基于HASM模型的高精度建模matlab仿真

1.程序功能描述
本课题主要使用HASM进行高精度建模，主要对HASM模型进行介绍以及在实际中如何进行简化实现的。HASM原始的模型如下所示：

2.测试软件版本以及运行结果展示
MATLAB2022A版本运行

3.核心程序

                   %第一类基本变量
                   E(i,j) = 1 + (( f(i,j+1,n) - f(i,j-1,n) )/( 2*h ))^2;
                   F(i,j) =     (( f(i,j+1,n) - f(i,j-1,n) )/( 2*h )) * (( f(i+1,j,n) - f(i-1,j,n) )/( 2*h ));
                   G(i,j) = 1 + (( f(i,j+1,n) - f(i,j-1,n) )/( 2*h ))^2;
  
                   %第二类基本变量
                   L(i,j) = ( f(i+1,j,n) - 2*f(i,j,n) + f(i-1,j,n) )/(sqrt( 1 +  (( f(i,j+1,n) - f(i,j-1,n) )/( 2*h ))^2  +  (( f(i+1,j,n) - f(i-1,j,n) )/( 2*h ))^2));
                   N(i,j) = ( f(i,j+1,n) - 2*f(i,j,n) + f(i,j-1,n) )/(sqrt( 1 +  (( f(i,j+1,n) - f(i,j-1,n) )/( 2*h ))^2  +  (( f(i+1,j,n) - f(i-1,j,n) )/( 2*h ))^2));
  
                   %第三类基本变量               
                   T1_11(i,j) = ( G(i,j) * ( E(i+1,j) - E(i-1,j) ) - 2*F(i,j)*( F(i+1,j) - F(i-1,j) ) + F(i,j)*( E(i,j+1) - E(i,j-1) ) )/( 4*( E(i,j)*G(i,j) - F(i,j)^2 )*h );
                   T2_11(i,j) =(2*E(i,j) * ( F(i+1,j) - F(i-1,j) ) -   E(i,j)*( E(i,j+1) - E(i,j-1) ) - F(i,j)*( E(i+1,j) - E(i-1,j) ) )/( 4*( E(i,j)*G(i,j) - F(i,j)^2 )*h );
                   T1_22(i,j) =(2*G(i,j) * ( F(i,j+1) - F(i,j-1) ) -   G(i,j)*( G(i+1,j) - G(i-1,j) ) - F(i,j)*( G(i,j+1) - G(i,j-1) ) )/( 4*( E(i,j)*G(i,j) - F(i,j)^2 )*h );
                   T2_22(i,j) =(  E(i,j) * ( G(i,j+1) - G(i,j-1) ) - 2*F(i,j)*( F(i,j+1) - F(i,j-1) ) + F(i,j)*( G(i+1,j) - G(i-1,j) ) )/( 4*( E(i,j)*G(i,j) - F(i,j)^2 )*h );
  
                end
  
figure;
Fmin  = max(min(min(f(:,:,Interation))),0);
Fmax  = max(max(f(:,:,Interation)))/3;
clims = [Fmin,Fmax];
data3 = f(:,:,Interation);
imagesc(data3,clims);
title('HASM迭代后的结果');
axis square;
  
%保存最后的计算结果
save result.mat data3
  
  
%将数据保存到txt文件中
fid = fopen('savedat.txt','wt');
for i = 1:r
    for j = 1:c
        fprintf(fid,'%d  ',data3(i,j));     
    end
    fprintf(fid,'\n');     
end
fclose(fid);
  
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