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紧急求助 2D FDTD 程序会的指点一下万分感谢

UID ：19721

注册：2008-10-21
登录：2011-11-15
发帖：62
等级：仿真一级

0楼发表于: 2009-05-09 12:51:56

— 本帖被 destroyer 从【互助速问速答有求速应】移动到本区(2009-11-28) —

ic=Nx/4; % 源的X位置
jc=Ny/4; % 源的Y位置

for i=1:Nx+1;
    for j=1:Ny+1;
        dz(i,j)=0; %z方向电位移
        ez(i,j)=0; % z方向电场
        hx(i,j)=0; % x方向磁场
        hy(i,j)=0; % y方向磁场
        ihx(i,j)=0;
        ihy(i,j)=0;
        iz(i,j)=0;  % z方向求和中间参量
    end;
end;

for i=2:Nx;
    for j=2:Ny;
        ga(i,j)=1;
    end;
end;
%PML参数的设置
for i=1:Nx;
    gi2(i)=1;
    gi3(i)=1;
    fi1(i)=0;
    fi2(i)=1;
    fi3(i)=1;
end

for j=1:Ny;
    gj2(j)=1;
    gj3(j)=1;
    fj1(j)=0;
    fj2(j)=1;
    fj3(j)=1;
end

for i=1:npml+1; %设置PML层中的参数
    xnum=npml+1-i;
    xn=0.33*(xnum/npml)^3; %这里的0.333并不是严格的计算，而是经验值
    gi2(i)=1.0/(1+xn);
    gi2(Nx-1-i)=1/(1+xn);
    gi3(i)=(1-xn)/(1+xn);
    gi3(Nx-1-i)=(1-xn)/(1+xn);

    xn=0.25*((xnum-0.5)/npml)^3; %这里的0.25和0.333也是一个道理
    fi1(i)=xn;
    fi1(Nx-2-i)=xn;
    fi2(i)=1.0/(1+xn);
    fi2(Nx-2-i)=1/(1+xn);
    fi3(i)=(1-xn)/(1+xn);
    fi3(Nx-2-i)=(1-xn)/(1+xn);
end

for i=1:npml+1;
    xnum=npml+1-i;
    xn=0.33*(xnum/npml)^3;
    gj2(i)=1.0/(1+xn);
    gj2(Ny-1-i)=1/(1+xn);
    gj3(i)=(1-xn)/(1+xn);
    gj3(Ny-1-i)=(1-xn)/(1+xn);

    xn=0.25*((xnum-0.5)/npml)^3;
    fj1(i)=xn;
    fj1(Ny-2-i)=xn;

    fj2(i)=1.0/(1+xn);
    fj2(Ny-2-i)=1/(1+xn);
    fj3(i)=(1-xn)/(1+xn);
    fj3(Ny-2-i)=(1-xn)/(1+xn);
end

%2.迭代求解电场和磁场

for t=1:T;
    for i=2:Nx;  % 为了使每个电场周围都有磁场进行数组下标处理
        for j=2:Ny;
      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;  % 电场循环结束

    pulse=sin(2*pi*f*t*dt);  % 正弦波源
  %pulse=exp(-4*pi*(t*dt-t0)^2/(2/f)^2);高斯脉冲情况
    dz(ic,jc)=dz(ic,jc)+pulse;  %软源，就是为了防止反射做的一个处理

    for i=1:Nx; %为了使每个电场周围都有磁场进行数组下标处理
        for j=1:Ny;
          ez(i,j)=ga(i,j)* dz(i,j);  %反映煤质的情况都是放到这里的
        end;
    end; % 电荷密度循环结束

    for j=1:Ny;
        ez(1,j)=0;
        ez(Nx,j)=0;
    end

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

    for i=1:Nx;  % 为使每个磁场周围都有电场进行数组下标处理
        for j=1:Ny-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; % 磁场HX循环结束

    for i=1:Nx-1;  % 为了使每个磁场周围都有电场进行数组下标处理
        for j=1:Ny;
            curl_e=ez(i+1,j)-ez(i,j);
      &n ..

