上传文件至 'FEM_test/WaveEq2D'

有限元方法案例，求解二维声波传播过程

FEM_test/WaveEq2D/D2waveEq.m

@@ -0,0 +1,170 @@
+%mesh
+%domain
+x_min = 0;
+y_min = 0;
+x_max = 100;
+y_max = 100;
+h    =  2;
+%mesh by distmesh
+fd    =  @(p) drectangle(p,x_min,x_max,y_min,y_max);
+[nodes,elements] =  distmesh2d(fd,@huniform,h,[x_min,y_min;x_max,y_max],[x_min,...
+               y_min;x_min,y_max;x_max,y_min;x_max,y_max]);
+%**************************************************************************
+% input parameter
+dt            = 0.0006; %the time interval(s)
+nt            = 101;
+v             = 1000;  %the velocity of acoustic wave(m/s).
+ppw           = 20;
+num           = length(nodes);
+num_elem      = length(elements);
+
+%allocate memory
+%%sparse
+K             = sparse(num,num);
+M             = sparse(num,num);
+F             = sparse(num,1);
+RES           = zeros(num,nt);
+P             = sparse(num,1);
+Pold          = sparse(num,1);
+Pnew          = sparse(num,1);
+II            = speye(num);
+distance      = zeros(num,1);
+grid_distance = zeros(num_elem,3);
+
+% search the load location,return node number
+loca_x = x_max/2;
+loca_y = y_max/2;
+for ii =1:1:num
+    distance(ii,1) = (nodes(ii,1)-loca_x)^2+(nodes(ii,2)-loca_y)^2;
+end
+srcnode = find(distance == min(distance));
+%**************************************************************************
+
+%assemble M,K
+for ii = 1:1:num_elem
+    % the nodes number
+    i  = elements(ii,1);
+    j  = elements(ii,2);
+    k  = elements(ii,3);
+    
+    %the coordinate of the nodes
+    xi = nodes(i,1);
+    yi = nodes(i,2);
+    
+    xj = nodes(j,1);
+    yj = nodes(j,2);
+    
+    xk = nodes(k,1);
+    yk = nodes(k,2);
+    
+    %to calculate the grid distance
+    grid_distance(ii,:) = pdist([xi,yi;xj,yj;xk,yk]);
+    
+    
+    %the area of the triangle
+    smatrix = [1,xi,yi;1,xj,yj;1,xk,yk];
+    s       = 0.5*abs(det(smatrix));
+       
+    %M matrix
+    M(i,i)  = s*(1/6)  + M(i,i);
+    M(i,j)  = s*(1/12) + M(i,j);
+    M(i,k)  = s*(1/12) + M(i,k);
+    
+    M(j,i)  = s*(1/12) + M(j,i);
+    M(j,j)  = s*(1/6)  + M(j,j);
+    M(j,k)  = s*(1/12) + M(j,k);
+    
+    M(k,i)  = s*(1/12) + M(k,i);
+    M(k,j)  = s*(1/12) + M(k,j);
+    M(k,k)  = s*(1/6)  + M(k,k);
+    
+    a = xi - xk;
+    b = xj - xk;  
+    c = yi - yk;
+    d = yj - yk;
+    cons = v^2/(4*s);
+
+    %K matrix
+    K(i,i) = K(i,i) + cons*(d*d+b*b);
+    K(i,j) = K(i,j) + cons*(-d*c-b*a);
+    K(i,k) = K(i,k) + cons*(d*(c-d)+b*(a-b));
+    
+    K(j,i) = K(j,i) + cons*(-c*d-a*b);
+    K(j,j) = K(j,j) + cons*(c*c+a*a);
+    K(j,k) = K(j,k) + cons*(c*(d-c)+a*(b-a));
+    
+    K(k,i) = K(k,i) + cons*(d*(c-d)+b*(a-b));
+    K(k,j) = K(k,j) + cons*(c*(d-c)+a*(b-a));
+    K(k,k) = K(k,k) + cons*((c-d)^2+(b-a)^2);
+   
+end
+%output the maximum and minimum grid distance
+maxgrid  =  max(max(grid_distance));
+mingrid  =  min(min(grid_distance));
+meangrid = 0.5*(maxgrid + mingrid);
+
+%the time series of source wavelet.
+% f0  = v/(ppw*h);%main frequency(Hz).
+f0  = 25;
+t   = 0:dt:(nt-1)*dt;
+t0  = 1/f0;
+amp = 1.0e7;
+src = amp*(1 - 2.*(pi*f0.*(t - t0)).^2).*exp( - (pi*f0.*(t - t0)).^2);
+%**************************************************************************
+%calculate 
+%sparse
+temp1  = full((dt)^2*(II/M));
+
+% %for gpu acceleration
+% temp1g = gpuArray(temp1);wxw20230914modify
+temp1g = temp1;
+
+formatSpec = 'The calculating time node is: it = %d.\n';
+for it =1:1:nt
+    fprintf(formatSpec,it);
+ 
+    F(srcnode,1)   = src(1,it); %load
+    
+    %sparse
+    temp2 = full(F-K'*P);
+
+    % gpu acceleration
+    % temp2g = gpuArray(temp2); wxw20230914modify
+    temp2g = temp2;
+    temp = temp1g*temp2g;
+    temp = gather(temp);
+    Pnew  = temp + 2*P - Pold;
+        
+    Pold        = P;
+    P           = Pnew;
+    RES(:,it)   = Pnew;
+ end
+% post-processing
+filename  = 'FEM2D.gif';
+x        = nodes(:,1);
+y        = nodes(:,2);
+[xx, yy] = meshgrid(x_min:x_max,y_min:y_max);
+zz = zeros(x_max+1, y_max+1, nt);
+figure('color','w');
+figure(1);
+for ii = 1:1:nt
+    time = ii*dt;%the present time(s)
+    zz(:,:,ii) = griddata(x, y, RES(:,ii), xx, yy);
+    imagesc(xx(1,:),yy(:,1),zz(:,:,ii));
+    caxis([-0.3 0.3]);
+    shading interp;
+    colorbar;
+    title(sprintf( 'Time Step = %d ; Time = %0.3f s ',ii,time));
+    xlabel('X(m)');
+    ylabel('Y(m)');
+    set(gca,'FontName','Times New Roman','FontSize',15);
+    drawnow; 
+    FF = getframe(gcf);
+    I = frame2im(FF); 
+    [I, map] = rgb2ind(I, 256); 
+    if ii == 1
+        imwrite(I,map, filename,'gif', 'Loopcount',inf,'DelayTime',0.1);
+    else
+        imwrite(I,map, filename,'gif','WriteMode','append','DelayTime',0.1);
+    end
+end