— Function File: [Ax,Ay] = MSH2Mdisplacementsmoothing(msh,k)

To displace the boundary of a 2D mesh, set a spring with force/length constant k along each edge and enforce equilibrium.

This function builds matrices containing the resulting (linearized) equation for x and y coordinates of each mesh node. Boundary conditions enforcing the displacement (Dirichlet type problem) or the force (Neumann type) at the boundary must be added to make the system solvable, e.g.:

          msh = MSH2Mstructmesh(linspace(0,1,10), linspace(0,1,10), 1,1:4, "left");
          dnodes = MSH2Mnodesonsides(msh,1:4);
          varnodes = setdiff([1:columns(msh.p)],dnodes);
          xd = msh.p(1,dnodes)';
          yd = msh.p(2,dnodes)';
          dx = dy = zeros(columns(msh.p),1);
          dxtot = dytot = -.5*sin(xd.*yd*pi/2);
          Nsteps = 10;
          for ii=1:Nsteps
          dx(dnodes) = dxtot;
          dy(dnodes) = dytot;
          [Ax,Ay] = MSH2Mdisplacementsmoothing(msh,1);
          dx(varnodes) = Ax(varnodes,varnodes) \ ...
          (-Ax(varnodes,dnodes)*dx(dnodes));
          dy(varnodes) = Ay(varnodes,varnodes) \ ...
          (-Ay(varnodes,dnodes)*dy(dnodes));
          msh.p += [ dx'/Nsteps; dy'/Nsteps ] ;
          triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');
          pause(.01)
          endfor

See also: MSH2Mjigglemesh