def reduced_error(mu, N):
(mesh, _, _, restrictions) = read_mesh()
W = generate_block_function_space(mesh, restrictions)
truth_solution = BlockFunction(W)
read_solution(mu, "truth_solve", truth_solution)
reduced_solution = BlockFunction(W)
read_solution(mu, "reduced_solve", reduced_solution)
return truth_solution - reduced_solution
def reconstruct_solution(reduced_solution, N):
(mesh, _, _, restrictions) = read_mesh()
W = generate_block_function_space(mesh, restrictions)
reconstructed_solution = BlockFunction(W)
basis_functions = read_basis_functions(W, N)
for c in components:
assign(reconstructed_solution.sub(c),
(basis_functions[c] * reduced_solution[c]).sub(c))
reconstructed_solution.apply("from subfunctions")
return reconstructed_solution
def assert_functions_manipulations(functions, block_V):
n_blocks = len(functions)
assert n_blocks in (1, 2)
# a) Convert from a list of Functions to a BlockFunction
block_function_a = BlockFunction(block_V)
for (index, function) in enumerate(functions):
assign(block_function_a.sub(index), function)
# Block vector should have received the data stored in the list of Functions
if n_blocks == 1:
assert_block_functions_equal(functions[0], block_function_a, block_V)
else:
assert_block_functions_equal((functions[0], functions[1]), block_function_a, block_V)
# b) Test block_assign
block_function_b = BlockFunction(block_V)
block_assign(block_function_b, block_function_a)
# Each sub function should now contain the same data as the original block function
for index in range(n_blocks):
assert array_equal(block_function_b.sub(index).vector().get_local(), block_function_a.sub(index).vector().get_local())
# The two block vectors should store the same data
assert array_equal(block_function_b.block_vector().get_local(), block_function_a.block_vector().get_local())
def perform_POD(N):
# export mesh - instead of generating mesh everytime
(mesh, _, _, restrictions) = read_mesh()
W = generate_block_function_space(mesh, restrictions)
# POD objects
X = get_inner_products(W, "POD")
POD = {c: ProperOrthogonalDecomposition(W, X[c]) for c in components}
# Solution storage
solution = BlockFunction(W)
# Training set
training_set = get_set("training_set")
# Read in snapshots
for mu in training_set:
print("Appending solution for mu =", mu, "to snapshots matrix")
read_solution(mu, "truth_solve", solution)
for c in components:
POD[c].store_snapshot(solution, component=c)
# Compress component by component
basis_functions_component = dict()
for c in components:
_, _, basis_functions_component[c], N_c = POD[c].apply(N, tol=0.)
assert N_c == N
print("Eigenvalues for component", c)
POD[c].print_eigenvalues(N)
POD[c].save_eigenvalues_file("basis", "eigenvalues_" + c)
# Collect all components and save to file
basis_functions = BasisFunctionsMatrix(W)
basis_functions.init(components)
for c in components:
basis_functions.enrich(basis_functions_component[c], component=c)
basis_functions.save("basis", "basis")
# Also save components to file, for the sake of the ParaView plugin
with open(os.path.join("basis", "components"), "w") as file_:
for c in components:
file_.write(c + "\n")
def apply_bc_and_block_bc_vector_non_linear(rhs, block_rhs, block_bcs, block_V):
if block_bcs is None:
return (None, None)
N = len(block_bcs)
assert N in (1, 2)
if N == 1:
function = Function(block_V[0])
[bc.apply(rhs, function.vector()) for bc in block_bcs[0]]
block_function = BlockFunction(block_V)
block_bcs.apply(block_rhs, block_function.block_vector())
return (function, block_function)
else:
function1 = Function(block_V[0])
[bc1.apply(rhs[0], function1.vector()) for bc1 in block_bcs[0]]
function2 = Function(block_V[1])
[bc2.apply(rhs[1], function2.vector()) for bc2 in block_bcs[1]]
block_function = BlockFunction(block_V)
block_bcs.apply(block_rhs, block_function.block_vector())
return ((function1, function2), block_function)
def initialization(mesh, subdomains, boundaries):
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
UCG = VectorElement("CG", mesh.ufl_cell(), 2)
BDM = FiniteElement("BDM", mesh.ufl_cell(), 1)
PDG = FiniteElement("DG", mesh.ufl_cell(), 0)
UCG_F = FunctionSpace(mesh, UCG)
BDM_F = FunctionSpace(mesh, BDM)
PDG_F = FunctionSpace(mesh, PDG)
W = BlockFunctionSpace([BDM_F, PDG_F], restrict=[None, None])
U = BlockFunctionSpace([UCG_F])
I = Identity(mesh.topology().dim())
