FDTD的MATLAB解决方案

%初始化Matlab工作空间
clear all;close all;clc;

%定义问题空间参数
define_problem_space_parameters;
define_geometry;
define_sources_and_lumped_elements;
define_output_parameters;

%初始化问题空间和参数
initialize_fdtd_material_grid;

if run_simulation
    initialize_fdtd_parameters_and_arrays;
    initialize_sources_and_lumped_elements;
    initialize_updating_coefficients;
    initialize_boundary_conditions;
    initialize_output_parameters;
    
    %FDTD主循环
    run_fdtd_time_marching_loop;
    
end

disp('defining the problem space parameters');

%最大的仿真时间步
number_of_time_steps=1000;

%高斯脉冲准确因子
number_of_cells_per_wavelength=20;

%x，y，z方向单位网格尺寸（米）
dx=0.389e-3;
dy=0.4e-3;
dz=0.265e-3;
ra_x=0.681;
ra_y=0.665;

%《边界条件》
%定义的边界条件参数
%'pec'：完美的电导体
%'cpml'：完美吸收边界PML
%当cpml_number_of_cells小于零时
%CPML吸收边界向仿真空间内部扩展

%边界形式定义，边界的网格数
boundary.type_xn='cpml';
boundary.air_buffer_number_of_cells_xn=10;%吸收边界与物体之间的网格数
boundary.cpml_number_of_cells_xn=8;

boundary.type_xp='cpml';
boundary.air_buffer_number_of_cells_xp=10;%吸收边界与物体之间的网格数
boundary.cpml_number_of_cells_xp=8;

boundary.type_yn='cpml';
boundary.air_buffer_number_of_cells_yn=10;%吸收边界与物体之间的网格数
boundary.cpml_number_of_cells_yn=8;

boundary.type_yp='cpml';
boundary.air_buffer_number_of_cells_yp=10;%吸收边界与物体之间的网格数
boundary.cpml_number_of_cells_yp=8;

boundary.type_zn='cpml';
boundary.air_buffer_number_of_cells_zn=10;%吸收边界与物体之间的网格数
boundary.cpml_number_of_cells_zn=8;

boundary.type_zp='cpml';
boundary.air_buffer_number_of_cells_zp=10;%吸收边界与物体之间的网格数
boundary.cpml_number_of_cells_zp=8;

%<材料形式>
%材料形式定义
%eps_r：相对介电常数
%mu_r：相对磁导率
%sigma_e：电导率
%sigma_m：磁电导率

%空气
material_types(1).eps_r=1;
material_types(1).mu_r=1;
material_types(1).sigma_e=0;
material_types(1).sigma_m=0;
material_types(1).color=[1 1 1];

%PEC：理想电导体
material_types(2).eps_r=1;
material_types(2).mu_r=1;
material_types(2).sigma_e=1e10;
material_types(2).sigma_m=0;
material_types(2).color=[1 0 0];

%PMC：理想磁导体
material_types(3).eps_r=1;
material_types(3).mu_r=1;
material_types(3).sigma_e=0;
material_types(3).sigma_m=1e10;
material_types(3).color=[0 1 0];

%一种介质
material_types(4).eps_r=2.2;
material_types(4).mu_r=1;
material_types(4).sigma_e=0;
material_types(4).sigma_m=0;
material_types(4).color=[0 0 1];

%一种介质
material_types(5).eps_r=3.2;
material_types(5).mu_r=1.4;
material_types(5).sigma_e=0.5;
material_types(5).sigma_m=0.3;
material_types(5).color=[1 1 0];

%空气，PEC，PMC材料索引

material_type_index_air=1;
material_type_index_pec=2;
material_type_index_pmc=3;

disp('defining the problem geometry');

bricks=[ ];
spheres=[ ];

%用材料四来定义一个立方体
bricks(1).min_x=0;
bricks(1).min_y=0;
bricks(1).min_z=0;
bricks(1).max_x=24e-3;
bricks(1).max_y=20e-3;
bricks(1).max_z=11e-3;
bricks(1).material_type=4;

%用材料二来定义一个立方体
bricks(2).min_x=-20e-3;
bricks(2).min_y=-20e-3;
bricks(2).min_z=-11e-3;
bricks(2).max_x=0;
bricks(2).max_y=0;
bricks(2).max_z=0;
bricks(2).material_type=2;

%用材料五定义一个球
spheres(1).radius=20e-3;
spheres(1).center_x=0;
spheres(1).center_y=0;
spheres(1).center_z=40e-3;
spheres(1).material_type=5;

