def _assemble_and_solve_adj_eq(self, dFdu_adj_form, dJdu, compute_bdy):
dJdu_copy = dJdu.copy()
bcs = self._homogenize_bcs()
solver = self.block_helper.adjoint_solver
if solver is None:
if self.assemble_system:
rhs_bcs_form = backend.inner(backend.Function(self.function_space),
dFdu_adj_form.arguments()[0]) * backend.dx
A, _ = backend.assemble_system(dFdu_adj_form, rhs_bcs_form, bcs)
else:
A = compat.assemble_adjoint_value(dFdu_adj_form)
[bc.apply(A) for bc in bcs]
solver = backend.LUSolver(A, self.method)
self.block_helper.adjoint_solver = solver
solver.parameters.update(self.lu_solver_parameters)
[bc.apply(dJdu) for bc in bcs]
adj_sol = backend.Function(self.function_space)
solver.solve(adj_sol.vector(), dJdu)
adj_sol_bdy = None
if compute_bdy:
adj_sol_bdy = compat.function_from_vector(self.function_space, dJdu_copy - compat.assemble_adjoint_value(
backend.action(dFdu_adj_form, adj_sol)))
return adj_sol, adj_sol_bdy
def _forward_solve(self, lhs, rhs, func, bcs, **kwargs):
solver = self.block_helper.forward_solver
if solver is None:
if self.assemble_system:
A, _ = backend.assemble_system(lhs, rhs, bcs,
**self.assemble_kwargs)
else:
A = compat.assemble_adjoint_value(lhs, **self.assemble_kwargs)
[bc.apply(A) for bc in bcs]
solver = backend.LUSolver(A, self.method)
self.block_helper.forward_solver = solver
if self.assemble_system:
system_assembler = backend.SystemAssembler(lhs, rhs, bcs)
b = backend.Function(self.function_space).vector()
system_assembler.assemble(b)
else:
b = compat.assemble_adjoint_value(rhs)
[bc.apply(b) for bc in bcs]
if self.ident_zeros_tol is not None:
A.ident_zeros(self.ident_zeros_tol)
solver.parameters.update(self.lu_solver_parameters)
solver.solve(func.vector(), b)
return func
def __init__(self, problem: ProblemForm, fields: Fields,
boundary_conditions: List[fenics.DirichletBC]):
super().__init__(problem, fields, boundary_conditions)
self.a_form = problem.get_weak_form_lhs(fields=fields)
self.L_form = problem.get_weak_form_rhs(fields=fields)
self.boundary_conditions = boundary_conditions
self.K, _ = fenics.assemble_system(self.a_form, self.L_form,
self.boundary_conditions)
self.solver = fenics.LUSolver(self.K, "mumps")
self.solver.parameters["symmetric"] = True
def _get_solvers_and_y():
if not bilinear_form_is_symmetric:
# Homogenized and original boundary conditions have equivalent effect on matrix
# corresponding to assembled bilinear form
A_solver = construct_solver(A, boundary_conditions)
b_vector = fenics.assemble(b)
adjoint_A_solver = construct_solver(
adjoint_A, homogenized_boundary_conditions)
solve_with_boundary_conditions(A_solver, boundary_conditions,
b_vector, x)
else:
A_matrix, b_vector = fenics.assemble_system(
A, b, boundary_conditions)
A_solver = fenics.LUSolver(A_matrix)
A_solver.parameters["symmetric"] = True
adjoint_A_solver = A_solver # A is symmetric therefore adjoint(A) == A
A_solver.solve(x.vector(), b_vector)
y = (x.vector()).get_local()[observation_dof_indices]
return A_solver, adjoint_A_solver, y
def test_minexample():
import scipy.integrate
import fenics as fe
import numpy as np
import magnics
# Material parameters
Ms = 8.6e5 # saturation magnetisation (A/m)
alpha = 0.1 # Gilbert damping
gamma = 2.211e5 # gyromagnetic ratio
A = 1e-11 # exchange constant (J/m)
#A = 0
D = 0*1.58e-3 # DMI constant (FeGe: D = 1.58e-3 J/m²)
K = 0*5e3 # anisotropy constant (Co: K = 4.5e5 J/m³)
