for i in range(edof):
for j in range(edof):
k[i,
j] = k[i, j] + (dhdx[i] * dhdx[j] +
dhdy[i] * dhdy[j]) * wtx * wty * detjacob
# extract system dofs for the element
index = feeldof.feeldof(nd, nnel, ndof)
# -------------------------
# assemble element matrices
# -------------------------
kk = feasmbl1.feasmbl1(kk, k, index)
# -------------------------
# apply boundary conditions
# -------------------------
kk, ff = feaplyc2.feaplyc2(kk, ff, bcdof, bcval)
# -------------------------
# solve the matrix equation
# -------------------------
fsol = np.linalg.solve(kk, ff)
# -------------------
# analytical solution
# -------------------
esol = np.zeros(nnode)
for i in range(nnode):
x = gcoord[i, 0]
y = gcoord[i, 1]
esol[i] = 100 * np.sinh(0.31415927 * y) * np.sin(
0.31415927 * x) / np.sinh(3.1415927)
k = felp2dt3.felp2dt3(x, y) # compute element matrix
m = felpt2t3.felpt2t3(x, y) # compute element matrix
kk = feasmbl1.feasmbl1(kk, k, index) # assemble element matrices
mm = feasmbl1.feasmbl1(mm, m, index) # assemble element matrices
# -------------------------
# loop for time integration
# -------------------------
fsol = np.zeros(sdof)
sol[0, 0] = fsol[7] # store time history solution for node 7
sol[1, 0] = fsol[8] # store time history solution for node 8
kk = mm + deltt * kk
for it in range(ntime): # start loop for time integration
fn = deltt * ff + np.dot(mm, fsol) # compute effective column vector
kk, fn = feaplyc2.feaplyc2(kk, fn, bcdof,
bcval) # apply boundary condition
fsol = np.linalg.solve(kk, fn) # solve the matrix equation
sol[0, it + 1] = fsol[7] # store time history solution for node 7
sol[1, it + 1] = fsol[8] # store time history solution for node 8
# ----------------------------------
# plot the solution at nodes 7 and 8
# ----------------------------------
time = np.arange(0, (ntime * deltt) + deltt, deltt)
fig, axis = plt.subplots()
axis.plot(time, sol[0, :], '*', label='Node 7')
axis.plot(time, sol[1, :], '-', label='Node 8')
axis.set_xlabel('Time')
axis.set_ylabel('Solution at nodes 7 and 8')
axis.legend()