%用材料一定义一个球
spheres(2).radius=15e-3;
spheres(2).center_x=0;
spheres(2).center_y=0;
spheres(2).center_z=40e-3;
spheres(2).material_type=1;

for ind=1:number_of_bricks
    
    %确定金属薄片的位置
    blx=round((bricks(ind).min_x)-fdtd_domain.min_x)/dx+1;
    bly=round((bricks(ind).min_y)-fdtd_domain.min_y)/dy+1;
    blz=round((bricks(ind).min_z)-fdtd_domain.min_z)/dz+1;
    
    bux=round((bricks(ind).min_x)-fdtd_domain.min_x)/dx+1;
    buy=round((bricks(ind).min_y)-fdtd_domain.min_y)/dy+1;
    buz=round((bricks(ind).min_z)-fdtd_domain.min_z)/dz+1;
    
    if(blx==bux)
        gay(blx,bly:buy-1,blz:buz)=0;
        gaz(blx,bly:buy,blz:buz-1)=0;
    end
    if(bly==buy)
        gaz(blx:bux,bly,blz:buz-1)=0;
        gax(blx:bux-1,bly,blz:buz)=0;
    end
    if(blz==buz)
        gax(blx:bux-1,bly:buy,blz)=0;
        gay(blx:bux,bly:buy-1,blz)=0;
    end
end

disp('initializing FDTD material grid');

%基于物体的位置和边界条件确定问题空间的尺寸
calculate_domain_size；

%空气填充所有问题空间
material_3d_space=ones(nx,ny,nz);

%生成球
create_spheres;

%生成立方体
create_bricks;

%初始化材料参数
eps_r_x=ones(nx,nyp1,nzp1);
eps_r_y=ones(nxp1,ny,nzp1);
eps_r_z=ones(nxp1,nyp1,nz);
mu_r_x=ones(nxp1,ny,nz);
mu_r_y=ones(nx,nyp1,nz);
mu_r_z=ones(nx,ny,nzp1);
sigma_e_x=zeros(nx,nyp1,nzp1);
sigma_e_y=zeros(nxp1,ny,nzp1);
sigma_e_z=zeros(nxp1,nyp1,nz);
sigma_m_x=zeros(nxp1,ny,nz);
sigma_m_y=zeros(nx,nyp1,nz);
sogma_m_z=zeros(nx,ny,nzp1);

%材料参数赋值（边界处材料取平均值）
calculate_material_component_values;

%生成零厚度PEC平板
create_PEC_plates;

disp('calculating the number of cells in the problem space');

number_of_spheres=size(spheres,2);
number_of_bricks=size(bricks,2);

%找到计算空间的所填充物体的最大值和最小值，并存储在fdtd_domain的结构体中
number_of_objects=1;
for i=1:number_of_spheres
    min_x(number_of_objects)=spheres(i).center_x-spheres(i).radius;
    min_y(number_of_objects)=spheres(i).center_y-spheres(i).radius;
    min_z(number_of_objects)=spheres(i).center_z-spheres(i).radius;
    max_x(number_of_objects)=spheres(i).center_x+spheres(i).radius;
    max_y(number_of_objects)=spheres(i).center_y+spheres(i).radius;
    max_z(number_of_objects)=spheres(i).center_z+spheres(i).radius;
    number_of_objects=number_of_objects+1;
end
for i=1:number_of_bricks
    min_x(number_of_objects)=bricks(i).min_x;
    min_y(number_of_objects)=bricks(i).min_y;
    min_z(number_of_objects)=bricks(i).min_z;
    max_x(number_of_objects)=bricks(i).max_x;
    max_y(number_of_objects)=bricks(i).max_y;
    max_z(number_of_objects)=bricks(i).max_z;
    number_of_objects=number_of_objects+1;
end

fdtd_domain.min_x=min(min_x);
fdtd_domain.min_y=min(min_y);
fdtd_domain.min_z=min(min_z);
fdtd_domain.max_x=max(max_x);
fdtd_domain.max_y=max(max_y);
fdtd_domain.max_z=max(max_z);

%在最大值和最小值上加入空气缓冲区的大小
fdtd_domain.min_x=fdtd_domain.min_x...
    -dx*boundary.air_buffer_number_of_cells_xn;
fdtd_domain.min_y=fdtd_domain.min_y...
    -dy*boundary.air_buffer_number_of_cells_yn;
fdtd_domain.min_z=fdtd_domain.min_z...
    -dz*boundary.air_buffer_number_of_cells_zn;
fdtd_domain.max_x=fdtd_domain.max_x...
    -dx*boundary.air_buffer_number_of_cells_xp;
fdtd_domain.max_y=fdtd_domain.max_y...
    -dy*boundary.air_buffer_number_of_cells_yp;
fdtd_domain.max_z=fdtd_domain.max_z...
    -dz*boundary.air_buffer_number_of_cells_zp;

