3d-fdtd.txt

三维的有限时域差分源程序

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
%***********************************************************************