def test_compare_analytic(self):
test_values = 2 ** np.arange(4, 11)
rel_errors = np.zeros(len(test_values))
u_max = 1
print("\n\nComparing mixed Neumann to analytical result")
for i, N in enumerate(test_values):
# p is coordinates of all nodes
# tri is a list of indicies (rows in p) of all nodes belonging to one element
# edge is lists of all nodes on the edge
p, tri, edge = gd.GetDisc(N)
neumann_edges = edge[(p[edge[:, 0]][:, 1] > 0) & (p[edge[:, 1]][:, 1] > 0)]
dirichlet_edges = edge[(p[edge[:, 0]][:, 1] <= 0) | (p[edge[:, 1]][:, 1] <= 0)]
u_max = np.max(np.abs(u(p.T)))
# numerical solution
U = solve(p, tri, dirichlet_edges, f=f, g=g, neumann_edges=neumann_edges, Nq=4)
max_error = np.max(np.abs(U - u(p.T)))
print(f"N = {N}, max error:", max_error)
self.assertAlmostEqual(max_error, 0, delta=1e2 / N)
rel_errors[i] = max_error
rel_errors /= u_max
fig = plt.figure(figsize=plt.figaspect(1))
plt.loglog(test_values, rel_errors, marker="o")
# plt.title("Convergence of relative error for partial Neumann")
plt.ylabel("Relative error")
plt.xlabel("$N$ nodes in mesh")
plt.savefig("figures/convergence_mixed_neumann.pdf")
plt.clf()
def test_plot(self):
N = 1024
fig = plt.figure(figsize=plt.figaspect(2))
p, tri, edge = gd.GetDisc(N)
neumann_edges = edge[(p[edge[:, 0]][:, 1] > 0) & (p[edge[:, 1]][:, 1] > 0)]
dirichlet_edges = edge[(p[edge[:, 0]][:, 1] <= 0) | (p[edge[:, 1]][:, 1] <= 0)]
U = solve(p, tri, dirichlet_edges, f, g, neumann_edges, Nq=4)
ax = fig.add_subplot(2, 1, 1, projection='3d')
# ax.set_title("Numerical solution for mixed Neumann")
ax.set_zlabel("$U_{i,j}$")
ax.plot_trisurf(p[:, 0], p[:, 1], U, cmap=cm.viridis)
# ax = fig.add_subplot(3, 1, 2, projection='3d')
# ax.set_title("Analytical solution")
# ax.set_zlabel("$U_{i,j}$")
# ax.plot_trisurf(p[:,0],p[:,1],u(p.T),cmap=cm.viridis)
ax2 = fig.add_subplot(2, 1, 2, projection='3d')
# ax2.set_title("Error")
ax2.set_zlabel("$U_{i,j} - u(x_i,y_j)$")
ax2.plot_trisurf(p[:, 0], p[:, 1], U - u(p.T), cmap=cm.viridis)
# ax.plot_trisurf(p[:, 0], p[:, 1], U)
plt.savefig("figures/plot_mixed_neumann.pdf")
fig.clf()
def test_plot_disc_mesh(self):
print("\n\nPlotting meshes")
n_list = 2 ** np.array([4, 6, 8])
fig, axis = plt.subplots(1, len(n_list), figsize=plt.figaspect(1/3))
for i in range(len(n_list)):
p, tri, edge = gd.GetDisc(n_list[i])
plt.sca(axis[i])
plot_disc(p, tri,plt)
plt.savefig("figures/plot_meshes.pdf")
plt.clf()
def test_singularity(self):
test_values = 2 ** np.arange(4, 11)
print("\n\nChecking matrix is singular before applying boundary conditions")
for N in test_values:
p, tri, edge = gd.GetDisc(N)
A, F = get_A_F(p, tri, [], f, Nq=4)
n = np.shape(A)[0]
rank = np.linalg.matrix_rank(A)
print("Rank of A: ", rank, ". Size of matrix A :(", n, " x ", n, ")")
self.assertNotEqual(n, rank)
def test_plot(self):
N = 1024
fig = plt.figure(figsize=plt.figaspect(2))
p, tri, edge = gd.GetDisc(N)
U = solve(p, tri, edge, f, Nq=4)
ax = fig.add_subplot(2, 1, 1, projection='3d')
# ax.set_title("Numerical solution for Dirichlet")
ax.set_zlabel("$U_{i,j}$")
ax.plot_trisurf(p[:, 0], p[:, 1], U, cmap=cm.viridis)
# ax = fig.add_subplot(3, 1, 2, projection='3d')
# ax.set_title("Analytical solution")
# ax.set_zlabel("$U_{i,j}$")
# ax.plot_trisurf(p[:,0],p[:,1],u(p.T),cmap=cm.viridis)
ax2 = fig.add_subplot(2, 1, 2, projection='3d')
# ax2.set_title("Error")
ax2.set_zlabel("$U_{i,j} - u(x_i,y_j)$")
ax2.plot_trisurf(p[:, 0], p[:, 1], U - u(p.T), cmap=cm.viridis)
# ax.plot_trisurf(p[:, 0], p[:, 1], U)
plt.savefig("figures/plot_homogeneous_dirichlet.pdf")
plt.clf()