Create laplacian smoothing matlab

Hi! I would like to create a laplacian smoothing like on the image i attach below. The necessary files I need to make this quadmesh (the mesh generator) and the nodeconnect.m file is also attached here. I managed to create a regular mesh using the quadmesh generator, but I dont know how to increase the boundaries to create a laplician smoothing mesh like on the picture.

The attached nodeconnect.m -> nodeconnect computes all nodes connected to a given node. Called as nnods = nodeconnect(nodes,inod); here nnods i a list of connected nodes to the node and nodes=p.Connectivity is the connectivity matrix. Thank you so much for your help! :)

Answer 1

[Precise Simulation]

You can get something quite similar with the following code, and tune it by playing around with the gridsmooth function, number of smoothing steps, and relaxation parameter.

    nx   = 24;
    ny   = 8;
    xmin = 0;
    xmax = 3;
    ymin = -0.5;
    ymax = 1.5;

    grid = rectgrid( nx, ny, [xmin,ymin,xmax,ymax] );
    subplot(2,2,1)
    plotgrid(grid)

    if( 1 )   % Squeeze only right side y-coordinates.
      grid.p(2,grid.p(1,:)==3) = linspace(0,1,ny+1);
    else   % Squeeze y-coordinates.
      yl = linspace(-0.5,1.5,ny+1);
      yr = linspace(0,1,ny+1);
      y  = [];
      for i=1:ny+1
  y = [ y linspace(yl(i),yr(i),nx+1) ];
      end
      grid.p(2,:) = y;
    end
    subplot(2,2,2)
    plotgrid(grid)

    % Remove boundary indicators from upper/lower 
    % boundaries to allow smoothing.
    b_orig = grid.b;
    grid.b(:,grid.b(3,:)==1) = [];   % Remove lower boundary indices.
    grid.b(:,grid.b(3,:)==3) = [];   % Remove upper boundary indices.

    grid = gridsmooth( grid, 60, 0.1, 2 );
    grid.b = b_orig;

    subplot(2,2,3)
    plotgrid( grid )

[somesh bharadwaj]

for this was getting error in smooth grid so how can i overcome that

[Precise Simulation]

What did the error message say?

If you just want something that looks like the image you neither need QuadMesh nor Laplacian smoothing:

    nx = 24; ny = 8; xmin = 0; xmax = 3; ymin = -0.5; ymax = 1.5;
    [x,y] = meshgrid( linspace(xmin,xmax,nx+1), ...
                      linspace(ymin,ymax,ny+1));

    % Shape/distribution 't' of y-points.
    t = linspace(0,1,nx+1).^(1./(2+[1:nx+1]));

    yl = linspace(-0.5,1.5,ny+1);
    yr = linspace(0,1,ny+1);
    y2 = [];
    for i=1:ny+1
      y_i = yl(i) - t*(yl(i)-yr(i));
      y2 = [ y2; y_i ];
    end

    surf(x,y2,ones(size(x))); view(2), axis equal