clear % clear all variables

n = 20; % grid dimension

N = n^2; % number of nodes

ne = 2*n*(n-1); % number of edges

% nodes that will have temperature fixed at 0

fixed_0 = [1:n:N, n:n:N];

% nodes that will have temperature fixed at 1

first = round(n/4)*n + round(n/4);

last = round((N+n)/2);

fixed_1 = first:(n+1):last;

% all nodes with fixed temperature

fixed = [fixed_0, fixed_1];

%%%% YOUR CODE STARTS HERE %%%%%%%%%%%%%%%%%

% build incidence matrix for grid

A = gen_incidence(n);

% build R^(-1), all thermal resistivities are 1

Rinv = speye(ne, ne);

% build stiffness matrix K

% build sparse NxN identity matrix

% build E

% build F

% build the vector d