有哪位大声有声学DtN边界或者PML的程序吗
如题自己写的程序老感觉运行结果有点问题，想对比一下，谢谢 一阶声波方程波场模拟，采用的是交错网格，二阶精度，pml边界%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%交错网格---非均匀介质二维声波方程(一阶压力--速度)、2阶时间差分、2阶空间差分精度
%%加上边界
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
close all;clear,clc
tic
%%***********************震源为Ricker子波*********
dtt=0.0001;
tt=-0.06:dtt:0.06;
fm=30;
A=0.01;
wave=A*(1-2*(pi*fm*tt).^2).*exp(-(pi*fm*tt).^2);
% plot(wave),title('震源子波--Ricker子波');
%%***********************************************
%% 模型参数设置
dz=5; % 纵向网格大小，单位m
dx=5; % 横向网格大小，单位m
dt=0.0001; % 时间步长，单位s
T=0.5; % 波动传播时间，单位s
wave(round(T/dt))=0; % 将子波后面部分补零
% %% 研究区域
% z=-75:dz:750; x=-1000:dz:1000;
pml=50; % 吸收层的网格数
plx=pml*dx; % 上下吸收层的厚度
plz=pml*dz; % 左右吸收层的厚度
z=-750-plz:dz:750+plz;
x=-1000-plx:dx:1000+plx;% 采样区间
n=length(z); m=length(x); % 采样点数
z0=round(n/2); x0=round(m/2); % 震源位置
Vmax=0; % 纵波最大速度
%%Setting Velocity & Density
zt=-750-plz:dz/2:750+plz;
xt=-1000-plx:dx/2:1000+plx; % 速度与密度采样区间
nt=length(zt); mt=length(xt); % 速度与密度采样点数目
V=zeros(n,m); % 介质速度,m/s
d=zeros(nt,mt); % 介质密度,kg/m^3
%%均匀介质模型
for i=1:n
for k=1:m
V(i,k)=2.0e3;
end
end
for i=1:n
for k=1:m
d(2*i,2*k)=2.3e3;
end
end
% % %%层状介质模型
% % for i=1:n
% % for k=1:m
% % if i < round(n/3)
% % V(i,k)=2.3e3;
% % else
% % V(i,k)=3.0e3;
% % end
% % end
% % end
for i=1:n-1
for k=1:m-1
d(2*i+1,2*k)=(d(2*i,2*k)+d(2*(i+1),2*k))/2;
d(2*i,2*k+1)=(d(2*i,2*k)+d(2*i,2*(k+1)))/2;
end
end
for i=1:n
for k=1:m
if V(i,k) > Vmax
Vmax=V(i,k);
end
end
end
%%**********************衰减系数************************
%% ddx、ddz 即，x方向和z方向的衰减系数
R=1e-6; % 理论反射系数
ddx=zeros(n,m); ddz=zeros(n,m);
for i=1:n
for k=1:m
%% 区域1
if i>=1 & i<=pml & k>=1 & k<=pml
x=pml-k;z=pml-i;
ddx(i,k)=-log(R)*3*Vmax*x^2/(2*plx^2);
ddz(i,k)=-log(R)*3*Vmax*z^2/(2*plz^2);
elseif i>=1 & i<=pml & k>m-pml & k<=m
x=k-(m-pml);z=pml-i;
ddx(i,k)=-log(R)*3*Vmax*x^2/(2*plx^2);
ddz(i,k)=-log(R)*3*Vmax*z^2/(2*plz^2);
elseif i>n-pml & i<=n & k>=1 & k<=pml
x=pml-k;z=i-(n-pml);
ddx(i,k)=-log(R)*3*Vmax*x^2/(2*plx^2);
ddz(i,k)=-log(R)*3*Vmax*z^2/(2*plz^2);
elseif i>n-pml & i<=n & k>m-pml & k<=m
x=k-(m-pml);z=i-(n-pml);
ddx(i,k)=-log(R)*3*Vmax*x^2/(2*plx^2);
ddz(i,k)=-log(R)*3*Vmax*z^2/(2*plz^2);
%% 区域2
elseif i<=pml & k>pml & k<m-pml+1
x=0;z=pml-i;
ddx(i,k)=0;ddz(i,k)=-log(R)*3*Vmax*z^2/(2*plz^2);
elseifi>n-pml & i<=n & k>pml & k<=m-pml
x=0;z=i-(n-pml);
ddx(i,k)=0;ddz(i,k)=-log(R)*3*Vmax*z^2/(2*plz^2);
%% 区域3
elseif i>pml & i<=n-pml & k<=pml
x=pml-k;z=0;
ddx(i,k)=-log(R)*3*Vmax*x^2/(2*plx^2);ddz(i,k)=0;
elseif i>pml & i<=n-pml & k>m-pml & k<=m
x=k-(m-pml);z=0;
ddx(i,k)=-log(R)*3*Vmax*x^2/(2*plx^2);ddz(i,k)=0;
end
end
end
% figure(1),imagesc(ddz),title('z方向衰减系数');
% figure(2),imagesc(ddx),title('x方向衰减系数');
%%**************************************************
%%**********************波场模拟********************
p0=zeros(n,m); p1=zeros(n,m);
px0=zeros(n,m); px1=zeros(n,m);
pz0=zeros(n,m); pz1=zeros(n,m);
K=zeros(n,m);
Vx1=zeros(nt,mt); Vx0=zeros(nt,mt);
Vz1=zeros(nt,mt); Vz0=zeros(nt,mt);
for t=dt:dt:T
p0(z0,x0)=dt*V(z0,x0)^2*wave(round(t/dt));
for i=2:n-1
for k=2:m-1
K(i,k)=d(2*i,2*k)*V(i,k)^2;
Vz1(2*i+1,2*k)=((1-0.5*dt*ddz(i,k))*Vz0(2*i+1,2*k)-dt*(p0(i+1,k)-p0(i,k))/(d(2*i+1,2*k)*dz))/(1+0.5*dt*ddz(i,k));
Vx1(2*i,2*k+1)=((1-0.5*dt*ddx(i,k))*Vx0(2*i,2*k+1)-dt*(p0(i,k+1)-p0(i,k))/(d(2*i,2*k+1)*dx))/(1+0.5*dt*ddx(i,k));
pz1(i,k)=((1-0.5*dt*ddz(i,k))*pz0(i,k)-K(i,k)*dt*(Vz1(2*i+1,2*k)-Vz1(2*i-1,2*k))/dz)/(1+0.5*dt*ddz(i,k));