C_cg = FiniteElement("CG", mesh.ufl_cell(), 1)
C_dg = FiniteElement("DG", mesh.ufl_cell(), 0)
mini = C_cg + C_dg
C = FunctionSpace(mesh, mini)
C = BlockFunctionSpace([C])
#TODO
solution0_h = BlockFunction(W)
solution0_m = BlockFunction(U)
solution0_c = BlockFunction(C)
solution1_h = BlockFunction(W)
solution1_m = BlockFunction(U)
solution1_c = BlockFunction(C)
solution2_h = BlockFunction(W)
solution2_m = BlockFunction(U)
solution2_c = BlockFunction(C)
solution_h = BlockFunction(W)
solution_m = BlockFunction(U)
solution_c = BlockFunction(C)
## mechanics
# 0 properties
alpha1 = 0.74
K1 = 8.4 * 1000.e6
nu1 = 0.18
alpha2 = 0.74
K2 = 8.4 * 1000.e6
nu2 = 0.18
alpha_values = [alpha1, alpha2]
K_values = [K1, K2]
nu_values = [nu1, nu2]
alpha_0 = Function(PM)
K_0 = Function(PM)
nu_0 = Function(PM)
alpha_0 = init_scalar_parameter(alpha_0, alpha_values[0], 500, subdomains)
K_0 = init_scalar_parameter(K_0, K_values[0], 500, subdomains)
nu_0 = init_scalar_parameter(nu_0, nu_values[0], 500, subdomains)
alpha_0 = init_scalar_parameter(alpha_0, alpha_values[1], 501, subdomains)
K_0 = init_scalar_parameter(K_0, K_values[1], 501, subdomains)
nu_0 = init_scalar_parameter(nu_0, nu_values[1], 501, subdomains)
K_mult_min = 1.0
K_mult_max = 1.0
mu_l_0, lmbda_l_0, Ks_0, K_0 = \
bulk_modulus_update(mesh,solution0_c[0],K_mult_min,K_mult_max,K_0,nu_0,alpha_0,K_0)
# n-1 properties
alpha1 = 0.74
K1 = 8.4 * 1000.e6
nu1 = 0.18
alpha2 = 0.74
K2 = 8.4 * 1000.e6
nu2 = 0.18
alpha_values = [alpha1, alpha2]
K_values = [K1, K2]
nu_values = [nu1, nu2]
alpha_1 = Function(PM)
K_1 = Function(PM)
nu_1 = Function(PM)
alpha_1 = init_scalar_parameter(alpha_1, alpha_values[0], 500, subdomains)
K_1 = init_scalar_parameter(K_1, K_values[0], 500, subdomains)
nu_1 = init_scalar_parameter(nu_1, nu_values[0], 500, subdomains)
alpha_1 = init_scalar_parameter(alpha_1, alpha_values[1], 501, subdomains)
K_1 = init_scalar_parameter(K_1, K_values[1], 501, subdomains)
nu_1 = init_scalar_parameter(nu_1, nu_values[1], 501, subdomains)
K_mult_min = 1.0
K_mult_max = 1.0
mu_l_1, lmbda_l_1, Ks_1, K_1 = \
bulk_modulus_update(mesh,solution0_c[0],K_mult_min,K_mult_max,K_1,nu_1,alpha_1,K_0)
# n properties
alpha1 = 0.74
K2 = 8.4 * 1000.e6
nu1 = 0.18
alpha2 = 0.74
K2 = 8.4 * 1000.e6
nu2 = 0.18
alpha_values = [alpha1, alpha2]
K_values = [K1, K2]
nu_values = [nu1, nu2]
alpha = Function(PM)
K = Function(PM)
nu = Function(PM)
alpha = init_scalar_parameter(alpha, alpha_values[0], 500, subdomains)
K = init_scalar_parameter(K, K_values[0], 500, subdomains)
nu = init_scalar_parameter(nu, nu_values[0], 500, subdomains)
alpha = init_scalar_parameter(alpha, alpha_values[1], 501, subdomains)
K = init_scalar_parameter(K, K_values[1], 501, subdomains)
nu = init_scalar_parameter(nu, nu_values[1], 501, subdomains)
K_mult_min = 1.0
K_mult_max = 1.0
mu_l, lmbda_l, Ks, K = \
bulk_modulus_update(mesh,solution0_c[0],K_mult_min,K_mult_max,K,nu,alpha,K_0)
## flow
# 0 properties
cf1 = 1e-10
phi1 = 0.2
rho1 = 1000.0
mu1 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k1 = np.array([kx, 0., 0., ky])
cf2 = 1e-10
phi2 = 0.2
rho2 = 1000.0
mu2 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k2 = np.array([kx, 0., 0., ky])
cf_values = [cf1, cf2]
phi_values = [phi1, phi2]
rho_values = [rho1, rho2]
mu_values = [mu1, mu2]
k_values = [k1, k2]
cf_0 = Function(PM)
phi_0 = Function(PM)
rho_0 = Function(PM)
mu_0 = Function(PM)
k_0 = Function(TM)
cf_0 = init_scalar_parameter(cf_0, cf_values[0], 500, subdomains)
phi_0 = init_scalar_parameter(phi_0, phi_values[0], 500, subdomains)
rho_0 = init_scalar_parameter(rho_0, rho_values[0], 500, subdomains)
mu_0 = init_scalar_parameter(mu_0, mu_values[0], 500, subdomains)
k_0 = init_tensor_parameter(k_0, k_values[0], 500, subdomains,
mesh.topology().dim())
cf_0 = init_scalar_parameter(cf_0, cf_values[1], 501, subdomains)
phi_0 = init_scalar_parameter(phi_0, phi_values[1], 501, subdomains)
rho_0 = init_scalar_parameter(rho_0, rho_values[1], 501, subdomains)
mu_0 = init_scalar_parameter(mu_0, mu_values[1], 501, subdomains)
k_0 = init_tensor_parameter(k_0, k_values[1], 501, subdomains,
mesh.topology().dim())
#filename = "perm4.csv"
#k_0 = init_from_file_parameter(k_0,0.,0.,filename)
# n-1 properties
cf1 = 1e-10
phi1 = 0.2
rho1 = 1000.0
mu1 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k1 = np.array([kx, 0., 0., ky])
cf2 = 1e-10
phi2 = 0.2
rho2 = 1000.0
