n = 200
dx = 1./n
t0 = time.time()
(topo,x,y) = lin_t3.mesh_t3(n,n,dx,dx)
t1 = time.time()
print('Mesh generation finished')
print('dofs = ' + str(x.shape[0]))
print('t mesh = ' + str(t1-t0))
T = 8
Theta = 0.5
t0 = time.time()
K = assemble.gradu_gradv_p1(topo,x,y)
M = assemble.u_v_p1(topo,x,y)
t1 = time.time()
print('Assembled mass and stiffness matrix')
print('t = ' + str(t1-t0))
err_BDF1 = np.zeros((5))
err_BDF2 = np.zeros((5))
err_Theta = np.zeros((5))
for t_ind in range(0, 5):
dt = 2**(-t_ind)
u_0 = analytical(0)
u_1 = analytical(dt)
M_BDF1 = M + dt*K
write_mesh()
ndofs_u = max(x_u.shape)
ndofs_p = max(x_p.shape) + topo_p.shape[0]
print('ndofs u = ' + str(2 * ndofs_u))
print('ndofs p = ' + str(ndofs_p))
u_n = np.zeros((2 * ndofs_u, 1))
p_n = np.zeros((ndofs_p, 1))
ux_n = np.zeros((ndofs_u, 1))
uy_n = np.zeros((ndofs_u, 1))
ux_n_old = np.zeros((ndofs_u, 1))
uy_n_old = np.zeros((ndofs_u, 1))
M11 = assemble.u_v_p1(topo_u, x_u, y_u)
A11 = assemble.gradu_gradv_p1(topo_u, x_u, y_u)
M22 = M11
(BT1, BT2) = assemble.divu_p_p1_iso_p2_p1p0(topo_p, x_p, y_p, topo_u, x_u, y_u,
c2f)
# (BT1,BT2) = assemble.divu_p_p1_iso_p2_p1(topo_p,x_p,y_p,
# topo_u,x_u,y_u,c2f)
BT = sparse.vstack([BT1, BT2])
B = BT.transpose()
mean_p = np.zeros((1, ndofs_p))
for row in topo_p:
x_l = x_p[row[0:3]]
y_l = y_p[row[0:3]]
eval_p = np.zeros((0, 2))
topo_p = np.load(f)
x_p = np.load(f)
y_p = np.load(f)
topo_u = np.load(f)
x_u = np.load(f)
y_u = np.load(f)
c2f = np.load(f)
topo_s = np.load(f)
xs_n = np.load(f)
ys_n = np.load(f)
s_lgr = np.load(f)
t_lgr = np.load(f)
f.close()
ndofs_u = x_u.shape[0]
mass_1D = assemble.u_v_p1(topo_u, x_u, y_u)
mass_matrix_u = sparse.vstack([
sparse.hstack([mass_1D, sparse.csr_matrix((ndofs_u, ndofs_u))]),
sparse.hstack([sparse.csr_matrix((ndofs_u, ndofs_u)), mass_1D])
])
ie_s = np.arange(0, s_lgr.shape[0])
ndofs_s = max(ie_s) + 1
mass_1D = assemble.u_v_p1_periodic(topo_s, s_lgr, t_lgr, ie_s)
mass_matrix_s = sparse.vstack([
sparse.hstack([mass_1D, sparse.csr_matrix((ndofs_s, ndofs_s))]),
sparse.hstack([sparse.csr_matrix((ndofs_s, ndofs_s)), mass_1D])
])
stiffness_1D = assemble.gradu_gradv_p1(topo_u, x_u, y_u)
stiffness_matrix_u = sparse.vstack([
dx = 1./n
print('dx = ' + str(dx))
T = 5
CN = 0.5
TOL = 1e-8
max_iter = 10
n_runs = 5
(topo_p,x_p,y_p,topo_u,x_u,y_u,c2f) = lin_t3.mesh_t3_iso_t6(n,n,dx,dx)
(topo_p,x_p,y_p) = lin_t3.mesh_t3_t0(n,n,dx,dx)
print('Mesh generation finished')
K = assemble.gradu_gradv_p1(topo_u,x_u,y_u)
M = assemble.u_v_p1(topo_u,x_u,y_u)
(BT1,BT2) = assemble.divu_p_p1_iso_p2_p1p0(topo_p,x_p,y_p,topo_u,x_u,y_u,c2f)
BT = sparse.vstack([BT1,BT2])
B = BT.transpose()
ndofs_u = BT1.shape[0]
ndofs_p = BT1.shape[1]
print('dofs u = ' + str(2*ndofs_u))
print('dofs p = ' + str(ndofs_p))
bc_id = np.where(y_u > 1-dx/10)
BT1 = la_utils.clear_rows(BT1,bc_id)
BT2 = la_utils.clear_rows(BT2,bc_id)
bc_id = np.where(y_u < dx/10)
BT1 = la_utils.clear_rows(BT1,bc_id)