diffusion_matrix_sparse.m

   1 function K = diffusion_matrix_sparse(integerN)
   2   ##
   3   ## A sparse representation of the matrix K in the advection-diffusion
   4   ## equation. See advection_matrix.m for details.
   5   ##
   6
   7   if (integerN < 2)
   8     K = NA;
   9     return
  10   end
  11
  12   ## The negative ones directly above the diagonal.
  13   top = [ [zeros(integerN-1, 1), -speye(integerN-1)]; ...
  14           zeros(1, integerN)];
  15
  16   ## The negative ones directly below the diagonal.
  17   bottom = [ [zeros(1, integerN-1); ...
  18              -speye(integerN-1)    ], zeros(integerN, 1)];
  19
  20   ## Combine the top and bottom.
  21   K = top + bottom + 2*speye(integerN);
  22
  23   ## Fill in the entries in the corner.
  24   K(1, integerN) = -1;
  25   K(integerN, 1) = -1;
  26 end