mu2 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k2 = np.array([kx, 0., 0., ky])
cf_values = [cf1, cf2]
phi_values = [phi1, phi2]
rho_values = [rho1, rho2]
mu_values = [mu1, mu2]
k_values = [k1, k2]
cf_1 = Function(PM)
phi_1 = Function(PM)
rho_1 = Function(PM)
mu_1 = Function(PM)
k_1 = Function(TM)
cf_1 = init_scalar_parameter(cf_1, cf_values[0], 500, subdomains)
phi_1 = init_scalar_parameter(phi_1, phi_values[0], 500, subdomains)
rho_1 = init_scalar_parameter(rho_1, rho_values[0], 500, subdomains)
mu_1 = init_scalar_parameter(mu_1, mu_values[0], 500, subdomains)
k_1 = init_tensor_parameter(k_1, k_values[0], 500, subdomains,
mesh.topology().dim())
cf_1 = init_scalar_parameter(cf_1, cf_values[1], 501, subdomains)
phi_1 = init_scalar_parameter(phi_1, phi_values[1], 501, subdomains)
rho_1 = init_scalar_parameter(rho_1, rho_values[1], 501, subdomains)
mu_1 = init_scalar_parameter(mu_1, mu_values[1], 501, subdomains)
k_1 = init_tensor_parameter(k_1, k_values[1], 501, subdomains,
mesh.topology().dim())
#filename = "perm4.csv"
#k_1 = init_from_file_parameter(k_1,0.,0.,filename)
# n properties
cf1 = 1e-10
phi1 = 0.2
rho1 = 1000.0
mu1 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k1 = np.array([kx, 0., 0., ky])
cf2 = 1e-10
phi2 = 0.2
rho2 = 1000.0
mu2 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k2 = np.array([kx, 0., 0., ky])
cf_values = [cf1, cf2]
phi_values = [phi1, phi2]
rho_values = [rho1, rho2]
mu_values = [mu1, mu2]
k_values = [k1, k2]
cf = Function(PM)
phi = Function(PM)
rho = Function(PM)
mu = Function(PM)
k = Function(TM)
cf = init_scalar_parameter(cf, cf_values[0], 500, subdomains)
phi = init_scalar_parameter(phi, phi_values[0], 500, subdomains)
rho = init_scalar_parameter(rho, rho_values[0], 500, subdomains)
mu = init_scalar_parameter(mu, mu_values[0], 500, subdomains)
k = init_tensor_parameter(k, k_values[0], 500, subdomains,
mesh.topology().dim())
cf = init_scalar_parameter(cf, cf_values[1], 501, subdomains)
phi = init_scalar_parameter(phi, phi_values[1], 501, subdomains)
rho = init_scalar_parameter(rho, rho_values[1], 501, subdomains)
mu = init_scalar_parameter(mu, mu_values[1], 501, subdomains)
k = init_tensor_parameter(k, k_values[1], 501, subdomains,
mesh.topology().dim())
#filename = "perm4.csv"
#k = init_from_file_parameter(k,0.,0.,filename)
### transport
# 0
dx1 = 1e-12
dy1 = 1e-12
d1 = np.array([dx1, 0., 0., dy1])
dx2 = 1e-12
dy2 = 1e-12
d2 = np.array([dx2, 0., 0., dy2])
d_values = [d1, d2]
d_0 = Function(TM)
d_0 = init_tensor_parameter(d_0, d_values[0], 500, subdomains,
mesh.topology().dim())
d_0 = init_tensor_parameter(d_0, d_values[1], 501, subdomains,
mesh.topology().dim())
# n-1
dx1 = 1e-12
dy1 = 1e-12
d1 = np.array([dx1, 0., 0., dy1])
dx2 = 1e-12
dy2 = 1e-12
d2 = np.array([dx2, 0., 0., dy2])
d_values = [d1, d2]
d_1 = Function(TM)
d_1 = init_tensor_parameter(d_1, d_values[0], 500, subdomains,
mesh.topology().dim())
d_1 = init_tensor_parameter(d_1, d_values[1], 501, subdomains,
mesh.topology().dim())
# n
dx1 = 1e-12
dy1 = 1e-12
d1 = np.array([dx1, 0., 0., dy1])
dx2 = 1e-12
dy2 = 1e-12
d2 = np.array([dx2, 0., 0., dy2])
d_values = [d1, d2]
d = Function(TM)
d = init_tensor_parameter(d, d_values[0], 500, subdomains,
mesh.topology().dim())
d = init_tensor_parameter(d, d_values[1], 501, subdomains,
mesh.topology().dim())
####initialization
# initial
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution0_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution0_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution0_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution0_c.sub(0), c0_project)
# n - 1
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution1_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution1_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution1_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution1_c.sub(0), c0_project)
# n - 2
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution2_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution2_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution2_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution2_c.sub(0), c0_project)
# n
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution_c.sub(0), c0_project)
###iterative parameters
phi_it = Function(PM)
assign(phi_it, phi_0)
print('c_sat', c_sat_cal(1.0e8, 20.))
c_sat = c_sat_cal(1.0e8, 20.)
