/usr/share/octave/packages/msh-1.0.10/msh2m_displacement_smoothing.m is in octave-msh 1.0.10-5.
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##
## This file is part of:
## MSH - Meshing Software Package for Octave
##
## MSH is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## MSH is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with MSH; If not, see <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
## author: Massimiliano Culpo <culpo _AT_ users.sourceforge.net>
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{Ax},@var{Ay}]} = @
## msh2m_displacement_smoothing(@var{msh},@var{k})
##
## Displace the boundary of a 2D mesh setting a spring with force/length
## constant @var{k} along each edge and enforcing 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.:
##
## @example
## msh = msh2m_structured_mesh(linspace(0,1,10),@
## linspace(0,1,10),@
## 1,1:4,"left");
##
## dnodes = msh2m_nodes_on_sides(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] = msh2m_displacement_smoothing(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
## @end example
##
## @seealso{msh2m_jiggle_mesh}
##
## @end deftypefn
function [Ax,Ay] = msh2m_displacement_smoothing(msh, k)
## Check input
if nargin != 2 # Number of input parameters
error("msh2m_displacement_smoothing: wrong number of input parameters.");
elseif !(isstruct(msh) && isfield(msh,"p") &&
isfield(msh,"t") && isfield(msh,"e"))
error("msh2m_displacement_smoothing: first input is not a valid mesh structure.");
elseif !isscalar(k)
error("msh2m_displacement_smoothing: k must be a valid scalar");
endif
## Construct matrices
x = msh.p(1,:);
y = msh.p(2,:);
dx2 = (x(msh.t([1 2 3],:))-x(msh.t([2 3 1],:))).^2;
dy2 = (y(msh.t([1 2 3],:))-y(msh.t([2 3 1],:))).^2;
l2 = dx2 + dy2;
Ax = spalloc(length(x),length(x),1);
Ay = spalloc(length(x),length(x),1);
ax = zeros(3,3,columns(msh.t));
ay = zeros(3,3,columns(msh.t));
for inode=1:3
for jnode=1:3
ginode(inode,jnode,:)=msh.t(inode,:);
gjnode(inode,jnode,:)=msh.t(jnode,:);
endfor
endfor
for ii=1:3
for jj=ii+1:3
ax(ii,jj,:) = ax(jj,ii,:) = reshape(-k * dx2(ii,:)./l2(ii,:),1,1,[]);
ay(ii,jj,:) = ay(jj,ii,:) = reshape(-k * dy2(ii,:)./l2(ii,:),1,1,[]);
ax(ii,ii,:) -= ax(ii,jj,:);
ax(jj,jj,:) -= ax(ii,jj,:);
ay(ii,ii,:) -= ay(ii,jj,:);
ay(jj,jj,:) -= ay(ii,jj,:);
endfor
endfor
Ax = sparse(ginode(:),gjnode(:),ax(:));
Ay = sparse(ginode(:),gjnode(:),ay(:));
endfunction
%!demo
%! msh = msh2m_structured_mesh(linspace(0,1,10),
%! linspace(0,1,10),
%! 1,1:4,"left");
%! dnodes = msh2m_nodes_on_sides(msh,1:4);
%! varnodes = setdiff([1:columns(msh.p)],dnodes);
%!
%! xd = msh.p(1,dnodes)';
%! yd = msh.p(2,dnodes)';
%!
%! dy = zeros(columns(msh.p),1);
%! dx = dy;
%!
%! dxtot = -.5*sin(xd.*yd*pi/2);
%! dytot = -.5*sin(xd.*yd*pi/2);
%!
%! Nsteps = 5;
%! for ii=1:Nsteps
%!
%! dx(dnodes) = dxtot;
%! dy(dnodes) = dytot;
%!
%! [Ax,Ay] = msh2m_displacement_smoothing(msh,1);
%!
%! dx(varnodes) = Ax(varnodes,varnodes) \ ...
%! (-Ax(varnodes,dnodes)*dx(dnodes));
%! dy(varnodes) = Ay(varnodes,varnodes) \ ...
%! (-Ay(varnodes,dnodes)*dy(dnodes));
%!
%! msh.p(1,:) += dx'/Nsteps;
%! msh.p(2,:) += dy'/Nsteps;
%!
%! if mod(ii,2)==0
%! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');
%! pause(.01)
%! endif
%! endfor
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