px1(i,k)=((1-0.5*dt*ddx(i,k))*px0(i,k)-K(i,k)*dt*(Vx1(2*i,2*k+1)-Vx1(2*i,2*k-1))/dx)/(1+0.5*dt*ddx(i,k));
p1(i,k)=px1(i,k)+pz1(i,k);
end
end
p0=p1;
pz0=pz1;px0=px1;
Vz0=Vz1;Vx0=Vx1;
for i=1:n-2*pml
for k=1:m-2*pml
p(i,k)=p1(i+pml,k+pml);
end
end
% imagesc(p1),title('声波波场'),pause(0.0000001);
end
figure(1),imagesc(p1);title('声波波场--交错网格，2阶');
figure(2),imagesc(p);title('声波方程--交错网格、加边界');
% figure(2),imagesc(pz1);title('z分量');
% figure(3),imagesc(px1);title('x分量');
%%*************************************************
toc
%***********************************************************************
% 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:
%
% ----------------------------------------------
% || 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 ||
% ----------------------------------------------
%
% 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;
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=;
sig=;
mur=;
sim=;
%***********************************************************************
% 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();
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();
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();
colorbar;
axis image;
axis off;
title(['Hz at time step = 0']);
rect=get(gcf,'Position');
rect(1:2)=;
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)-...
ex(1:ie,1));
hzybcf(iebc+ie+1:iefbc,jebc)=...
dahzybcf(iebc+ie+1:iefbc,jebc).*hzybcf(iebc+ie+1:iefbc,jebc)-...
dbhzybcf(iebc+ie+1:iefbc,jebc).*(exbcf(iebc+ie+1:iefbc,jebc)-...
exbcr(1:iebc,1));
% BACK
hzybcb(1:iefbc,2:jebc)=dahzybcb(1:iefbc,2:jebc).*hzybcb(1:iefbc,2:jebc)-...
dbhzybcb(1:iefbc,2:jebc).*(exbcb(1:iefbc,2:jebc)-exbcb(1:iefbc,3:jbbc));
hzybcb(1:iebc,1)=dahzybcb(1:iebc,1).*hzybcb(1:iebc,1)-...
dbhzybcb(1:iebc,1).*(exbcl(1:iebc,jb)-exbcb(1:iebc,2));
hzybcb(iebc+1:iebc+ie,1)=...
dahzybcb(iebc+1:iebc+ie,1).*hzybcb(iebc+1:iebc+ie,1)-...
dbhzybcb(iebc+1:iebc+ie,1).*(ex(1:ie,jb)-exbcb(iebc+1:iebc+ie,2));
hzybcb(iebc+ie+1:iefbc,1)=...
dahzybcb(iebc+ie+1:iefbc,1).*hzybcb(iebc+ie+1:iefbc,1)-...
dbhzybcb(iebc+ie+1:iefbc,1).*(exbcr(1:iebc,jb)-...
exbcb(iebc+ie+1:iefbc,2));
% LEFT
hzybcl(:,1:je)=dahzybcl(:,1:je).*hzybcl(:,1:je)-...
dbhzybcl(:,1:je).*(exbcl(:,1:je)-exbcl(:,2:jb));
% RIGHT
hzybcr(:,1:je)=dahzybcr(:,1:je).*hzybcr(:,1:je)-...
dbhzybcr(:,1:je).*(exbcr(:,1:je)-exbcr(:,2:jb));
%***********************************************************************
% Visualize fields
%***********************************************************************
if mod(n,4)==0;
timestep=int2str(n);
subplot(3,1,1),pcolor(ex');
shading flat;
caxis([-80.0 80.0]);
axis();
colorbar;
axis image;
axis off;
title(['Ex at time step = ',timestep]);
subplot(3,1,2),pcolor(ey');
shading flat;
caxis([-80.0 80.0]);
axis();
colorbar;
axis image;
axis off;
title(['Ey at time step = ',timestep]);
subplot(3,1,3),pcolor(hz');
shading flat;
caxis([-0.2 0.2]);
axis();
colorbar;
axis image;
axis off;
title(['Hz at time step = ',timestep]);
nn=n/4;
M(:,nn)=getframe(gcf,rect);
end;
%***********************************************************************
% END TIME-STEPPING LOOP
%***********************************************************************
end
movie(gcf,M,0,10,rect); 下面是二阶声波方程的PML边界处理程序，Visual C++的
风花雪月 发表于 2016-3-21 15:39
下面是二阶声波方程的PML边界处理程序，Visual C++的
多谢大神，不知道是否有基于有限元的没啊
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