c_sat = project(c_sat, PM)
c_inject = Constant(0.0)
c_inject = project(c_inject, PM)
mu_c1_1 = 1.e-4
mu_c2_1 = 5.e-0
mu_c1_2 = 1.e-4
mu_c2_2 = 5.e-0
mu_c1_values = [mu_c1_1, mu_c1_2]
mu_c2_values = [mu_c2_1, mu_c2_2]
mu_c1 = Function(PM)
mu_c2 = Function(PM)
mu_c1 = init_scalar_parameter(mu_c1, mu_c1_values[0], 500, subdomains)
mu_c2 = init_scalar_parameter(mu_c2, mu_c2_values[0], 500, subdomains)
mu_c1 = init_scalar_parameter(mu_c1, mu_c1_values[1], 501, subdomains)
mu_c2 = init_scalar_parameter(mu_c2, mu_c2_values[1], 501, subdomains)
coeff_for_perm_1 = 22.2
coeff_for_perm_2 = 22.2
coeff_for_perm_values = [coeff_for_perm_1, coeff_for_perm_2]
coeff_for_perm = Function(PM)
coeff_for_perm = init_scalar_parameter(coeff_for_perm,
coeff_for_perm_values[0], 500,
subdomains)
coeff_for_perm = init_scalar_parameter(coeff_for_perm,
coeff_for_perm_values[1], 501,
subdomains)
solutionIt_h = BlockFunction(W)
return solution0_m, solution0_h, solution0_c \
,solution1_m, solution1_h, solution1_c \
,solution2_m, solution2_h, solution2_c \
,solution_m, solution_h, solution_c \
,alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0 \
,alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1 \
,alpha, K, mu_l, lmbda_l, Ks \
,cf_0, phi_0, rho_0, mu_0, k_0 \
,cf_1, phi_1, rho_1, mu_1, k_1 \
,cf, phi, rho, mu, k \
,d_0, d_1, d, I \
,phi_it, solutionIt_h, mu_c1, mu_c2 \
,nu_0, nu_1, nu, coeff_for_perm \
,c_sat, c_inject
def transport_linear(integrator_type, mesh, subdomains, boundaries, t_start, dt, T, solution0, \
alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0, \
alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1, \
alpha, K, mu_l, lmbda_l, Ks, \
cf_0, phi_0, rho_0, mu_0, k_0,\
cf_1, phi_1, rho_1, mu_1, k_1,\
cf, phi, rho, mu, k, \
d_0, d_1, d_t,
vel_c, p_con, A_0, Temp, c_extrapolate):
# Create mesh and define function space
parameters["ghost_mode"] = "shared_facet" # required by dS
dx = Measure('dx', domain=mesh, subdomain_data=subdomains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)
C_cg = FiniteElement("CG", mesh.ufl_cell(), 1)
C_dg = FiniteElement("DG", mesh.ufl_cell(), 0)
mini = C_cg + C_dg
C = FunctionSpace(mesh, mini)
C = BlockFunctionSpace([C])
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)
h = vc / fc
h_avg = (vc('+') + vc('-')) / (2 * avg(fc))
penalty1 = Constant(1.0)
tau = Function(PM)
tau = tau_cal(tau, phi, -0.5)
tuning_para = 0.25
vel_norm = (dot(vel_c, n) + abs(dot(vel_c, n))) / 2.0
cell_size = CellDiameter(mesh)
vnorm = sqrt(dot(vel_c, vel_c))
I = Identity(mesh.topology().dim())
d_eff = Function(TM)
d_eff = diff_coeff_cal_rev(d_eff, d_0, tau,
phi) + tuning_para * cell_size * vnorm * I
monitor_dt = dt
# Define variational problem
dc, = BlockTrialFunction(C)
dc_dot, = BlockTrialFunction(C)
psic, = BlockTestFunction(C)
block_c = BlockFunction(C)
c, = block_split(block_c)
block_c_dot = BlockFunction(C)
c_dot, = block_split(block_c_dot)
theta = -1.0
a_time = phi * rho * inner(c_dot, psic) * dx
a_dif = dot(rho*d_eff*grad(c),grad(psic))*dx \
- dot(avg_w(rho*d_eff*grad(c),weight_e(rho*d_eff,n)), jump(psic, n))*dS \
+ theta*dot(avg_w(rho*d_eff*grad(psic),weight_e(rho*d_eff,n)), jump(c, n))*dS \
+ penalty1/h_avg*k_e(rho*d_eff,n)*dot(jump(c, n), jump(psic, n))*dS
a_adv = -dot(rho*vel_c*c,grad(psic))*dx \
+ dot(jump(psic), rho('+')*vel_norm('+')*c('+') - rho('-')*vel_norm('-')*c('-') )*dS \
+ dot(psic, rho*vel_norm*c)*ds(3)
R_c = R_c_cal(c_extrapolate, p_con, Temp)
c_D1 = Constant(0.5)
rhs_c = R_c * A_s_cal(phi, phi_0, A_0) * psic * dx - dot(
rho * phi * vel_c, n) * c_D1 * psic * ds(1)
r_u = [a_dif + a_adv]
j_u = block_derivative(r_u, [c], [dc])
r_u_dot = [a_time]
j_u_dot = block_derivative(r_u_dot, [c_dot], [dc_dot])
r = [r_u_dot[0] + r_u[0] - rhs_c]
