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