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离线flanky

UID ：19721

注册：2008-10-21
登录：2011-11-15
发帖：62
等级：仿真一级

1楼发表于: 2009-05-05 20:36:59

谁对FDTD比较擅长的，帮小弟一把，谢谢，这是一个用FDTD仿真2维TM波金属方柱散射

%  FDTD_2D_RCS
%  本程序实现FDTD仿真2维TM波金属方柱散射
%  TM波沿Y方向传播，X方向极化
%  采用UPML吸收，脉冲源激励

%  20050330
%   模拟区域的范围以及编号的处理：
%   数字代表区域方向上的编号；
%           ------------------------------------------------------
%           |  |                BACK PML 2                      |  |
%            ------------------------------------------------------
%           |L |    __________________________________         /| R|
%           |E |   |                                  | (ib,jb) | I|
%           |F |   |                                  |         | G|
%           |T |   |                                  |         | H|
%           |3 |   |             MAIN GRID            |         | T|
%           |P |   |                                  |         |4 |
%           |M |   |                                  |         | P|
%           |L |   |                                  |         | M|
%           |  |/  |__________________________________|         | L|
%            -----------------------------------------------------
%           |  |                FRONT PML  1                    |  |
%            -----------------------------------------------------

clear;clc;
% load('rcs1');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%*******************************初始化***********************************%%
tic;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
v=3*10^8;              %  波速
f=0.3*10^(9);          %  频率
lamda=v/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=sqrt(mu/epsz);       %  真空波阻抗
epsilon=1;             %  相对介电常数
sigma=0.0;               %  电导率
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N=120;                 %  网格数量
L=1000;                 %  迭代次数
ddx=lamda/20;          %  网格尺寸
dt=ddx/(2*v);          %  时间间隔

lstart=1;              %  空间起始行坐标
lend=N;                %  空间终止行坐标
rstart=1;              %  空间起始列坐标
rend=N;                %  空间终止列坐标

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

pa=ia-5;               %  外推区域x左
pb=ib+5;               %  外推区域x右
qa=pa;                 %  外推区域x下
qb=pb;                 %  外推区域x上
length=pb-pa+1;        %  每个边上的总长度

npml=N/8;              %  PML点数
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  方柱参数
side=2*lamda;                 %  方柱边长
halfgrid=round(side/(2*ddx)); %  方柱占据网格大小

%%  媒质参数
for i=lstart:lend;  %  控制媒质分部区域
    for j=rstart:rend;
        ga(i,j)=1/(epsilon+sigma*dt/epsz);  %  求和参量
        gb(i,j)=sigma*dt/epsz;              %  求和参量
    end;
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  源参数
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

%%  输入平面波
ez_inc=zeros(1,N);
hx_inc=zeros(1,N);

%%  平面波吸收条件变量初始化
ez_v1=0;
ez_v2=0;
ez_v3=0;
ez_v4=0;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  迭待电磁场参量
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

%%  相位和幅度提取(傅里叶变换)
ine=0;
inh=0;
ez_out=zeros(4,length+1);
hx_out=zeros(4,length);
hy_out=zeros(4,length);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%*********************************PML设置********************************%%
%%  PML初始化
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;

%%  阻抗渐变设置
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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%***************************迭代求解电场和磁场****************************%%

for T=1:L;
    disp(T);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%*************************电场由磁场更新*********************************%%

%%  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;

%%  平面波吸收条件
    ez_inc(1)=ez_v2;
    ez_v2=ez_v1;
    ez_v1=ez_inc(2);

    ez_inc(N)=ez_v3;
    ez_v3=ez_v4;
    ez_v4=ez_inc(N-1);

%%  入射电场傅里叶变换(必须用边界加入)
    % 注意：当计算频谱用的是其他的位置的入射波时候，会产生很大的误差；

    ine=ine+exp(-sqrt(-1)*2*pi*f*T*dt)*ez_inc(ja-1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  电荷密度Dz
    for i=2:N-1;      %  为了使每个电场周围都有磁场进行数组下标处理
        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;