# External magnetic field.
B = 0.1 # (T)
mu0 = 4 * np.pi * 1e-7 # vacuum permeability
# Zeeman field
H = Ms / 2 * fe.Constant((0,0,1))
# easy axis
ea = fe.Constant((0,1,1))
# mesh parameters
d = 100e-9
thickness = 100e-9
nx = ny = 20
nz = 10
# create mesh
p1 = fe.Point(0, 0, 0)
p2 = fe.Point(d, d, thickness)
mesh = fe.BoxMesh(p1, p2, nx, ny, nz)
m, Heff, u, v, V = magnics.vectorspace(mesh)
def effective_field(m, volume=None):
w_Zeeman = - mu0 * Ms * fe.dot(m, H)
w_exchange = A * fe.inner(fe.grad(m), fe.grad(m))
w_DMI = D * fe.inner(m, fe.curl(m))
w_ani = - K * fe.inner(m, ea)**2
w = w_Zeeman + w_exchange + w_DMI + w_ani
return -1/(mu0*Ms) * fe.derivative(w*fe.dx, m)
# Effective field
Heff_form = effective_field(m)
# Preassemble projection Matrix
Amat = fe.assemble(fe.dot(u, v)*fe.dx)
LU = fe.LUSolver()
LU.set_operator(Amat)
def compute_dmdt(m):
"""Convenience function that does all in one go"""
# Assemble RHS
b = fe.assemble(Heff_form)
# Project onto Heff
LU.solve(Heff.vector(), b)
LLG = -gamma/(1+alpha*alpha)*fe.cross(m, Heff) - alpha*gamma/(1+alpha*alpha)*fe.cross(m, fe.cross(m, Heff))
result = fe.assemble(fe.dot(LLG, v)*fe.dP)
return result.array()
# function for integration of system of ODEs
def rhs_micromagnetic(m_vector_array, t, counter=[0]):
assert isinstance(m_vector_array, np.ndarray)
m.vector()[:] = m_vector_array[:]
dmdt = compute_dmdt(m)
return dmdt
m_init = fe.Constant((1, 0, 0))
m = fe.interpolate(m_init, V)
ts = np.linspace(0, 1e-11, 100)
# empty call of time integrator, just to get FEniCS to cache all forms etc
rhs_micromagnetic(m.vector().array(), 0)
ms = scipy.integrate.odeint(rhs_micromagnetic, y0=m.vector().array(), t=ts, rtol=1e-10, atol=1e-10)
def macrospin_analytic_solution(alpha, gamma, H, t_array):
"""
Computes the analytic solution of magnetisation x component
as a function of time for the macrospin in applied external
magnetic field H.
Source: PhD Thesis Matteo Franchin,
http://eprints.soton.ac.uk/161207/1.hasCoversheetVersion/thesis.pdf,
Appendix B, page 127
"""
t0 = 1 / (gamma * alpha * H) * np.log(np.sin(np.pi / 2) / \
(1 + np.cos(np.pi / 2)))
mx_analytic = []
for t in t_array:
phi = gamma * H * t # (B16)
costheta = np.tanh(gamma * alpha * H * (t - t0)) # (B17)
sintheta = 1 / np.cosh(gamma * alpha * H * (t - t0)) # (B18)
mx_analytic.append(sintheta * np.cos(phi))
return np.array(mx_analytic)
mx_analytic = macrospin_analytic_solution(alpha, gamma, Ms/2, ts)
tmp2 = ms[:,0:1] # might be m_x, m_y, m_z of first vector
difference = tmp2[:,0] - mx_analytic
print("max deviation: {}".format(max(abs(difference))))
# add quick test
eps = 0.01
#ref = 0.0655908475021 # for tmax = 1e-10
ref = 0.0422068879247 # for tmax = 5e-11
ref = 0.00765261606231 # for tmax = 1e-11
assert ref - eps < max(abs(difference)) < ref + eps
def fwi_si(gt_data, i_guess, n_receivers, noise_lv, path):
"""
This is the main function of the project.
