C8;
W{1=O)w
Q(oWaG
D3hx(2:ie_tot,1:pys-1,pzs:pze-1)=D3;
W\N-~9UA
D4hx(2:ie_tot,1:pys-1,pzs:pze-1)=D4;
D@>P%k$$s>
D5hx(pxs+1:pxe-1,1:pys-1,1:ke_tot)=D5;
D'|#5>G
D6hx(pxs+1:pxe-1,1:pys-1,1:ke_tot)=D6;
? u'JhZ
cV&(L]k >`
D1hy(1:ie_tot,2:pys,pzs:pze-1)=D1;
F{b ET
D2hy(1:ie_tot,2:pys,pzs:pze-1)=D2;
K&D -1u
D3hy(pxs:pxe-1,2:pys,1:ke_tot)=D3;
#9#N+
D4hy(pxs:pxe-1,2:pys,1:ke_tot)=D4;
[~f%z(vI
#++MoW}'g
D1hz(pxs:pxe-1,1:pys-1,2:ke_tot)=D1;
Y\dK- M{$
D2hz(pxs:pxe-1,1:pys-1,2:ke_tot)=D2;
q fadsVp
D5hz(1:ie_tot,1:pys-1,pzs+1:pze-1)=D5;
3ZC to[Y
D6hz(1:ie_tot,1:pys-1,pzs+1:pze-1)=D6;
x>&1;g2r
P ,xa yy
% PEC walls
IDdhBdQ
% C3ex(:,1,:)=-1;
Ds&)0Iwf
% C3ex(:,jh_tot,:)=-1;
.7+_ubj&,
% C4ex(:,1,:)=0;
Vy-H3BR
% C4ex(:,jh_tot,:)=0;
?n? Ep [D
% C5ez(:,1,:)=-1;
; vQ7[Pv.j
% C5ez(:,jh_tot,:)=-1;
W{ =>c/
% C6ez(:,1,:)=0;
xfos>|0N
% C6ez(:,jh_tot,:)=0;
Vnv<]D zC
,Y &Q,
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&nZ=w# _
% z-varying material properties
1a/@eqF''
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
75Jh(hd(
2X]2;W)S;
delbc=upml*delta;
`r+e! o
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1)/(2*delbc);
goIn7ei92
%sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1));
lv&<kYWY
kmax=1;
v;?t=}NwF
kfactor=(kmax-1)/delta/(orderbc+1)/delbc^orderbc;
Il~ph9{JH
WTY{sq\' o
% Coefficients for field components in the center of the grid cell
N%_-5Q)so
6.KR(V
r_center = ([1:upml] - 0.25)/upml;
9);a 0}*5
for k=1:upml
TcO@q ]+S
7 EQ |p
%z1=(upml-k+1)*delta;
Z;7f D
%z2=(upml-k)*delta;
ToDNBt.u{+
%sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1));
ra_`NsKF}
%ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1));
XZ Z Ml
sigma(k) = sigmam * r_center(k)^orderbc;
:* A6Ba
ki = 1;
lJ R",_
facm=(2*epsr*epsz*ki-sigma(k)*dt);
A}H)ojG'v
facp=(2*epsr*epsz*ki+sigma(k)*dt);
/_ o1b_1 U
Uu }ai."iB
C7ez(:,:,upml-k+1)=facp;
&R\ .^3
C7ez(:,:,ke_tot-upml+k)=facp;
wH{lp/
C8ez(:,:,upml-k+1)=facm;
i?4vdL8M
C8ez(:,:,ke_tot-upml+k)=facm;
9t7_7{Q+;
D1hy(:,:,upml-k+1)=facm/facp;
.~ZNlI {K
D1hy(:,:,ke_tot-upml+k)=facm/facp;
-[0)n{AVvU
D2hy(:,:,upml-k+1)=2*epsr*epsz*dt/facp;
]*[S# Jk
D2hy(:,:,ke_tot-upml+k)=2*epsr*epsz*dt/facp;
)q &uvfQ1(
D3hx(:,:,upml-k+1)=facm/facp;
4K[U *-\"
D3hx(:,:,ke_tot-upml+k)=facm/facp;
a mlE5GK;
D4hx(:,:,upml-k+1)=1/facp/mur/muz;
fCO!M1 t
D4hx(:,:,ke_tot-upml+k)=1/facp/mur/muz;
Ks8S^77
&qM SJ
end
y5|`B(
M2my>
WH/r$.&
% Coefficients for field components on the grid cell boundary
