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[求助]菜鸟求助，PML边界问题

UID ：55262

注册：2010-03-21
登录：2011-11-27
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0楼发表于: 2010-03-21 19:26:52

我在做一个光学电磁波仿真，并没有学过电磁场，找到一个matlab写的计算TE波的程序，现在想算TM，但是对着书研究了几天也没明白PML这块怎么回事，555
我只想用一下，并不想了解细节，请问这个程序有TM波的版本吗？或者哪位仁兄知道怎么修改吗？？？万分感谢了！！！

%***********************************************************************
%     2-D FDTD TE code with PML absorbing boundary conditions
%***********************************************************************
%
%     Program author: Susan C. Hagness
%                     Department of Electrical and Computer Engineering
%                     University of Wisconsin-Madison
%                     1415 Engineering Drive
%                     Madison, WI 53706-1691
%                     608-265-5739
%                     hagness@engr.wisc.edu
%
%     Date of this version: February 2000
%
%     This MATLAB M-file implements the finite-difference time-domain
%     solution of Maxwell's curl equations over a two-dimensional
%     Cartesian space lattice comprised of uniform square grid cells.
%
%     To illustrate the algorithm, a 6-cm-diameter metal cylindrical
%     scatterer in free space is modeled. The source excitation is
%     a Gaussian pulse with a carrier frequency of 5 GHz.
%
%     The grid resolution (dx = 3 mm) was chosen to provide 20 samples
%     per wavelength at the center frequency of the pulse (which in turn
%     provides approximately 10 samples per wavelength at the high end
%     of the excitation spectrum, around 10 GHz).
%
%     The computational domain is truncated using the perfectly matched
%     layer (PML) absorbing boundary conditions. The formulation used
%     in this code is based on the original split-field Berenger PML. The
%     PML regions are labeled as shown in the following diagram:
%           y
%            ----------------------------------------------
%           | |                BACK PML                | |
%            ----------------------------------------------
%           |L |                                       /| R|
%           |E |                                (ib,jb) | I|
%           |F |                                        | G|
%           |T |                                        | H|
%           | |                MAIN GRID               | T|
%           |P |                                        | |
%           |M |                                        | P|
%           |L | (1,1)                                  | M|
%           | |/                                       | L|
%            ----------------------------------------------
%           | |                FRONT PML               | |
%            ----------------------------------------------   x
%
%     To execute this M-file, type "fdtd2D" at the MATLAB prompt.
%     This M-file displays the FDTD-computed Ex, Ey, and Hz fields at
%     every 4th time step, and records those frames in a movie matrix,
%     M, which is played at the end of the simulation using the "movie"
%     command.
