Helpful Matlab hints for Challenge 2;

1.  To set up the geometry matrix d1, used as input to initmesh,
do this:

d1 = [ 2     2     2     2
       0    20    20     0
      20    20     0     0
       0     0  hght  hght
       0  hght  hght     0
       1     1     1     1
       0     0     0     0 ];

where hght = 2 + thickness_of_heat_sink

2.  The PDEToolbox has a very odd format for specifying boundary
    conditions and it is not well-documented.  For this problem, 
    to set up the boundary condition matrix bc (the 3rd argument 
    to parabolic), define the variables h_heat_transf and 
    room_temp and then:

z  = mat2str(0);
tmp = h_heat_transf*room_temp;
g = mat2str(tmp);
q  = mat2str(h_heat_transf);
lz = length(z);
lg = length(g);
lq = length(q);
z1q = z*ones(1,lq);
z1g = z*ones(1,lg);
bc = [1      1       1       1
      0      0       0       0
      lz     lq      lq      lq
      lz     lg      lg      lg
       z1q'  (q*1)' (q*1)' (q*1)'
       z1g'  (g*1)' (g*1)' (g*1)' ];

    I learned this from reading solveBV.m by Hongxue Cai 
    http://www.mathworks.it/matlabcentral/fileexchange/9824-solve-boundary-value-problem-by-command-lines

3.  The initial conditions are specified at the points in the
    array p returned by refinemesh.

3.  The last four arguments to Matlab's parabolic
     are c, a, f, and d.  These specify the pde to be
      d u_t - grad . (c grad u) + a u = f.
    In this problem, d and a are scalars (1 and 0, respectively).
    The vectors c and f need to be the values of the functions
    at the centroids of the triangles.  The centroid of triangle
    j is (p(:,t(1,j))+p(:,t(2,j))+p(:,t(3,j)) ) / 3,
    where p and t are returned by refinemesh.
    This is can be confusing, so be careful: intial conditions
    are specified at the points p, while pde coefficients are
    specified at centroids of the triangles in the mesh.

4.  We really should restrict the mesh so that no triangle 
    crosses the silicon and the copper.  This would give a more
    accurate solution for a smaller number of triangles,
    but we won't do this in this homework.