-UUP hGC
r_boundary = ([1:upml] - 0.75)/upml;
:E@"4O?<Y)
for k=1:upml
0qw,R4YK
%z1=(upml-k+1.5)*delta;
C1)TEkc"C
%z2=(upml-k+0.5)*delta;
k2 k/v[60
%sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1));
)Qp?N<&'
%ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1));
p&:R SO
sigma(k) = sigmam * r_boundary(k)^orderbc;
ox H S7b
ki = 1;
,F6i5128{
facm=(2*epsr*epsz*ki-sigma(k)*dt);
c5R58#XK=
facp=(2*epsr*epsz*ki+sigma(k)*dt);
{xr4CDP
Le|Ho^h,Y
C3ey(:,:,upml-k+2)=facm/facp;
w KXK c\r
C3ey(:,:,ke_tot-upml+k)=facm/facp;
H.|FEV@
C4ey(:,:,upml-k+2)=2*epsr*epsz/facp;
Z fL\3Mn
C4ey(:,:,ke_tot-upml+k)=2*epsr*epsz/facp;
3MNo&0M9
C5ex(:,:,upml-k+2)=facm/facp;
Co[ rhs
C5ex(:,:,ke_tot-upml+k)=facm/facp;
2@uo2]o)
C6ex(:,:,upml-k+2)=1/facp;
B~caHG1b
C6ex(:,:,ke_tot-upml+k)=1/facp;
>[O @u4
D5hz(:,:,upml-k+2)=facp;
sW3-JA]
D5hz(:,:,ke_tot-upml+k)=facp;
NU I|4 X
D6hz(:,:,upml-k+2)=facm;
|v[{k>7f
D6hz(:,:,ke_tot-upml+k)=facm;
q`"gT;3S
?P0$n 7,
end
#f\U3p
7evE;KL
**fJAANc
h1FM)n[E7
D0lgKQ
%zp z的正方向
M=`F $
C7ex(pxs:pxe-1,2:je_tot,pze:ke_tot)=C7;
EAj2uV
C8ex(pxs:pxe-1,2:je_tot,pze:ke_tot)=C8;
oizD:|
C3ex(1:ie_tot,pys+1:pye-1,pze:ke_tot)=C3;
7MOjZD4?
C4ex(1:ie_tot,pys+1:pye-1,pze:ke_tot)=C4;
p sgXJe$
>9uDY+70I3
C5ey(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=C5;
fC&Egy
C6ey(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=C6;
6b6}HO
C7ey(2:ie_tot,pys:pye-1,pze:ke_tot)=C7;
-P(q<T2MV'
C8ey(2:ie_tot,pys:pye-1,pze:ke_tot)=C8;
3oE *86
T&w3IKb|}
C5ez(2:ie_tot,pys+1:pye-1,pze:ke_tot)=C5;
[0Z r z+q
C6ez(2:ie_tot,pys+1:pye-1,pze:ke_tot)=C6;
H2E!A2\m
C3ez(pxs+1:pxe-1,2:je_tot,pze:ke_tot)=C3;
|XLx6E2F
C4ez(pxs+1:pxe-1,2:je_tot,pze:ke_tot)=C4;
2}b1PMpZG
-81usu&NH
D1hx(2:ie_tot,pys:pye-1,pze:ke_tot)=D1;
A^bg*t,
D2hx(2:ie_tot,pys:pye-1,pze:ke_tot)=D2;
Z[ZqQ` 7N
D5hx(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=D5;
8`U5/!6fu
D6hx(pxs+1:pxe-1,1:je_tot,pze:ke_tot)=D6;
~BD Vm Qa
&r/a\t,8n
D3hy(pxs:pxe-1,2:je_tot,pze:ke_tot)=D3;
lRZt)) 3
D4hy(pxs:pxe-1,2:je_tot,pze:ke_tot)=D4;
#- f 7 hg*
D5hy(1:ie_tot,pys+1:pye-1,pze:ke_tot)=D5;
jF_K *:gQ
D6hy(1:ie_tot,pys+1:pye-1,pze:ke_tot)=D6;
jxZ R%D
azS"*#r6}
D1hz(pxs:pxe-1,1:je_tot,pze:ke_tot)=D1;
)0yY|E\
D2hz(pxs:pxe-1,1:je_tot,pze:ke_tot)=D2;
,*@m<{DX)
D3hz(1:ie_tot,pys:pye-1,pze:ke_tot)=D3;
7t0\}e
D4hz(1:ie_tot,pys:pye-1,pze:ke_tot)=D4;
A_CEpG]
CP]BSyim'
%zn z的负方向
t /EB y"N#
C7ex(pxs:pxe-1,2:je_tot,2:pzs)=C7;
-KCm#!