%
%***********************************************************************
clear
%***********************************************************************
%     Fundamental constants
%***********************************************************************
cc=2.99792458e8;            %speed of light in free space
muz=4.0*pi*1.0e-7;          %permeability of free space
epsz=1.0/(cc*cc*muz);       %permittivity of free space
freq=5.0e+9;                %center frequency of source excitation
lambda=cc/freq;             %center wavelength of source excitation
omega=2.0*pi*freq;
%***********************************************************************
%     Grid parameters
%***********************************************************************
ie=100;           %number of grid cells in x-direction
je=50;            %number of grid cells in y-direction
ib=ie+1;
jb=je+1;
is=15;            %location of z-directed hard source
js=je/2;          %location of z-directed hard source
dx=3.0e-3;        %space increment of square lattice
dt=dx/(2.0*cc);   %time step
nmax=300;         %total number of time steps
iebc=8;           %thickness of left and right PML region
jebc=8;           %thickness of front and back PML region
rmax=0.00001;
orderbc=2;              %二阶边界条件？？？
ibbc=iebc+1;
jbbc=jebc+1;
iefbc=ie+2*iebc;
jefbc=je+2*jebc;
ibfbc=iefbc+1;
jbfbc=jefbc+1;
%***********************************************************************
%     Material parameters
%***********************************************************************
media=2;
eps=[1.0 1.0];
sig=[0.0 1.0e+7];
mur=[1.0 1.0];
sim=[0.0 0.0];
%***********************************************************************
%     Wave excitation
%***********************************************************************
rtau=160.0e-12;
tau=rtau/dt;
delay=3*tau;
source=zeros(1,nmax);
for n=1:7.0*tau
source(n)=sin(omega*(n-delay)*dt)*exp(-((n-delay)^2/tau^2));
end
%***********************************************************************
%     Field arrays
%***********************************************************************
ex=zeros(ie,jb);           %fields in main grid
ey=zeros(ib,je);
hz=zeros(ie,je);
exbcf=zeros(iefbc,jebc);   %fields in front PML region
eybcf=zeros(ibfbc,jebc);
hzxbcf=zeros(iefbc,jebc);
hzybcf=zeros(iefbc,jebc);
exbcb=zeros(iefbc,jbbc);   %fields in back PML region
eybcb=zeros(ibfbc,jebc);
hzxbcb=zeros(iefbc,jebc);
hzybcb=zeros(iefbc,jebc);
exbcl=zeros(iebc,jb);      %fields in left PML region
eybcl=zeros(iebc,je);
hzxbcl=zeros(iebc,je);
hzybcl=zeros(iebc,je);
exbcr=zeros(iebc,jb);      %fields in right PML region
eybcr=zeros(ibbc,je);
hzxbcr=zeros(iebc,je);
hzybcr=zeros(iebc,je);
%***********************************************************************
%     Updating coefficients
%***********************************************************************
for i=1:media
eaf =dt*sig(i)/(2.0*epsz*eps(i));
ca(i)=(1.0-eaf)/(1.0+eaf);
cb(i)=dt/epsz/eps(i)/dx/(1.0+eaf);
haf =dt*sim(i)/(2.0*muz*mur(i));
da(i)=(1.0-haf)/(1.0+haf);
db(i)=dt/muz/mur(i)/dx/(1.0+haf);
end