Entries
gt_data: string path to the ground truth image data
i_guess: integer pointing the algorithm initialization guess
n_shots: integer, number of strikes for the FWI
n_receivers: integer, number of receivers for the FWI
noise_lv: float type variable that we use to compute noise level
path: string type variable, path to local results directory
"""
# Implementing parallel processing at shots level """
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
n_shots = comm.Get_size()
seism_vel = [4.12, 1.95]
image_phi = mpimg.imread(gt_data)
chi0 = np.int64(image_phi == 0)
chi1 = 1.0 - chi0
synth_model = seism_vel[0] * chi1 + seism_vel[1] * chi0
#scale in meter
xMin = 0.0
xMax = 1.0
zMin = 0.0
zMax = 0.650
#scale in seconds
tMin = 0.0
tMax = 1.0
# Damping layer width and damping limits
damp_layer = 0.1 * xMax
dmp_xMin = xMin + damp_layer
dmp_xMax = xMax - damp_layer
dmp_zMax = zMax - damp_layer
# Number of grid points are determined by the loaded image size
# Nz, Nx are (#) of grid point
Nz, Nx = synth_model.shape
delta_x = xMax / Nx
delta_z = zMax / Nz
CFL = 0.4
delta_t = (CFL * min(delta_x, delta_z)) / max(seism_vel)
gc_t = np.arange(tMin, tMax, delta_t)
Nt = len(gc_t)
# Level set parameters
MainItMax = 5000
gamma = 0.8
gamma2 = 0.8
stop_coeff = 1.0e-8
add_weight = True
ls_max = 3
ls = 0
beta0_init = 1.5 # 1.2 #0.8 #0.5 #0.3
beta0 = beta0_init
beta = beta0
stop_decision_limit = 150
stop_decision = 0
alpha1 = 0.01
alpha2 = 0.97
# wave Parameters
PlotFields = True
add_noise = False if noise_lv == 0 else True
src_Zpos = 5.0
source_peak_frequency = 5.0 # (kilo hertz)
# Grid coordinates
gc_x = np.arange(xMin, xMax, delta_x)
gc_z = np.arange(zMin, zMax, delta_z)
# Compute receivers
id_dmp_xMin = np.where(gc_x == dmp_xMin)[0][0]
id_dmp_xMax = np.where(gc_x == dmp_xMax)[0][0]
id_dmp_zMax = np.where(gc_z == dmp_zMax)[0][0]
rec_index = np.linspace(id_dmp_xMin,
id_dmp_xMax,
n_receivers + 1,
dtype='int')
try:
assert (len(rec_index) < id_dmp_xMax - id_dmp_xMin)
except AssertionError:
"receivers in different positions"
# Build the HUGE parameter dictionary
parameters = {
"gamma": gamma,
"gamma2": gamma2,
"ls_max": ls_max,
"stop_coeff": stop_coeff,
"add_noise": add_noise,
"add_weight": add_weight,
"beta0_init": beta0_init,
"stop_decision_limit": stop_decision_limit,
"alpha1": alpha1,
"alpha2": alpha2,
"CFL": CFL,
"source_peak_frequency": source_peak_frequency,
"src_Zpos": src_Zpos,
"i_guess": i_guess,
"n_shots": n_shots,
"n_receivers": n_receivers,
"add_weight": add_weight,
"nz": Nz,
"nx": Nx,
"nt": Nt,
"gc_t": gc_t,
"gc_x": gc_x,
"gc_z": gc_z,
"xMin": xMin,
"xMax": xMax,
"zMin": zMin,
"zMax": zMax,
"tMin": tMin,
"tMax": tMax,
"hz": delta_z,
"hx": delta_x,
"ht": delta_t,
"dmp_xMin": dmp_xMin,
"dmp_xMax": dmp_xMax,
"dmp_zMax": dmp_zMax,
"dmp_layer": damp_layer,
"id_dmp_xMin": id_dmp_xMin,
"id_dmp_xMax": id_dmp_xMax,
"id_dmp_zMax": id_dmp_zMax,
"rec": gc_x[rec_index],
"rec_index": rec_index,
'noise_lv': noise_lv,
"path": path,
"path_misfit": path + 'misfit/',
"path_phi": path + 'phi/'
}
# Compute initial guess matrix
if rank == 0:
outputs_and_paths(parameters)
gnu_data(image_phi, 'ground_truth.dat', parameters)
mkDirectory(parameters["path_phi"])
comm.Barrier()
phi_mat = initial_guess(parameters)
ind = inside_shape(phi_mat)
ind_c = np.ones_like(phi_mat) - ind
vel_field = seism_vel[0] * ind + seism_vel[1] * ind_c
# Initialization of Fenics-Dolfin functions
# ----------------------------------------
# Define mesh for the entire domain Omega
# ----------------------------------------
mesh = fc.RectangleMesh(comm, fc.Point(xMin, zMin), fc.Point(xMax, zMax),