%%  脉冲或正弦源的加入
    source=exp((-0.5)*((t0-T)/spread ).^2);      %  脉冲源
%     source=sin(2*pi*f*T*dt);                    %  正弦波源
    ez_inc(1)=source;                             %  TM平面波源
    %dz(is,js)=source;                        %  源
   % dz(is,js)=source;

%%  电荷密度Dz加入射场
    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;

%%  边界电场置零,作为辅助PML
    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;


%%  金属边界条件
    for i=N/2-halfgrid:N/2+halfgrid-1;
        for j=N/2-halfgrid:N/2+halfgrid-1;
          ez(i,j)=0;
        end;
    end;


%  傅里叶变换Ez;
    s=0;
    for i=pa:pb+1;
        s=s+1;
        ez_out(1,s)=ez_out(1,s)+exp(-sqrt(-1)*2*pi*f*T*dt)*ez(i,qa);  %  下
        ez_out(2,s)=ez_out(2,s)+exp(-sqrt(-1)*2*pi*f*T*dt)*ez(i,qb);  %  上
    end;
    s=0;
    for j=qa:qb+1;
        s=s+1;
        ez_out(3,s)=ez_out(3,s)+exp(-sqrt(-1)*2*pi*f*T*dt)*ez(pa,j);  %  左
        ez_out(4,s)=ez_out(4,s)+exp(-sqrt(-1)*2*pi*f*T*dt)*ez(pb,j);  %  右
    end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%*************************磁场由电场更新*********************************%%

%%  更新平面波磁场
    for j=1:N-1;
        hx_inc(j)=hx_inc(j)+0.5*(ez_inc(j)-ez_inc(j+1));
    end;

%%  入射磁场傅里叶变换
    inh=inh+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hx_inc(ja-1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  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;

%%  磁场Hx加入射场
    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;

%  傅里叶变换Hx;
    s=0;
    % 注意：电场和磁场相差半个时间步
    for i=pa:pb;
        s=s+1;
        hx_out(1,s)=hx_out(1,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hx(i,qa);  %  下
        hx_out(2,s)=hx_out(2,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hx(i,qb);  %  上
    end;
    s=0;
    for j=qa:qb;
        s=s+1;
        hx_out(3,s)=hx_out(3,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hx(pa,j);  %  左
        hx_out(4,s)=hx_out(4,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hx(pb,j);  %  右
    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;

%%  磁场Hy加入射场
    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;

%  傅里叶变换Hy;
    s=0;
    for i=pa:pb;
        s=s+1;
        hy_out(1,s)=hy_out(1,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hy(i,qa);  %  下
        hy_out(2,s)=hy_out(2,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hy(i,qb);  %  上
    end;
    s=0;
    for j=qa:qb;
        s=s+1;
        hy_out(3,s)=hy_out(3,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hy(pa,j);  %  左
        hy_out(4,s)=hy_out(4,s)+exp(-sqrt(-1)*2*pi*f*(T+1/2)*dt)*hy(pb,j);  %  右
    end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  显示
     plot(hx(40,:));

    mesh(ez)
    axis([1 120 1 120 -0.5 0.5]);
    drawnow;
end;

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%****************************近远场外推**********************************%%
%
%%  电场平均
for i=1:length
    ez_outave(:,i)=(ez_out(:,i)+ez_out(:,i+1))/2;
end

current=zeros(4,length);    %  电流z方向
magnetic_x=zeros(4,length); %  磁流x方向
magnetic_y=zeros(4,length); %  磁流y方向

%%  电流z
current(1,:)=hx_out(1,:);   %  下
current(2,:)=-hx_out(2,:);  %  上
current(3,:)=-hy_out(3,:);  %  左
current(4,:)=hy_out(4,:);   %  右

%%  磁流x
magnetic_x(1,:)=ez_outave(1,:);   %  下
magnetic_x(2,:)=-ez_outave(2,:);  %  上
magnetic_x(3,:)=0;                %  左
magnetic_x(4,:)=0;                %  右