%***********************************************************************
%     Geometry specification (main grid)
%***********************************************************************
%     Initialize entire main grid to free space
caex(1:ie,1:jb)=ca(1);
cbex(1:ie,1:jb)=cb(1);
caey(1:ib,1:je)=ca(1);
cbey(1:ib,1:je)=cb(1);
dahz(1:ie,1:je)=da(1);
dbhz(1:ie,1:je)=db(1);
%     Add metal cylinder
diam=20;          % diameter of cylinder: 6 cm
rad=diam/2.0;     % radius of cylinder: 3 cm
icenter=4*ie/5;   % i-coordinate of cylinder's center
jcenter=je/2;     % j-coordinate of cylinder's center
for i=1:ie
for j=1:je
dist2=(i+0.5-icenter)^2 + (j-jcenter)^2;
if dist2 <= rad^2
     caex(i,j)=ca(2);
     cbex(i,j)=cb(2);
end
dist2=(i-icenter)^2 + (j+0.5-jcenter)^2;
if dist2 <= rad^2
     caey(i,j)=ca(2);
     cbey(i,j)=cb(2);
end
end
end
%***********************************************************************
%     Fill the PML regions
%***********************************************************************
delbc=iebc*dx;
sigmam=-log(rmax/100.0)*epsz*cc*(orderbc+1)/(2*delbc);
bcfactor=eps(1)*sigmam/(dx*(delbc^orderbc)*(orderbc+1));
%     FRONT region
caexbcf(1:iefbc,1)=1.0;
cbexbcf(1:iefbc,1)=0.0;
for j=2:jebc
y1=(jebc-j+1.5)*dx;
y2=(jebc-j+0.5)*dx;
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
ca1=exp(-sigmay*dt/(epsz*eps(1)));
cb1=(1.0-ca1)/(sigmay*dx);
caexbcf(1:iefbc,j)=ca1;
cbexbcf(1:iefbc,j)=cb1;
end
sigmay = bcfactor*(0.5*dx)^(orderbc+1);
ca1=exp(-sigmay*dt/(epsz*eps(1)));
cb1=(1-ca1)/(sigmay*dx);
caex(1:ie,1)=ca1;
cbex(1:ie,1)=cb1;
caexbcl(1:iebc,1)=ca1;
cbexbcl(1:iebc,1)=cb1;
caexbcr(1:iebc,1)=ca1;
cbexbcr(1:iebc,1)=cb1;
for j=1:jebc
y1=(jebc-j+1)*dx;
y2=(jebc-j)*dx;
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
sigmays=sigmay*(muz/(epsz*eps(1)));
da1=exp(-sigmays*dt/muz);
db1=(1-da1)/(sigmays*dx);
dahzybcf(1:iefbc,j)=da1;
dbhzybcf(1:iefbc,j)=db1;
caeybcf(1:ibfbc,j)=ca(1);
cbeybcf(1:ibfbc,j)=cb(1);
dahzxbcf(1:iefbc,j)=da(1);
dbhzxbcf(1:iefbc,j)=db(1);
end
%**************************************************************************
%
%     BACK region
caexbcb(1:iefbc,jbbc)=1.0;
cbexbcb(1:iefbc,jbbc)=0.0;
for j=2:jebc
y1=(j-0.5)*dx;
y2=(j-1.5)*dx;
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
ca1=exp(-sigmay*dt/(epsz*eps(1)));
cb1=(1-ca1)/(sigmay*dx);
caexbcb(1:iefbc,j)=ca1;
cbexbcb(1:iefbc,j)=cb1;
end
sigmay = bcfactor*(0.5*dx)^(orderbc+1);
ca1=exp(-sigmay*dt/(epsz*eps(1)));
cb1=(1-ca1)/(sigmay*dx);
caex(1:ie,jb)=ca1;
cbex(1:ie,jb)=cb1;
caexbcl(1:iebc,jb)=ca1;
cbexbcl(1:iebc,jb)=cb1;
caexbcr(1:iebc,jb)=ca1;
cbexbcr(1:iebc,jb)=cb1;
for j=1:jebc
y1=j*dx;
y2=(j-1)*dx;
sigmay=bcfactor*(y1^(orderbc+1)-y2^(orderbc+1));
sigmays=sigmay*(muz/(epsz*eps(1)));
da1=exp(-sigmays*dt/muz);
db1=(1-da1)/(sigmays*dx);
dahzybcb(1:iefbc,j)=da1;
dbhzybcb(1:iefbc,j)=db1;
caeybcb(1:ibfbc,j)=ca(1);
cbeybcb(1:ibfbc,j)=cb(1);
dahzxbcb(1:iefbc,j)=da(1);
dbhzxbcb(1:iefbc,j)=db(1);
end
%     LEFT region
caeybcl(1,1:je)=1.0;
cbeybcl(1,1:je)=0.0;
for i=2:iebc
x1=(iebc-i+1.5)*dx;
x2=(iebc-i+0.5)*dx;
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
