實現(xiàn)有限差分法計算電場強(qiáng)度最新

1、實驗一：有限差分法研究靜電場邊值問題實驗報告人： 年級和班級： 學(xué)號：1. 實驗用軟件工具： Matlab2. 實驗原理：電磁場課本P36-381) 差分方程2) 差分方程組的解簡單迭代法高斯-賽德爾迭代法逐次超松弛法3. 實驗步驟：1）簡單迭代法程序：hx=41;hy=21;v1=zeros(hy,hx);v1(hy,:)=zeros(1,hx);v1(1,:)=ones(1,hx)*100;v1(:,1)=zeros(hy,1);v1(:,hx)=zeros(hy,1);v1v2=v1;maxt=1;t=0;k=0;while(maxt>1e-5) k=k+1; maxt=0;for

2、 i=2:hy-1 for j=2:hx-1 v2(i,j)=(v1(i,j+1)+v1(i+1,j)+v1(i-1,j)+v1(i,j-1)/4; t=abs(v2(i,j)-v1(i,j); if(t>maxt) maxt=t;end endendv1=v2;endv2kclfsubplot(1,2,1),mesh(v2)axis(0,41,0,21,0,100)subplot(1,2,2),contour(v2,15)hold onaxis(-1,42,-1,25)plot(1,1,hx,hx,1,1,hy+1,hy+1,1,1,'r')text(hx/2,0.3,

3、'0V','fontsize',11);text(hx/2-0.5,hy+0.5,'100V','fontsize',11);text(-0.5,hy/2,'0V','fontsize',11);text(hx+0.3,hy/2,'0V','fontsize',11);hold off當(dāng)W=1e-5, 迭代次數(shù)：1401次2）高斯-賽德爾迭代法程序：hx=41;hy=21;v1=ones(hy,hx);v1(hy,:)=zeros(1,hx);v1(1,:)=ones

4、(1,hx)*100;v1(:,1)=zeros(hy,1);v1(:,hx)=zeros(hy,1);v2=v1;maxt=1;t=0;k=0;while(maxt>1e-5) k=k+1; maxt=0;for i=2:hy-1 for j=2:hx-1 v2(i,j)=(v1(i,j+1)+v1(i+1,j)+v2(i-1,j)+v2(i,j-1)/4; t=abs(v2(i,j)-v1(i,j); if(t>maxt) maxt=t;end endendv1=v2;endv2kclfsubplot(1,2,1),mesh(v2)axis(0,41,0,21,0,100)su

5、bplot(1,2,2),contour(v2,15)hold onaxis(-1,42,-1,25)plot(1,1,hx,hx,1,1,hy+1,hy+1,1,1,'r')text(hx/2,0.3,'0V','fontsize',11);text(hx/2-0.5,hy+0.5,'100V','fontsize',11);text(-0.5,hy/2,'0V','fontsize',11);text(hx+0.3,hy/2,'0V','fontsize&

6、#39;,11);hold off當(dāng)W=1e-5, 迭代次數(shù)：740次3）逐次超松弛法程序：hx=41;hy=21;v1=zeros(hy,hx);v1(hy,:)=zeros(1,hx);v1(1,:)=ones(1,hx)*100;v1(:,1)=zeros(hy,1);v1(:,hx)=zeros(hy,1);v1v2=v1;maxt=1;t=0;alpha=input('please input the value of alpha(alpha>=1 && alpha<2):');k=0;while(maxt>1e-5) k=k+1;

7、maxt=0;for i=2:hy-1 for j=2:hx-1 v2(i,j)=v1(i,j)+(v1(i,j+1)+v1(i+1,j)+v2(i-1,j)+v2(i,j-1)-4*v1(i,j)*alpha/4; t=abs(v2(i,j)-v1(i,j); if(t>maxt) maxt=t;end endendv1=v2;endv2kclfsubplot(1,2,1),mesh(v2)axis(0,41,0,21,0,100)subplot(1,2,2),contour(v2,15)hold onaxis(-1,42,-1,25)plot(1,1,hx,hx,1,1,hy+1,h

8、y+1,1,1,'r')text(hx/2,0.3,'0V','fontsize',11);text(hx/2-0.5,hy+0.5,'100V','fontsize',11);text(-0.5,hy/2,'0V','fontsize',11);text(hx+0.3,hy/2,'0V','fontsize',11);hold off當(dāng)W=1e-5, alpha取不同值時迭代次數(shù)alpha1.01.11.21.31.41.51.61.71.81.9迭

9、代次數(shù)742616509417336263197133801614）畫三維曲面圖和等位線圖（逐次超松弛法最佳迭代次數(shù)時）程序：hx=41;hy=21;v1=zeros(hy,hx);v1(hy,:)=zeros(1,hx);v1(1,:)=ones(1,hx)*100;v1(:,1)=zeros(hy,1);v1(:,hx)=zeros(hy,1);v1v2=v1;maxt=1;t=0;alpha=1.8;k=0;while(maxt>1e-5) k=k+1; maxt=0;for i=2:hy-1 for j=2:hx-1 v2(i,j)=v1(i,j)+(v1(i,j+1)+v1(i

10、+1,j)+v2(i-1,j)+v2(i,j-1)-4*v1(i,j)*alpha/4; t=abs(v2(i,j)-v1(i,j); if(t>maxt) maxt=t;end endendv1=v2;endv2kclfsubplot(1,2,1),mesh(v2)axis(0,41,0,21,0,100)subplot(1,2,2),contour(v2,15)hold onaxis(-1,42,-1,25)plot(1,1,hx,hx,1,1,hy+1,hy+1,1,1,'r')text(hx/2,0.3,'0V','fontsize'

11、;,11);text(hx/2-0.5,hy+0.5,'100V','fontsize',11);text(-0.5,hy/2,'0V','fontsize',11);text(hx+0.3,hy/2,'0V','fontsize',11);hold off貼圖：4實驗結(jié)論（1）matlab軟件在使用有限差分法研究靜電場邊值問題中有著重要的作用，它能夠快捷有效并且準(zhǔn)確的解決邊值問題，是解決計算相對復(fù)雜問題的有效工具。（2）從各個方法的迭代次數(shù)可以看出：在給定相同的最大允許誤差W的條件下，簡單迭代法使用的次數(shù)最多，為1401次