C8ex(pxs:pxe-1,2:je_tot,2:pzs)=C8;
7'J}|m{7
C3ex(1:ie_tot,pys+1:pye-1,2:pzs)=C3;
q, PB; TT
C4ex(1:ie_tot,pys+1:pye-1,2:pzs)=C4;
_u dH(NC
) e;)9~
C5ey(pxs+1:pxe-1,1:je_tot,2:pzs)=C5;
tceQn ^| <
C6ey(pxs+1:pxe-1,1:je_tot,2:pzs)=C6;
]lXTIej`dy
C7ey(2:ie_tot,pys:pye-1,2:pzs)=C7;
?h<I:[oZ
C8ey(2:ie_tot,pys:pye-1,2:pzs)=C8;
UyEyk$6SU
8ooj)
C5ez(2:ie_tot,pys+1:pye-1,1:pzs-1)=C5;
UF|v=|*{#
C6ez(2:ie_tot,pys+1:pye-1,1:pzs-1)=C6;
$s)G0/~W
C3ez(pxs+1:pxe-1,2:je_tot,1:pzs-1)=C3;
XB50>??NE
C4ez(pxs+1:pxe-1,2:je_tot,1:pzs-1)=C4;
vp[~%~1(
]uWx<aD B
D1hx(2:ie_tot,pys:pye-1,1:pzs-1)=D1;
O5{ >k
D2hx(2:ie_tot,pys:pye-1,1:pzs-1)=D2;
:G9.}V rU
D5hx(pxs+1:pxe-1,1:je_tot,1:pzs-1)=D5;
O)Nj'Hcu
D6hx(pxs+1:pxe-1,1:je_tot,1:pzs-1)=D6;
\3O#H
(SkI9[1\@3
D3hy(pxs:pxe-1,2:je_tot,1:pzs-1)=D3;
.B6$U>>NS^
D4hy(pxs:pxe-1,2:je_tot,1:pzs-1)=D4;
V\r5
D5hy(1:ie_tot,pys+1:pye-1,1:pzs-1)=D5;
z"Gk K T
D6hy(1:ie_tot,pys+1:pye-1,1:pzs-1)=D6;
zY bSv~)
4u"V52
D1hz(pxs:pxe-1,1:je_tot,2:pzs)=D1;
#T99p+O
D2hz(pxs:pxe-1,1:je_tot,2:pzs)=D2;
y 4C_G?
D3hz(1:ie_tot,pys:pye-1,2:pzs)=D3;
=zK7`5
D4hz(1:ie_tot,pys:pye-1,2:pzs)=D4;
.%M=dL>
u/h Ff3
&b i Bm
u;F++ $=
\T/~" w
% PEC walls
DSM,dO'
% C3ey(:,:,1)=-1;
N|h`}*:x=
% C3ey(:,:,kh_tot)=-1;
o/CSIvz1
% C4ey(:,:,1)=0;
gk >A
% C4ey(:,:,kh_tot)=0;
|F iL1_
% C5ex(:,:,1)=-1;
J&@[=zBYw
% C5ex(:,:,kh_tot)=-1;
/=FQ {tLr
% C6ex(:,:,1)=0;
7M<7^)9
% C6ex(:,:,kh_tot)=0;
A%"mySW
xD8x1-
%figure
)^|zuYz N
%set(gcf,'DoubleBuffer','on')
CD +,&id
I8Y[d$z
%***********************************************************************
I o|NL6[
% Begin time stepping loop
.o]vjNrd/
%***********************************************************************
y LW iY~Fd
s~6?p% 2]
for n=1:nmax
;E,%\<
V#ZF0a]
% Update magnetic field
eg3zp gZ
bstore=bx;
`2o/W]SSk
bx(2:ie_tot,:,:)=D1hx(2:ie_tot,:,:).* bx(2:ie_tot,:,:)-...
L @ _IGH
D2hx(2:ie_tot,:,:).*((ez(2:ie_tot,2:jh_tot,:)-ez(2:ie_tot,1:je_tot,:))-...
z%} ^9
(ey(2:ie_tot,:,2:kh_tot)-ey(2:ie_tot,:,1:ke_tot)))./delta;
ullq}}
hx(2:ie_tot,:,:)= D3hx(2:ie_tot,:,:).*hx(2:ie_tot,:,:)+...
v< xe(dC
D4hx(2:ie_tot,:,:).*(D5hx(2:ie_tot,:,:).*bx(2:ie_tot,:,:)-...