ca1=exp(-sigmax*dt/(epsz*eps(1)));
cb1=(1-ca1)/(sigmax*dx);
caeybcl(i,1:je)=ca1;
cbeybcl(i,1:je)=cb1;
caeybcf(i,1:jebc)=ca1;
cbeybcf(i,1:jebc)=cb1;
caeybcb(i,1:jebc)=ca1;
cbeybcb(i,1:jebc)=cb1;
end
sigmax=bcfactor*(0.5*dx)^(orderbc+1);
ca1=exp(-sigmax*dt/(epsz*eps(1)));
cb1=(1-ca1)/(sigmax*dx);
caey(1,1:je)=ca1;
cbey(1,1:je)=cb1;
caeybcf(iebc+1,1:jebc)=ca1;
cbeybcf(iebc+1,1:jebc)=cb1;
caeybcb(iebc+1,1:jebc)=ca1;
cbeybcb(iebc+1,1:jebc)=cb1;
for i=1:iebc
x1=(iebc-i+1)*dx;
x2=(iebc-i)*dx;
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
sigmaxs=sigmax*(muz/(epsz*eps(1)));
da1=exp(-sigmaxs*dt/muz);
db1=(1-da1)/(sigmaxs*dx);
dahzxbcl(i,1:je)=da1;
dbhzxbcl(i,1:je)=db1;
dahzxbcf(i,1:jebc)=da1;
dbhzxbcf(i,1:jebc)=db1;
dahzxbcb(i,1:jebc)=da1;
dbhzxbcb(i,1:jebc)=db1;
caexbcl(i,2:je)=ca(1);
cbexbcl(i,2:je)=cb(1);
dahzybcl(i,1:je)=da(1);
dbhzybcl(i,1:je)=db(1);
end
%     RIGHT region
caeybcr(ibbc,1:je)=1.0;
cbeybcr(ibbc,1:je)=0.0;
for i=2:iebc
x1=(i-0.5)*dx;
x2=(i-1.5)*dx;
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
ca1=exp(-sigmax*dt/(epsz*eps(1)));
cb1=(1-ca1)/(sigmax*dx);
caeybcr(i,1:je)=ca1;
cbeybcr(i,1:je)=cb1;
caeybcf(i+iebc+ie,1:jebc)=ca1;
cbeybcf(i+iebc+ie,1:jebc)=cb1;
caeybcb(i+iebc+ie,1:jebc)=ca1;
cbeybcb(i+iebc+ie,1:jebc)=cb1;
end
sigmax=bcfactor*(0.5*dx)^(orderbc+1);
ca1=exp(-sigmax*dt/(epsz*eps(1)));
cb1=(1-ca1)/(sigmax*dx);
caey(ib,1:je)=ca1;
cbey(ib,1:je)=cb1;
caeybcf(iebc+ib,1:jebc)=ca1;
cbeybcf(iebc+ib,1:jebc)=cb1;
caeybcb(iebc+ib,1:jebc)=ca1;
cbeybcb(iebc+ib,1:jebc)=cb1;
for i=1:iebc
x1=i*dx;
x2=(i-1)*dx;
sigmax=bcfactor*(x1^(orderbc+1)-x2^(orderbc+1));
sigmaxs=sigmax*(muz/(epsz*eps(1)));
da1=exp(-sigmaxs*dt/muz);
db1=(1-da1)/(sigmaxs*dx);
dahzxbcr(i,1:je) = da1;
dbhzxbcr(i,1:je) = db1;
dahzxbcf(i+ie+iebc,1:jebc)=da1;
dbhzxbcf(i+ie+iebc,1:jebc)=db1;
dahzxbcb(i+ie+iebc,1:jebc)=da1;
dbhzxbcb(i+ie+iebc,1:jebc)=db1;
caexbcr(i,2:je)=ca(1);
cbexbcr(i,2:je)=cb(1);
dahzybcr(i,1:je)=da(1);
dbhzybcr(i,1:je)=db(1);
end
%***********************************************************************
%     Movie initialization
%***********************************************************************
subplot(3,1,1),pcolor(ex');
shading flat;
caxis([-80.0 80.0]);
axis([1 ie 1 jb]);
colorbar;
axis image;
axis off;
title(['Ex at time step = 0']);
subplot(3,1,2),pcolor(ey');
shading flat;
caxis([-80.0 80.0]);
axis([1 ib 1 je]);
colorbar;
axis image;
axis off;
title(['Ey at time step = 0']);
subplot(3,1,3),pcolor(hz');
shading flat;
caxis([-0.2 0.2]);
axis([1 ie 1 je]);
colorbar;
axis image;
axis off;
title(['Hz at time step = 0']);
rect=get(gcf,'Position');
rect(1:2)=[0 0];
M=moviein(nmax/4,gcf,rect);
%***********************************************************************
%     BEGIN TIME-STEPPING LOOP
%***********************************************************************
for n=1:nmax
%***********************************************************************
%     Update electric fields (EX and EY) in main grid
%***********************************************************************
ex(:,2:je)=caex(:,2:je).*ex(:,2:je)+...