# this part is not applied.
exact_solution_expression1 = Expression("1.0",
t=0,
element=C[0].ufl_element())
def bc(t):
p5 = DirichletBC(C.sub(0),
exact_solution_expression1,
boundaries,
1,
method="geometric")
return BlockDirichletBC([p5])
# Define problem wrapper
class ProblemWrapper(object):
def set_time(self, t):
pass
# Residual and jacobian functions
def residual_eval(self, t, solution, solution_dot):
return r
def jacobian_eval(self, t, solution, solution_dot,
solution_dot_coefficient):
return [[
Constant(solution_dot_coefficient) * j_u_dot[0, 0] + j_u[0, 0]
]]
# Define boundary condition
def bc_eval(self, t):
pass
# Define initial condition
def ic_eval(self):
return solution0
# Define custom monitor to plot the solution
def monitor(self, t, solution, solution_dot):
pass
problem_wrapper = ProblemWrapper()
(solution, solution_dot) = (block_c, block_c_dot)
solver = TimeStepping(problem_wrapper, solution, solution_dot)
solver.set_parameters({
"initial_time": t_start,
"time_step_size": dt,
"monitor": {
"time_step_size": monitor_dt,
},
"final_time": T,
"exact_final_time": "stepover",
"integrator_type": integrator_type,
"problem_type": "linear",
"linear_solver": "mumps",
"report": True
})
export_solution = solver.solve()
return export_solution, T
def m_linear(integrator_type, mesh, subdomains, boundaries, t_start, dt, T, solution0, \
alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0, \
alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1, \
alpha, K, mu_l, lmbda_l, Ks, \
cf_0, phi_0, rho_0, mu_0, k_0,\
cf_1, phi_1, rho_1, mu_1, k_1,\
cf, phi, rho, mu, k, \
pressure_freeze):
# Create mesh and define function space
parameters["ghost_mode"] = "shared_facet" # required by dS
dx = Measure('dx', domain=mesh, subdomain_data=subdomains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)
C = VectorFunctionSpace(mesh, "CG", 2)
C = BlockFunctionSpace([C])
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)
h = vc/fc
h_avg = (vc('+') + vc('-'))/(2*avg(fc))
monitor_dt = dt
f_stress_x = Constant(-1.e3)
f_stress_y = Constant(-20.0e6)
f = Constant((0.0, 0.0)) #sink/source for displacement
I = Identity(mesh.topology().dim())
# Define variational problem
psiu, = BlockTestFunction(C)
block_u = BlockTrialFunction(C)
u, = block_split(block_u)
w = BlockFunction(C)
theta = -1.0
a_time = inner(-alpha*pressure_freeze*I,sym(grad(psiu)))*dx #quasi static
a = inner(2*mu_l*strain(u)+lmbda_l*div(u)*I, sym(grad(psiu)))*dx
rhs_a = inner(f,psiu)*dx \
+ dot(f_stress_y*n,psiu)*ds(2)
r_u = [a]
#DirichletBC
bcd1 = DirichletBC(C.sub(0).sub(0), 0.0, boundaries, 1) # No normal displacement for solid on left side
bcd3 = DirichletBC(C.sub(0).sub(0), 0.0, boundaries, 3) # No normal displacement for solid on right side
bcd4 = DirichletBC(C.sub(0).sub(1), 0.0, boundaries, 4) # No normal displacement for solid on bottom side
bcs = BlockDirichletBC([bcd1,bcd3,bcd4])
AA = block_assemble([r_u])
FF = block_assemble([rhs_a - a_time])
bcs.apply(AA)
bcs.apply(FF)
block_solve(AA, w.block_vector(), FF, "mumps")
export_solution = w
return export_solution, T
def truth_solve(mu_unkown):
print("Performing truth solve at mu =", mu_unkown)
(mesh, subdomains, boundaries, restrictions) = read_mesh()
# (mesh, subdomains, boundaries, restrictions) = create_mesh()
dx = Measure('dx', subdomain_data=subdomains)
ds = Measure('ds', subdomain_data=boundaries)
W = generate_block_function_space(mesh, restrictions)
# Test and trial functions
block_v = BlockTestFunction(W)
v, q = block_split(block_v)
block_du = BlockTrialFunction(W)
du, dp = block_split(block_du)
block_u = BlockFunction(W)
u, p = block_split(block_u)
# gap
# V2 = FunctionSpace(mesh, "CG", 1)
# gap = Function(V2, name="Gap")
# obstacle
R = 0.25
d = 0.15
x_0 = mu_unkown[0]
y_0 = mu_unkown[1]
obstacle = Expression("-d+(pow(x[0]-x_0,2)+pow(x[1]-y_0, 2))/2/R", d=d, R=R , x_0 = x_0, y_0 = y_0, degree=0)
# Constitutive parameters
E = Constant(10.0)
nu = Constant(0.3)
mu, lmbda = Constant(E/(2*(1 + nu))), Constant(E*nu/((1 + nu)*(1 - 2*nu)))
B = Constant((0.0, 0.0, 0.0)) # Body force per unit volume
T = Constant((0.0, 0.0, 0.0)) # Traction force on the boundary
# Kinematics
# -----------------------------------------------------------------------------
mesh_dim = mesh.topology().dim() # Spatial dimension
I = Identity(mesh_dim) # Identity tensor
F = I + grad(u) # Deformation gradient
C = F.T*F # Right Cauchy-Green tensor
J = det(F) # 3rd invariant of the deformation tensor
# Strain function
def P(u): # P = dW/dF:
return mu*(F - inv(F.T)) + lmbda*ln(J)*inv(F.T)
def eps(v):
return sym(grad(v))
def sigma(v):
return lmbda*tr(eps(v))*Identity(3) + 2.0*mu*eps(v)
# Definition of The Mackauley bracket <x>+
def ppos(x):
return (x+abs(x))/2.
