fdtd_for_2d_metal_plane_object.m

FDTD for 2D metal plane object, It is very valuable reference because is the basement for 3D FDTD pr

clear;clc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
c=3*10^8; % 波速
f=3*10^9; % 频率
lamda=c/f; % 波长
k=2*pi/lamda; % 波数

epsz=1/(4*pi*9*10^9); % 真空介电常数
mu=4*pi*10.^(-7); % 真空磁导率
Z=120*pi; % 真空波阻抗
epsilon=1; % 相对介电常数
sigma=0; % 电导率

N=100; % 网格数量
L=800; % 迭代次数
ddx=lamda/20; % 网格尺寸
dt=ddx/(2*c); % 时间间隔

ia=N/4; % 总场区域x左
ib=3*N/4; % 总场区域x右
ja=ia; % 总场区域x下
jb=ib; % 总场区域x上

npml=N/8; % PML点数
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

r=2*lamda; 
M=r/(2*ddx);

for i=1:N 
for j=1:N
ga(i,j)=1/(epsilon+sigma*dt/epsz); % 求和参量
gb(i,j)=sigma*dt/epsz; % 求和参量
end
end

spread=8; % 脉冲宽度
t0=25; % 脉冲高度
is=N/2; % 源的X位置
js=N/2; % 源的Y位置

ez_inc=zeros(1,N);
hx_inc=zeros(1,N);

ez_low1=0;
ez_low2=0;
ez_low3=0;
ez_low4=0;

dz=zeros(N,N); % z方向电荷密度
ez=zeros(N,N); % z方向电场
iz=zeros(N,N); % z方向电场求和参量
hx=zeros(N,N); % x方向磁场
hy=zeros(N,N); % y方向磁场
ihx=zeros(N,N); % x方向磁场参量
ihy=zeros(N,N); % y方向磁场参量

%%%%%%%%%%%%%%%%%%%%%%%%PML%%%%%%%%%%%%%%%%%%%
for i=1:N
gi2(i)=1;
gi3(i)=1;
fi1(i)=0;
fi2(i)=1;
fi3(i)=1;
end
for j=1:N
gj2(j)=1;
gj3(j)=1;
fj1(j)=0;
fj2(j)=1;
fj3(j)=1;
end

for i=1:npml+1
xnum=npml-i+1;
xxn=xnum/npml; 
xn=0.33*(xxn^3);
gi2(i)=1/(1+xn);
gi2(N-i+1)=1/(1+xn);
gi3(i)=(1-xn)/(1+xn);
gi3(N-i+1)=(1-xn)/(1+xn);

xxn=(xnum-0.5)/npml;
xn=0.25*(xxn^3);
fi1(i)=xn;
fi1(N-i)=xn;
fi2(i)=1/(1+xn);
fi2(N-i)=1/(1+xn);
fi3(i)=(1-xn)/(1+xn);
fi3(N-i)=(1-xn)/(1+xn);
end

for j=1:npml+1
xnum=npml-j+1;
xxn=xnum/npml; 
xn=0.33*(xxn^3);
gj2(j)=1/(1+xn);
gj2(N-j+1)=1/(1+xn);
gj3(j)=(1-xn)/(1+xn);
gj3(N-j+1)=(1-xn)/(1+xn);

xxn=(xnum-0.5)/npml;
xn=0.25*(xxn^3);
fj1(j)=xn;
fj1(N-j)=xn;
fj2(j)=1/(1+xn);
fj2(N-j)=1/(1+xn);
fj3(j)=(1-xn)/(1+xn);
fj3(N-j)=(1-xn)/(1+xn);
end

for T=1:L
%%%%%%%%%%%%%%TM波Y方向传播%%%%%%%%%%%%%%%%%%%%%
for j=2:N-1
ez_inc(j)=ez_inc(j)+0.5*(hx_inc(j-1)-hx_inc(j));
end

ez_inc(1)=ez_low2;
ez_low2=ez_low1;
ez_low1=ez_inc(2);
ez_inc(N)=ez_low3;
ez_low3=ez_low4;
ez_low4=ez_inc(N-1);
%% %%%%%%%%%%%%%% 电荷密度dz%%%%%%%%%%%%%%%%%%%%%%%%%
for i=2:N-1 
for j=2:N
dz(i,j)=gi3(i)*gj3(j)*dz(i,j)+gi2(i)*gj2(j)*0.5*( hy(i,j)-hy(i-1,j)-hx(i,j)+hx(i,j-1) );
end
end 
%%%%%%%%%%%%%%%%%%脉冲的加入%%%%%%%%%%%%%%%%%%%
source=exp((-0.5)*( (t0-T)/spread ).^2); 
ez_inc(5)=source; 

for i=ia:ib
dz(i,ja)=dz(i,ja)+0.5*hx_inc(ja-1);
dz(i,jb)=dz(i,jb)-0.5*hx_inc(jb);
end
%%%%%%%%%%%%%% 电场ez%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N 
for j=1:N
ez(i,j)=ga(i,j)*( dz(i,j)-iz(i,j) );
iz(i,j)=iz(i,j)+gb(i,j)*ez(i,j) ;
end
end 
%%%%%%%%%%%%%%%%%%%%边界电场%%%%%%%%%%%%%%%%%%%%%%%
for j=1:N
ez(1,j)=0;
ez(N,j)=0;
end

for i=1:N
ez(i,1)=0;
ez(i,N)=0;
end 

%%%%%%%%%%%%%%%%%%%%%%边界条件%%%%%%%%%%%%%%%%%%%%%%%%
for i=N/2-M:N/2+M-1
for j=N/2-M:N/2+M-1
ez(i,j)=0;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%磁场%%%%%%%%%%%%%%%%%%%%%%%%
for j=1:N-1
hx_inc(j)=hx_inc(j)+0.5*(ez_inc(j)-ez_inc(j+1));
end
%%%%%%%%%%%%%%%%%%%%%%%%磁场Hx%%%%%%%%%%%%%%%%%%%%%%
for i=1:N 
for j=1:N-1
curl_e=ez(i,j)-ez(i,j+1);
ihx(i,j)=ihx(i,j)+fi1(i)*curl_e;
hx(i,j)=fj3(j)*hx(i,j)+fj2(j)*0.5*(curl_e+ihx(i,j));
end
end; 

for i=ia:ib
hx(i,ja-1)=hx(i,ja-1)+0.5*ez_inc(ja);
hx(i,jb)=hx(i,jb)-0.5*ez_inc(jb);
end
%%%%%%%%磁场Hy%%%%%%%%%%%%%%%%%%%
for i=1:N-1 
for j=1:N
curl_e=ez(i+1,j)-ez(i,j);
ihy(i,j)=ihy(i,j)+fj1(j)*curl_e;
hy(i,j)=fi3(i)*hy(i,j)+fi2(i)*0.5*(curl_e+ihy(i,j));
end
end 

for j=ja:jb;
hy(ia-1,j)=hy(ia-1,j)-0.5*ez_inc(j);
hy(ib,j)=hy(ib,j)+0.5*ez_inc(j);
end

mesh(ez)
drawnow;
end