Nx - 1, Nz - 1)
# ----------------------------------------
# Function spaces
# ----------------------------------------
V = fc.FunctionSpace(mesh, "Lagrange", 1)
VF = fc.VectorFunctionSpace(mesh, "Lagrange", 1)
theta = fc.TrialFunction(VF)
csi = fc.TestFunction(VF)
# ----------------------------------------
# Define boundaries of the domain
# ----------------------------------------
tol = fc.DOLFIN_EPS # tolerance for coordinate comparisons
class Left(fc.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and abs(x[0] - xMin) < tol
class Right(fc.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and abs(x[0] - xMax) < tol
class Bottom(fc.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and abs(x[1] - zMin) < tol
class Top(fc.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and abs(x[1] - zMax) < tol
# --------------------------------------
# Initialize sub-domain instances
# --------------------------------------
left = Left()
top = Top()
right = Right()
bottom = Bottom()
# ----------------------------------------------
# Initialize mesh function for boundary domains
# ----------------------------------------------
boundaries = fc.MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
domains = fc.MeshFunction("size_t", mesh, mesh.topology().dim())
left.mark(boundaries, 3)
top.mark(boundaries, 4)
right.mark(boundaries, 5)
bottom.mark(boundaries, 6)
# ---------------------------------------
# Define operator for speed vector theta
# ---------------------------------------
dtotal = Measure("dx")
dircond = 1
# ---------------------------------------
# setting shape derivative weights
# re-balancing sensibility to be greater at the bottom
# ---------------------------------------
wei_equation = '1.0e8*(pow(x[0] - 0.5, 16) + pow(x[1] - 0.325, 10))+100'
wei = fc.Expression(str(wei_equation), degree=1)
# Building the left hand side of the bi-linear system
# to obtain the descendant direction from shape derivative
if dircond < 4:
bcF = [
fc.DirichletBC(VF, (0, 0), boundaries, 3),
fc.DirichletBC(VF, (0, 0), boundaries, 4),
fc.DirichletBC(VF, (0, 0), boundaries, 5),
fc.DirichletBC(VF, (0, 0), boundaries, 6)
]
if dircond == 1:
lhs = wei * alpha1 * inner(grad(theta), grad(csi)) * dtotal \
+ wei * alpha2 * inner(theta, csi) * dtotal
#
elif dircond == 2:
lhs = alpha1 * inner(grad(theta), grad(csi)) * \
dtotal + alpha2 * inner(theta, csi) * dtotal
elif dircond == 3:
lhs = inner(grad(theta), grad(csi)) * dtotal
elif dircond == 5:
lhs = inner(grad(theta), grad(csi)) * \
dtotal + inner(theta, csi) * dtotal
aV = fc.assemble(lhs)
#
if dircond < 4:
for bc in bcF:
bc.apply(aV)
#
# solver_V = fc.LUSolver(aV, "mumps")
solver_V = fc.LUSolver(aV)
# ------------------------------
# Initialize Level set function
# ------------------------------
phi = fc.Function(V)
phivec = phi.vector()
phivalues = phivec.get_local() # empty values
my_first, my_last = V.dofmap().ownership_range()
tabcoord = V.tabulate_dof_coordinates().reshape((-1, 2))
unowned = V.dofmap().local_to_global_unowned()
dofs = list(
filter(
lambda dof: V.dofmap().local_to_global_index(dof) not in unowned,
[i for i in range(my_last - my_first)]))
tabcoord = tabcoord[dofs]
phivalues[:] = phi_mat.reshape(Nz * Nx)[dofs] # assign values
phivec.set_local(phivalues)
phivec.apply('insert')
cont = 0
boundaries = fc.MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