}e9E+2}Z\
D6hx(2:ie_tot,:,:).*bstore(2:ie_tot,:,:));
Y@c! \0e$
bstore=by;
j\P47q'v#
by(:,2:je_tot,:)=D1hy(:,2:je_tot,:).* by(:,2:je_tot,:)-...
3G~ T_J &
D2hy(:,2:je_tot,:).*((ex(:,2:je_tot,2:kh_tot)-ex(:,2:je_tot,1:ke_tot))-...
@-NdgM<
(ez(2:ih_tot,2:je_tot,:)-ez(1:ie_tot,2:je_tot,:)))./delta;
|4\.",Bg
hy(:,2:je_tot,:)= D3hy(:,2:je_tot,:).*hy(:,2:je_tot,:)+...
N*|Mfpf
D4hy(:,2:je_tot,:).*(D5hy(:,2:je_tot,:).*by(:,2:je_tot,:)-...
^}ngb Dn
D6hy(:,2:je_tot,:).*bstore(:,2:je_tot,:));
smoz5~
bstore=bz;
%i]q} M
bz(:,:,2:ke_tot)=D1hz(:,:,2:ke_tot).* bz(:,:,2:ke_tot)-...
$"!"=v%B
D2hz(:,:,2:ke_tot).*((ey(2:ih_tot,:,2:ke_tot)-ey(1:ie_tot,:,2:ke_tot))-...
HH&`f3
(ex(:,2:jh_tot,2:ke_tot)-ex(:,1:je_tot,2:ke_tot)))./delta;
[@eNb^ R
hz(:,:,2:ke_tot)= D3hz(:,:,2:ke_tot).*hz(:,:,2:ke_tot)+...
R.Ao%VT
D4hz(:,:,2:ke_tot).*(D5hz(:,:,2:ke_tot).*bz(:,:,2:ke_tot)-...
KA0Ui,q3
D6hz(:,:,2:ke_tot).*bstore(:,:,2:ke_tot));
1Yo9Wf;vP
$-|`#|CBd
% PEC on the PML outer boundary
-|~6Zf"
p,* rVz[Y
% tangential ex=0 on front-back plane
_SJ#k|vcq
ex(:,1,:)=0.0;
1ZJP.T`
ex(:,jh_tot,:)=0.0;
J)6RXt*!
5s ao+dZ"|
% tangential ex=0 on down-up plane
CSN]k )\N(
ex(:,:,1)=0.0;
[;7&E{,C
ex(:,:,kh_tot)=0.0;
Egi<m
a-MDZT<xA+
HC@E&t
% tangential ey=0 on left-right plane
63#Sf$p{v
ey(1,:,:)=0.0;
Q0Y0Zt,h
ey(ih_tot,:,:)=0.0;
l5b? 'L
S#/[>C b
w`bojM@e1
% tangential ey=0 on down-up plane
z:u e]7(.
ey(:,:,1)=0.0;
2 1O!CvX
ey(:,:,kh_tot)=0.0;
<Qe30_< K
+ t({:>E
7{ (t_N >
% tangential ez=0 on left-right plane
,P3 nZ
ez(1,:,:)=0.0;
|bk. gh
ez(ih_tot,:,:)=0.0;
^8,HJG,!
AMp[f%X
c`yLn %Of%
% tangential ez=0 on front-back plane
U]riBlg>
ez(:,1,:)=0.0;
?\L@Pr|=Dr
ez(:,jh_tot,:)=0.0;
ryy".'v
4GH?$p|LX
% Update electric field
$z"3_4a
_ n,Ye&m
p1store=px1;
h\Ck""&
px1(:,2:je_tot,2:ke_tot)=C1ex(:,2:je_tot,2:ke_tot).* px1(:,2:je_tot,2:ke_tot)+...
@MWrUx
C2ex(:,2:je_tot,2:ke_tot).*((hz(:,2:je_tot,2:ke_tot)-hz(:,1:je_tot-1,2:ke_tot))-...
t|0Zpp;
( hy(:,2:je_tot,2:ke_tot)-hy(:,2:je_tot,1:ke_tot-1)))./delta;
_Jn-# du
p2store=px2;
z4D[>2*
px2(:,2:je_t ..
ow,I|A
P3jDx{F
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xiaoyuan
UID ：53338
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2010-02-28
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2015-12-05
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仿真二级
1楼
发表于: 2010-08-29 06:21:02
这是代码，可以下载，刚刚没弄明白怎么上传代码。呵呵。
UPML_3D_Boyuan_lossy.rar
(5 K) 下载次数:17
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