           cbex(:,2:je).*(hz(:,2:je)-hz(:,1:je-1));
ey(2:ie,:)=caey(2:ie,:).*ey(2:ie,:)+...
           cbey(2:ie,:).*(hz(1:ie-1,:)-hz(2:ie,:));
%***********************************************************************
%     Update EX in PML regions
%***********************************************************************
%     FRONT
exbcf(:,2:jebc)=caexbcf(:,2:jebc).*exbcf(:,2:jebc)-...
cbexbcf(:,2:jebc).*(hzxbcf(:,1:jebc-1)+hzybcf(:,1:jebc-1)-...
                      hzxbcf(:,2:jebc)-hzybcf(:,2:jebc));
ex(1:ie,1)=caex(1:ie,1).*ex(1:ie,1)-...
cbex(1:ie,1).*(hzxbcf(ibbc:iebc+ie,jebc)+...
                hzybcf(ibbc:iebc+ie,jebc)-hz(1:ie,1));
%     BACK
exbcb(:,2:jebc-1)=caexbcb(:,2:jebc-1).*exbcb(:,2:jebc-1)-...
cbexbcb(:,2:jebc-1).*(hzxbcb(:,1:jebc-2)+hzybcb(:,1:jebc-2)-...
                        hzxbcb(:,2:jebc-1)-hzybcb(:,2:jebc-1));
ex(1:ie,jb)=caex(1:ie,jb).*ex(1:ie,jb)-...
cbex(1:ie,jb).*(hz(1:ie,jb-1)-hzxbcb(ibbc:iebc+ie,1)-...
                 hzybcb(ibbc:iebc+ie,1));
%     LEFT
exbcl(:,2:je)=caexbcl(:,2:je).*exbcl(:,2:je)-...
cbexbcl(:,2:je).*(hzxbcl(:,1:je-1)+hzybcl(:,1:je-1)-...
                    hzxbcl(:,2:je)-hzybcl(:,2:je));
exbcl(:,1)=caexbcl(:,1).*exbcl(:,1)-...
cbexbcl(:,1).*(hzxbcf(1:iebc,jebc)+hzybcf(1:iebc,jebc)-...
                 hzxbcl(:,1)-hzybcl(:,1));
exbcl(:,jb)=caexbcl(:,jb).*exbcl(:,jb)-...
cbexbcl(:,jb).*(hzxbcl(:,je)+hzybcl(:,je)-...
                  hzxbcb(1:iebc,1)-hzybcb(1:iebc,1));
%     RIGHT
exbcr(:,2:je)=caexbcr(:,2:je).*exbcr(:,2:je)-...
cbexbcr(:,2:je).*(hzxbcr(:,1:je-1)+hzybcr(:,1:je-1)-...
                    hzxbcr(:,2:je)-hzybcr(:,2:je));
exbcr(:,1)=caexbcr(:,1).*exbcr(:,1)-...
cbexbcr(:,1).*(hzxbcf(1+iebc+ie:iefbc,jebc)+...
                 hzybcf(1+iebc+ie:iefbc,jebc)-...
                 hzxbcr(:,1)-hzybcr(:,1));
exbcr(:,jb)=caexbcr(:,jb).*exbcr(:,jb)-...
cbexbcr(:,jb).*(hzxbcr(:,je)+hzybcr(:,je)-...
                  hzxbcb(1+iebc+ie:iefbc,1)-...
                  hzybcb(1+iebc+ie:iefbc,1));
%***********************************************************************
%     Update EY in PML regions
%***********************************************************************
%     FRONT
eybcf(2:iefbc,:)=caeybcf(2:iefbc,:).*eybcf(2:iefbc,:)-...
cbeybcf(2:iefbc,:).*(hzxbcf(2:iefbc,:)+hzybcf(2:iefbc,:)-...
                       hzxbcf(1:iefbc-1,:)-hzybcf(1:iefbc-1,:));
%     BACK
eybcb(2:iefbc,:)=caeybcb(2:iefbc,:).*eybcb(2:iefbc,:)-...
cbeybcb(2:iefbc,:).*(hzxbcb(2:iefbc,:)+hzybcb(2:iefbc,:)-...
                       hzxbcb(1:iefbc-1,:)-hzybcb(1:iefbc-1,:));
%     LEFT
eybcl(2:iebc,:)=caeybcl(2:iebc,:).*eybcl(2:iebc,:)-...
cbeybcl(2:iebc,:).*(hzxbcl(2:iebc,:)+hzybcl(2:iebc,:)-...
                      hzxbcl(1:iebc-1,:)-hzybcl(1:iebc-1,:));
ey(1,:)=caey(1,:).*ey(1,:)-...
cbey(1,:).*(hz(1,:)-hzxbcl(iebc,:)-hzybcl(iebc,:));
%     RIGHT
eybcr(2:iebc,:)=caeybcr(2:iebc,:).*eybcr(2:iebc,:)-...
cbeybcr(2:iebc,:).*(hzxbcr(2:iebc,:)+hzybcr(2:iebc,:)-...
                      hzxbcr(1:iebc-1,:)-hzybcr(1:iebc-1,:));
ey(ib,:)=caey(ib,:).*ey(ib,:)-...
cbey(ib,:).*(hzxbcr(1,:)+hzybcr(1,:)- hz(ie,:));