# Define the augmented lagrangian
def aug_l(x):
return x + pen*(obstacle-u[2])
pen = Constant(1e4)
# Boundary conditions
# bottom_bc = DirichletBC(W.sub(0), Constant((0., 0., 0.)), boundaries, 2)
# left_bc = DirichletBC(W.sub(0), Constant((0., 0., 0.)), boundaries, 3)
# right_bc = DirichletBC(W.sub(0), Constant((0., 0., 0.)), boundaries, 4)
# front_bc = DirichletBC(W.sub(0), Constant((0., 0., 0.)), boundaries, 5)
# back_bc = DirichletBC(W.sub(0), Constant((0., 0., 0.)), boundaries, 6)
# # sym_x_bc = DirichletBC(W.sub(0).sub(0), Constant(0.), boundaries, 2)
# # sym_y_bc = DirichletBC(W.sub(0).sub(1), Constant(0.), boundaries, 3)
# # bc = BlockDirichletBC([bottom_bc, sym_x_bc, sym_y_bc])
# bc = BlockDirichletBC([bottom_bc, left_bc, right_bc, front_bc, back_bc])
bottom_bc = DirichletBC(W.sub(0), Constant((0., 0., 0.)), boundaries, 2)
left_bc_x = DirichletBC(W.sub(0).sub(0), Constant(0.), boundaries, 3)
left_bc_y = DirichletBC(W.sub(0).sub(1), Constant(0.), boundaries, 3)
right_bc_x = DirichletBC(W.sub(0).sub(0), Constant(0.), boundaries, 4)
right_bc_y = DirichletBC(W.sub(0).sub(1), Constant(0.), boundaries, 4)
front_bc_x = DirichletBC(W.sub(0).sub(0), Constant(0.), boundaries, 5)
front_bc_y = DirichletBC(W.sub(0).sub(1), Constant(0.), boundaries, 5)
back_bc_x = DirichletBC(W.sub(0).sub(0), Constant(0.), boundaries, 6)
back_bc_y = DirichletBC(W.sub(0).sub(1), Constant(0.), boundaries, 6)
# sym_x_bc = DirichletBC(W.sub(0).sub(0), Constant(0.), boundaries, 2)
# sym_y_bc = DirichletBC(W.sub(0).sub(1), Constant(0.), boundaries, 3)
# bc = BlockDirichletBC([bottom_bc, sym_x_bc, sym_y_bc])
bc = BlockDirichletBC([bottom_bc, left_bc_x, left_bc_y, \
right_bc_x, right_bc_y, front_bc_x, front_bc_y, \
back_bc_x, back_bc_y])
# Variational forms
# F = inner(sigma(u), eps(v))*dx + pen*dot(v[2], ppos(u[2]-obstacle))*ds(1)
# F = [inner(sigma(u), eps(v))*dx - aug_l(l)*v[2]*ds(1) + ppos(aug_l(l))*v[2]*ds(1),
# (obstacle-u[2])*v*ds(1) - (1/pen)*ppos(aug_l(l))*v*ds(1)]
# F_a = inner(sigma(u), eps(v))*dx
# F_b = - aug_l(p)*v[2]*ds(1) + ppos(aug_l(p))*v[2]*ds(1)
# F_c = (obstacle-u[2])*q*ds(1)
# F_d = - (1/pen)*ppos(aug_l(p))*q*ds(1)
#
# block_F = [[F_a, F_b],
# [F_c, F_d]]
F_a = inner(P(u), grad(v))*dx - dot(B, v)*dx - dot(T, v)*ds \
- aug_l(p)*v[2]*ds(1) + ppos(aug_l(p))*v[2]*ds(1)
F_b = (obstacle-u[2])*q*ds(1) - (1/pen)*ppos(aug_l(p))*q*ds(1)
block_F = [F_a,
F_b]
J = block_derivative(block_F, block_u, block_du)
# Setup solver
problem = BlockNonlinearProblem(block_F, block_u, bc, J)
solver = BlockPETScSNESSolver(problem)
solver.parameters.update({
"linear_solver": "mumps",
"absolute_tolerance": 1E-4,
"relative_tolerance": 1E-4,
"maximum_iterations": 50,
"report": True,
"error_on_nonconvergence": True
})