%%  磁流y
magnetic_y(1,:)=0;                  %  下
magnetic_y(2,:)=0;                  %  上
magnetic_y(3,:)=-ez_outave(3,:);    %  左
magnetic_y(4,:)=ez_outave(4,:);     %  右

%%  外推边界坐标X,Y
posx=zeros(4,length);
posy=zeros(4,length);

posx(1,:)=linspace(pa*ddx,pb*ddx,length)+ddx/2;   %  下
posx(2,:)=linspace(pa*ddx,pb*ddx,length)+ddx/2;   %  上
posx(3,:)=pa*ddx;  %  左
posx(4,:)=pb*ddx;  %  右

posy(1,:)=qa*ddx;  %  下
posy(2,:)=qb*ddx;  %  上
posy(3,:)=linspace(qa*ddx,qb*ddx,length)+ddx/2;  %  左
posy(4,:)=linspace(qa*ddx,qb*ddx,length)+ddx/2;  %  右

%%  归一化fz,fmx,fmy求解
fz=ddx*current/abs(inh);
fmx=ddx*magnetic_x/abs(inh);
fmy=ddx*magnetic_y/abs(inh);

%%  RCS求解;
co=0;
for phi=pi/2:pi/180:pi+pi/2;
    co=co+1;
    ss=0;
    for t=1:4;
        for s=1:length
            kr=posx(t,s)*cos(phi)+posy(t,s)*sin(phi);
            ss=ss+(-fz(t,s)-fmx(t,s)*sin(phi)+fmy(t,s)*cos(phi))*exp(sqrt(-1)*k*kr);  %%  外推公式
        end
    end;
    rcs(co)=k/4*(abs(ss)).^2;
end;
rcs=10*log10(rcs/(lamda));
save fdtdupml rcs;
figure(2)
plot(rcs,'g');

rcs_upml=rcs;
save rcs_upml.mat rcs_upml;

toc;
% hold on;

那位能告诉我红色的那段程序用的是什么公式吗？为什么总是看不懂，还有0.5是哪边来的，谢谢各位留言。。

离线gwzhao

方恨少

UID ：17098

注册：2008-08-24
登录：2019-01-09
发帖：1374
等级：荣誉管理员

2楼发表于: 2009-05-06 11:12:17

    for j=2:N-1;
        ez_inc(j)=ez_inc(j)+0.5*(hx_inc(j-1)-hx_inc(j));
    end;
    for j=1:N-1;
        hx_inc(j)=hx_inc(j)+0.5*(ez_inc(j)-ez_inc(j+1));
    end;

这个是1D FDTD来模拟平面波的，你随便找个FDTD的书，看一下1D FDTD的简单例子就明白了。

共1条评分

alai318

rf币 +5

感谢您的资料

2009-05-06

逆流而上

离线flanky

UID ：19721

注册：2008-10-21
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3楼发表于: 2009-05-06 18:03:22

谢谢楼上的。。

离线cem-uestc

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4楼发表于: 2009-05-07 14:14:12

对应书上来分析代码，是最好的学习FDTD方式

欢迎光临
http://www.mwtee.com/home.php?mod=space&uid=13535

离线tapioca

UID ：73610

注册：2011-03-11
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5楼发表于: 2011-06-03 16:49:02

有木有人知道斜入射怎么仿真啊。。。一维波的斜入射打到海平面。。。FDTD网格怎么设置呢

离线gwzhao

方恨少

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6楼发表于: 2011-06-06 21:16:47

回 5楼(tapioca) 的帖子

论坛里有很多类似问题的帖子，你可以找找看。

逆流而上

离线jiandan1986

UID ：77042

注册：2011-05-09
登录：2012-04-16
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7楼发表于: 2011-06-09 21:04:49

dz应该是对应的系数，在使用中心差分时定义的。

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紧急求助 2D FDTD 程序 会的指点一下 万分感谢

紧急求助 2D FDTD 程序会的指点一下万分感谢