domains = fc.MeshFunction("size_t", mesh, mesh.topology().dim())
# -----------------------------
# Define measures
# -----------------------------
dx = Measure('dx')(subdomain_data=domains)
# -------------------------------
# Define function Omega1
# -------------------------------
class Omega1(fc.SubDomain):
def __init__(self) -> None:
super(Omega1, self).__init__()
def inside(self, x, on_boundary):
return True if phi(x) <= 0 and x[0] >= xMin and x[0] <= xMax and x[
1] >= zMin and x[1] <= zMax else False
# instantiate variables
eta = dmp(parameters)
source = Source(parameters)
FT = source.inject()
phi_mat_old = np.zeros_like(phi_mat)
vel_field_new = np.zeros_like(vel_field)
theta1_mat = np.zeros((Nz * Nx))
theta2_mat = np.zeros_like(theta1_mat)
MainItEff = 0
MainIt = 0
stop_decision = 0
st_mem_usage = 0.0
adj_mem_usage = 0.0
Jevaltotal = np.zeros((MainItMax))
norm_theta = np.zeros((MainItMax))
# path to recording phi function
# path to recording misfit function
if rank == 0:
plot_mat(parameters, 'Damping', 'Damping function', eta)
mkDirectory(parameters["path_phi"])
mkDirectory(parameters["path_misfit"])
comm.Barrier()
# -------------------------------
# Seismograms
# -------------------------------
wavesolver = WaveSolver(parameters, eta)
start = time.time()
d_send = np.empty((Nz, Nx, Nt), np.dtype('float'))
d = wavesolver.measurements(d_send[0:Nz, 0:Nx, 0:Nt], synth_model,
FT[rank, 0:Nz, 0:Nx, 0:Nt], add_noise)
seismograms = d[0, rec_index, 0:Nt].copy(order='C')
end = time.time()
# Plot Seismograms
if PlotFields:
print("{:.1f}s to build synthetic seismograms".format(end - start))
plotMeasurements(parameters, seismograms, rank)
if rank == 0:
plot_displacement_field(parameters, d)
sys.stdout.flush()
del (d, d_send)
###################################################
# Main Loop
###################################################
gradshape = ShapeDerivative(parameters, csi, V, dtotal, seism_vel)
while MainIt < MainItMax:
# ----------------------------------------------
# Initialize mesh function for boundary domains
# ----------------------------------------------
if MainIt > 0:
vel_field = vel_field_new
domains.set_all(0)
omega1 = Omega1()
omega1.mark(domains, 1)
dx = Measure('dx')(subdomain_data=domains)
u = np.empty((Nz, Nx, Nt), np.dtype('float'))
P = np.empty((Nz, Nx, Nt), np.dtype('float'))
if MainIt > 0:
vel_field = vel_field_new
# ------------------------------------
# Compute STATE. u stands for displacement field
# ------------------------------------
start = time.time()
u[0:Nz, 0:Nx, 0:Nt] = wavesolver.state(u[0:Nz, 0:Nx, 0:Nt], vel_field,
FT[rank, 0:Nz, 0:Nx, 0:Nt])
end = time.time()
# ------------------------------------
# Compute ADJOINT. P stands for the adjoint variable
# ------------------------------------
start1 = time.time()
tr_u = u[0, rec_index, 0:Nt].copy(order='C')
misfit = tr_u - seismograms
P[0:Nz, 0:Nx, 0:Nt] = wavesolver.adjoint(P[0:Nz, 0:Nx, 0:Nt],
vel_field, misfit)
end1 = time.time()
comm.Barrier()
print(
'{:.1f}s to compute state and {:.1f}s to compute adjoint with {:d} shots. '
.format(end - start, end1 - start1, n_shots))
del (start, end, start1, end1)
# Plot state/adjoint in 1st-iteration only
if MainIt == 0 and PlotFields:
if rank == 0:
mkDirectory(path + 'initial_state_%03d/' % (n_shots))
plotadjoint(parameters, P[0:Nz, 0:Nx, 0:Nt])
folder_name = 'initial_state_%03d/' % (n_shots)
plotstate(parameters, u[0:Nz, 0:Nx, 0:Nt], folder_name, rank)