# solver.parameters.update({
# "linear_solver": "cg",
# "absolute_tolerance": 1E-4,
# "relative_tolerance": 1E-4,
# "maximum_iterations": 50,
# "report": True,
# "error_on_nonconvergence": True
# })
# Perform a fake loop over time. Note how up will store the solution at the last time.
# Q. for?
# A. You can remove it, since your problem is stationary. The template was targeting
# a final application which was transient, but in which the ROM should have only
# described the final solution (when reaching the steady state).
# for _ in range(2):
# solver.solve()
a1 = solver.solve()
print(a1)
# save all the solution here as a function of time
# Return the solution at the last time
# Q. block_u or block
# A. I think block_u, it will split split among the components elsewhere
return block_u
PM = FunctionSpace(mesh, "DG", 0)
TM = TensorFunctionSpace(mesh, "DG", 0)
I = Identity(mesh.topology().dim())
dx = Measure("dx", domain=mesh, subdomain_data=subdomains)
ds = Measure("ds", domain=mesh, subdomain_data=boundaries)
dS = Measure("dS", domain=mesh, subdomain_data=boundaries)
# Test and trial functions
vq = BlockTestFunction(W)
(v, q) = block_split(vq)
up = BlockTrialFunction(W)
(u, p) = block_split(up)
w = BlockFunction(W)
w0 = BlockFunction(W)
(u0, p0) = block_split(w0)
n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)
h = vc / fc
h_avg = (vc("+") + vc("-")) / (2 * avg(fc))
penalty1 = 1.0
penalty2 = 10.0
theta = 1.0
# Constitutive parameters
def train_data_driven(N):
(mesh, _, _, restrictions) = read_mesh()
W = generate_block_function_space(mesh, restrictions)
# L2 projection object
basis_functions = read_basis_functions(W, N)
X = get_inner_products(W, "L2 projection")
l2_projection = {
c: L2ProjectionSolver(X[c], basis_functions[c], N)
for c in components
}
# Solution storage
solution = BlockFunction(W)
# Training set
training_set = get_set("training_set")
mu_len = len(training_set[0])
# Read in snapshots
snapshots_matrix = SnapshotsMatrix(W)
for i, mu in enumerate(training_set):
print("Appending solution for mu =", mu, "to snapshots matrix")
read_solution(mu, "truth_solve", solution)
snapshots_matrix.enrich(solution)
filename = os.path.join("dis_x", "dis_x_" + str(i))
write_file = open(filename, 'wb')
pickle.dump(snapshots_matrix[-1][0].vector()[::3], write_file)
write_file.close()
filename = os.path.join("dis_y", "dis_y_" + str(i))
write_file = open(filename, 'wb')
pickle.dump(snapshots_matrix[-1][0].vector()[1::3], write_file)
write_file.close()
filename = os.path.join("dis_z", "dis_z_" + str(i))
write_file = open(filename, 'wb')
pickle.dump(snapshots_matrix[-1][0].vector()[2::3], write_file)
write_file.close()
quit()
# Data driven training component by component
normalize_inputs = NormalizeInputs(mu_range)
for c in components:
projected_snapshots = [
l2_projection[c].solve(mu, c, snapshots_matrix[i])
for i, mu in enumerate(training_set)
]
inputs = torch.unsqueeze(torch.FloatTensor(training_set._list),
dim=mu_len)
inputs = normalize_inputs(inputs)
outputs = torch.stack([
torch.from_numpy(projected_snapshot)
for projected_snapshot in projected_snapshots
])
with open(
os.path.join("networks",
"output_normalization_" + c + "_" + str(N)),
"w") as file_:
file_.write(str(torch.min(outputs).detach().numpy()) + "\n")
file_.write(str(torch.max(outputs).detach().numpy()) + "\n")
normalize_outputs = NormalizeOutputs(
os.path.join("networks",
"output_normalization_" + c + "_" + str(N)))
outputs = normalize_outputs(outputs)
# print(len(training_set[0]))
# print(len(training_set))
# print(mu_len)
# print(inputs.shape)
# print(outputs.shape)
# quit()
network = Network(mu_len, c, N)
network.apply(init_weights)
criterion = nn.MSELoss()
learning_rate = 0.3
optimizer = optim.Adam(network.parameters(),
lr=learning_rate,
eps=1.e-08)
torch_dataset = TensorDataset(inputs.float(), outputs.float())
n_snpashots = len(training_set)
n_trainining = 4 * int(n_snpashots / 6)
n_validation = n_snpashots - n_trainining
batch_size_training = int(round(np.sqrt(n_snpashots)))
batch_size_validation = int(round(np.sqrt(n_snpashots)))
epochs = 10000
n_epochs_stop = epochs
training_dataset, validation_dataset = random_split(
torch_dataset, [n_trainining, n_validation])
training_loader = DataLoader(dataset=training_dataset,
batch_size=batch_size_training)
validation_loader = DataLoader(dataset=validation_dataset,
batch_size=batch_size_validation)
training_losses = [None] * epochs
validation_losses = [None] * epochs
min_validation_loss = np.Inf
for epoch in range(epochs):
for param_group in optimizer.param_groups:
param_group["lr"] = learning_rate / (1 + np.sqrt(epoch))
total_training_loss = 0.0
for batch_x, batch_y in training_loader: # for each training step
network.train()
optimizer.zero_grad()
batch_x_normalized = batch_x.squeeze(1)
prediction = network(batch_x_normalized)
loss = criterion(prediction, batch_y)
loss.backward()
optimizer.step()
total_training_loss += loss.item()
training_losses[epoch] = total_training_loss / len(training_loader)
print("[%d] Training loss: %.10f" %
(epoch + 1, training_losses[epoch]))
network.eval()
total_validation_loss = 0.0
with torch.no_grad():
for validation_x, validation_y in validation_loader:
validation_x_normalized = validation_x.squeeze(1)
network_y = network(validation_x_normalized)
loss = criterion(network_y, validation_y)
total_validation_loss += loss.item()
validation_losses[epoch] = total_validation_loss / len(
validation_loader)
print("[%d] Validation loss: %.10f" %
(epoch + 1, validation_losses[epoch]))
# add less than or eq
if validation_losses[epoch] <= min_validation_loss:
epochs_no_improvement = 0
min_validation_loss = validation_losses[epoch]
torch.save(
network.state_dict(),
os.path.join("networks", "network_" + c + "_" + str(N)))
else:
epochs_no_improvement += 1
if epochs_no_improvement == n_epochs_stop:
print("Early stopping!")