%根据边界条件加入吸收边界的网格数
if strcmp(boundary.type_xn,'cpml')&&...
        (boundary.cpml_number_of_cells_xn>0)
    fdtd_domain.min_x=fdtd_domain.min_x...
        -dx*boundary.cpml_number_of_cells_xn;
end
if strcmp(boundary.type_xp,'cpml')&&...
        (boundary.cpml_number_of_cells_xp>0)
    fdtd_domain.max_x=fdtd_domain.max_x...
        +dx*boundary.cpml_number_of_cells_xp;
end
if strcmp(boundary.type_yn,'cpml')&&...
        (boundary.cpml_number_of_cells_yn>0)
    fdtd_domain.min_y=fdtd_domain.min_y...
        -dy*boundary.cpml_number_of_cells_yn;
end
if strcmp(boundary.type_yp,'cpml')&&...
        (boundary.cpml_number_of_cells_yp>0)
    fdtd_domain.max_y=fdtd_domain.max_y...
        +dy*boundary.cpml_number_of_cells_yp;
end
if strcmp(boundary.type_zn,'cpml')&&...
        (boundary.cpml_number_of_cells_zn>0)
    fdtd_domain.min_z=fdtd_domain.min_z...
        -dz*boundary.cpml_number_of_cells_zn;
end
if strcmp(boundary.type_zp,'cpml')&&...
        (boundary.cpml_number_of_cells_zp>0)
    fdtd_domain.max_z=fdtd_domain.max_z...
        +dz*boundary.cpml_number_of_cells_zp;
end

%确定问题空间的大小
fdtd_domain.size_x=fdtd_domain.max_x-fdtd_domain.min_x;
fdtd_domain.size_y=fdtd_domain.max_y-fdtd_domain.min_y;
fdtd_domain.size_z=fdtd_domain.max_z-fdtd_domain.min_z;

%确定在x，y，z方向的网格数
nx=round(fdtd_domain.size_x/dx);
ny=round(fdtd_domain.size_y/dy);
nz=round(fdtd_domain.size_z/dz);

%根据网格数，重新调整域的大小
fdtd_domain.size_x=nx*dx;
fdtd_domain.size_y=ny*dy;
fdtd_domain.size_z=nz*dz;

fdtd_domain.max_x=fdtd_domain.min_x+fdtd_domain.size_x;
fdtd_domain.max_y=fdtd_domain.min_y+fdtd_domain.size_y;
fdtd_domain.max_z=fdtd_domain.min_z+fdtd_domain.size_z;

%根据电磁场位置确定的辅助参数
nxp1=nx+1;
nyp1=ny+1;
nzp1=nz+1;
nxm1=nx-1;
nxm2=nx-2;
nym1=ny-1;
nym2=ny-2;
nzm1=nz-1;
nzm2=nz-2;

%创建阵列存储的网格的中心坐标
fdtd_domain.cell_center_coordinates_x=zeros(nx,ny,nz);
fdtd_domain.cell_center_coordinates_y=zeros(nx,ny,nz);
fdtd_domain.cell_center_coordinates_z=zeros(nx,ny,nz);
for ind=1:nx
    fdtd_domain.cell_center_coordinates_x(ind,:,:)=...
        (ind-0.5)*dx+fdtd_domain.min_x;
end
for ind=1:ny
    fdtd_domain.cell_center_coordinates_y(ind,:,:)=...
        (ind-0.5)*dy+fdtd_domain.min_y;
end
for ind=1:nz
    fdtd_domain.cell_center_coordinates_z(ind,:,:)=...
        (ind-0.5)*dz+fdtd_domain.min_z;
end

cx=fdtd_domain.cell_center_coordinates_x;
cy=fdtd_domain.cell_center_coordinates_y;
cz=fdtd_domain.cell_center_coordinates_z;

for ind=1:number_of_spheres
    %distance为网格中心点到球中心点距离
    distance=sqrt((spheres(ind).center_x-cx).^2 ...
                    +(spheres(ind).center_y-cy).^2 ...
                    +(spheres(ind).center_z-cz).^2 );
        I=find(distance<=spheres(ind).radius);
        material_3d_space(I)=spheres(ind).material_type;
end
clear cx cy cz;

disp('creating bricks');

for ind=1:number_of_bricks
    %确定每个立方体的坐标
    blx=round((bricks(ind).min_x-fdtd_domain.min_x)/dx)+1;
    bly=round((bricks(ind).min_y-fdtd_domain.min_y)/dy)+1;
    blz=round((bricks(ind).min_z-fdtd_domain.min_z)/dz)+1;
    
    bux=round((bricks(ind).max_x-fdtd_domain.min_x)/dx)+1;
    buy=round((bricks(ind).max_y-fdtd_domain.min_y)/dy)+1;
    buz=round((bricks(ind).max_z-fdtd_domain.min_z)/dz)+1;
    
    %给每个立方体赋材料属性
    material_3d_space(blx:bux-1,bly:buy-1,blz:buz-1)...
        =bricks(ind).material_type;
end