%***********************************************************************
%     Update magnetic fields (HZ) in main grid
%***********************************************************************
hz(1:ie,1:je)=dahz(1:ie,1:je).*hz(1:ie,1:je)+...
              dbhz(1:ie,1:je).*(ex(1:ie,2:jb)-ex(1:ie,1:je)+...
                                ey(1:ie,1:je)-ey(2:ib,1:je));
hz(is,js)=source(n);

%***********************************************************************
%     Update HZX in PML regions
%***********************************************************************
%     FRONT
hzxbcf(1:iefbc,:)=dahzxbcf(1:iefbc,:).*hzxbcf(1:iefbc,:)-...
dbhzxbcf(1:iefbc,:).*(eybcf(2:ibfbc,:)-eybcf(1:iefbc,:));
%     BACK
hzxbcb(1:iefbc,:)=dahzxbcb(1:iefbc,:).*hzxbcb(1:iefbc,:)-...
dbhzxbcb(1:iefbc,:).*(eybcb(2:ibfbc,:)-eybcb(1:iefbc,:));
%     LEFT
hzxbcl(1:iebc-1,:)=dahzxbcl(1:iebc-1,:).*hzxbcl(1:iebc-1,:)-...
dbhzxbcl(1:iebc-1,:).*(eybcl(2:iebc,:)-eybcl(1:iebc-1,:));
hzxbcl(iebc,:)=dahzxbcl(iebc,:).*hzxbcl(iebc,:)-...
dbhzxbcl(iebc,:).*(ey(1,:)-eybcl(iebc,:));
%     RIGHT
hzxbcr(2:iebc,:)=dahzxbcr(2:iebc,:).*hzxbcr(2:iebc,:)-...
dbhzxbcr(2:iebc,:).*(eybcr(3:ibbc,:)-eybcr(2:iebc,:));
hzxbcr(1,:)=dahzxbcr(1,:).*hzxbcr(1,:)-...
dbhzxbcr(1,:).*(eybcr(2,:)-ey(ib,:));
%***********************************************************************
%     Update HZY in PML regions
%***********************************************************************
%     FRONT
hzybcf(:,1:jebc-1)=dahzybcf(:,1:jebc-1).*hzybcf(:,1:jebc-1)-...
dbhzybcf(:,1:jebc-1).*(exbcf(:,1:jebc-1)-exbcf(:,2:jebc));
hzybcf(1:iebc,jebc)=dahzybcf(1:iebc,jebc).*hzybcf(1:iebc,jebc)-...
dbhzybcf(1:iebc,jebc).*(exbcf(1:iebc,jebc)-exbcl(1:iebc,1));
hzybcf(iebc+1:iebc+ie,jebc)=...
dahzybcf(iebc+1:iebc+ie,jebc).*hzybcf(iebc+1:iebc+ie,jebc)-...
dbhzybcf(iebc+1:iebc+ie,jebc).*(exbcf(iebc+1:iebc+ie,jebc)-...
             &nb ..

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离线etynqk

UID ：44492

注册：2009-10-20
登录：2011-03-13
发帖：33
等级：仿真一级

1楼发表于: 2010-03-22 15:00:05

论坛里的火狐同学写过一个教程，讲得还是非常不错，你可以看看

附件:

Yee原胞及PML修订版.pdf (461 K) 下载次数:49

离线alex0flex

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注册：2010-03-24
登录：2019-09-09
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2楼发表于: 2010-03-24 18:30:53

正在学这个呢，谢谢。

羽然.A

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