break
def function(self):
if self.split:
return (Function(self.W), Function(self.Q))
else:
return BlockFunction(self.mixedSpace)
def h_linear(integrator_type, mesh, subdomains, boundaries, t_start, dt, T, solution0, \
alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0, \
alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1, \
alpha, K, mu_l, lmbda_l, Ks, \
cf_0, phi_0, rho_0, mu_0, k_0,\
cf_1, phi_1, rho_1, mu_1, k_1,\
cf, phi, rho, mu, k, \
sigma_v_freeze, dphi_c_dt):
# Create mesh and define function space
parameters["ghost_mode"] = "shared_facet" # required by dS
dx = Measure('dx', domain=mesh, subdomain_data=subdomains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)
BDM = FiniteElement("BDM", mesh.ufl_cell(), 1)
PDG = FiniteElement("DG", mesh.ufl_cell(), 0)
BDM_F = FunctionSpace(mesh, BDM)
PDG_F = FunctionSpace(mesh, PDG)
W = BlockFunctionSpace([BDM_F, PDG_F], restrict=[None, None])
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)
h = vc / fc
h_avg = (vc('+') + vc('-')) / (2 * avg(fc))
I = Identity(mesh.topology().dim())
monitor_dt = dt
p_outlet = 0.1e6
p_inlet = 1000.0
M_inv = phi_0 * cf + (alpha - phi_0) / Ks
# Define variational problem
trial = BlockTrialFunction(W)
dv, dp = block_split(trial)
trial_dot = BlockTrialFunction(W)
dv_dot, dp_dot = block_split(trial_dot)
test = BlockTestFunction(W)
psiv, psip = block_split(test)
block_w = BlockFunction(W)
v, p = block_split(block_w)
block_w_dot = BlockFunction(W)
v_dot, p_dot = block_split(block_w_dot)
a_time = Constant(0.0) * inner(v_dot, psiv) * dx #quasi static
# k is a function of phi
#k = perm_update_rutqvist_newton(p,p0,phi0,phi,coeff)
lhs_a = inner(dot(v, mu * inv(k)), psiv) * dx - p * div(
psiv
) * dx #+ 6.0*inner(psiv,n)*ds(2) # - inner(gravity*(rho-rho0), psiv)*dx
b_time = (M_inv + pow(alpha, 2.) / K) * p_dot * psip * dx
lhs_b = div(v) * psip * dx #div(rho*v)*psip*dx #TODO rho
rhs_v = -p_outlet * inner(psiv, n) * ds(3)
rhs_p = -alpha / K * sigma_v_freeze * psip * dx - dphi_c_dt * psip * dx
r_u = [lhs_a, lhs_b]
j_u = block_derivative(r_u, block_w, trial)
r_u_dot = [a_time, b_time]
j_u_dot = block_derivative(r_u_dot, block_w_dot, trial_dot)
r = [r_u_dot[0] + r_u[0] - rhs_v, \
r_u_dot[1] + r_u[1] - rhs_p]
def bc(t):
#bc_v = [DirichletBC(W.sub(0), (.0, .0), boundaries, 4)]
v1 = DirichletBC(W.sub(0), (1.e-4 * 2.0, 0.0), boundaries, 1)
v2 = DirichletBC(W.sub(0), (0.0, 0.0), boundaries, 2)
v4 = DirichletBC(W.sub(0), (0.0, 0.0), boundaries, 4)
bc_v = [v1, v2, v4]
return BlockDirichletBC([bc_v, None])
# Define problem wrapper
class ProblemWrapper(object):
def set_time(self, t):
pass
#g.t = t
# Residual and jacobian functions
def residual_eval(self, t, solution, solution_dot):
#print(as_backend_type(assemble(p_time - p_time_error)).vec().norm())
#print("gravity effect", as_backend_type(assemble(inner(gravity*(rho-rho0), psiv)*dx)).vec().norm())
return r
def jacobian_eval(self, t, solution, solution_dot,
solution_dot_coefficient):
return [[Constant(solution_dot_coefficient)*j_u_dot[0, 0] + j_u[0, 0], \
Constant(solution_dot_coefficient)*j_u_dot[0, 1] + j_u[0, 1]], \
[Constant(solution_dot_coefficient)*j_u_dot[1, 0] + j_u[1, 0], \
Constant(solution_dot_coefficient)*j_u_dot[1, 1] + j_u[1, 1]]]
# Define boundary condition
def bc_eval(self, t):
return bc(t)
# Define initial condition
def ic_eval(self):
return solution0
# Define custom monitor to plot the solution
def monitor(self, t, solution, solution_dot):
pass
# Solve the time dependent problem
problem_wrapper = ProblemWrapper()
(solution, solution_dot) = (block_w, block_w_dot)
solver = TimeStepping(problem_wrapper, solution, solution_dot)
solver.set_parameters({
"initial_time": t_start,
"time_step_size": dt,
"monitor": {
"time_step_size": monitor_dt,
},
"final_time": T,
"exact_final_time": "stepover",
"integrator_type": integrator_type,
"problem_type": "linear",
"linear_solver": "mumps",
"report": True
})
export_solution = solver.solve()
return export_solution, T