# plot_displacement_field(parameters, u[1, 0:Nz, 0:Nx, 0:Nt])
st_mem_usage = (u.size * u.itemsize) / 1_073_741_824 # 1GB
adj_mem_usage = (P.size * P.itemsize) / 1_073_741_824 # 1GB
# Plotting reconstructions
if rank == 0 and (MainItEff % 10 == 0
or stop_decision == stop_decision_limit - 1):
plottype1(parameters, synth_model, phi_mat, cont)
plottype2(parameters, synth_model, phi_mat, cont)
plottype3(parameters, synth_model, phi_mat, MainIt, cont)
plotcostfunction(parameters, Jevaltotal, MainItEff)
plotnormtheta(parameters, norm_theta, MainItEff)
np.save(path + 'last_phi_mat.npy', phi_mat)
gnu_data(phi_mat, 'reconstruction.dat', parameters)
plot_misfit(parameters, 'misfit', 'Misfit', misfit,
rank) if (MainItEff % 50 == 0 and PlotFields) else None
# -------------------------
# Compute Cost Function
# -------------------------
J_omega = np.zeros((1))
l2_residual = np.sum(np.power(misfit, 2), axis=0)
if MainIt == 0 and add_weight:
weights = 1.0e-5
comm.Reduce(simpson_rule(l2_residual[0:Nt], gc_t), J_omega, op=MPI.SUM)
Jevaltotal[MainItEff] = 0.5 * (J_omega / weights)
del (J_omega)
# -------------------------
# Evaluate shape derivative
# -------------------------
start = time.time()
shapeder = (1.0 / weights) * gradshape.compute(u[0:Nz, 0:Nx, 0:Nt],
P[0:Nz, 0:Nx, 0:Nt], dx)
# Build the rhs of bi-linear system
shapeder = fc.assemble(shapeder)
end = time.time()
print('{}s to compute shape derivative.'.format(end - start))
del (start, end)
del (u, P)
with open(path + "cost_function.txt", "a") as file_costfunction:
file_costfunction.write('{:d} - {:.4e} \n'.format(
MainItEff, Jevaltotal[MainItEff]))
# ====================================
# ---------- Line search -------------
# ====================================
if MainIt > 0 and Jevaltotal[MainItEff] > Jevaltotal[
MainItEff - 1] and ls < ls_max:
ls = ls + 1
beta = beta * gamma
phi_mat = phi_mat_old
# ------------------------------------------------------------
# Update level set function using the descent direction theta
# ------------------------------------------------------------
hj_input = [
theta1_mat, theta2_mat, phi_mat, parameters, beta, MainItEff
]
phi_mat = hamiltonjacobi(*hj_input)
del (hj_input)
ind = inside_shape(phi_mat)
ind_c = np.ones_like(phi_mat) - ind
vel_field_new = seism_vel[0] * ind + seism_vel[1] * ind_c
phivec = phi.vector()
phivalues = phivec.get_local() # empty values
my_first, my_last = V.dofmap().ownership_range()
tabcoord = V.tabulate_dof_coordinates().reshape((-1, 2))
set_trace()
unowned = V.dofmap().local_to_global_unowned()
dofs = list(
filter(
lambda dof: V.dofmap().local_to_global_index(dof) not in
unowned, [i for i in range(my_last - my_first)]))
tabcoord = tabcoord[dofs]
phivalues[:] = phi_mat.reshape(Nz * Nx)[dofs] # assign values
phivec.set_local(phivalues)
phivec.apply('insert')
else:
print("----------------------------------------------")
print("Record in: {}".format(path))
print("----------------------------------------------")
print("ITERATION NUMBER (MainItEff) : {:d}".format(MainItEff))
print("ITERATION NUMBER (MainIt) : {:d}".format(MainIt))
print("----------------------------------------------")
print("Grid Size : {:d} x {:d}".format(Nx, Nz))
print("State memory usage : {:.4f} GB".format(st_mem_usage))
print("Adjoint memory usage : {:.4f} GB".format(adj_mem_usage))
print("----------------------------------------------")
print("Line search iterations : {:d}".format(ls))
print("Step length beta : {:.4e}".format(beta))
if ls == ls_max:
beta0 = max(beta0 * gamma2, 0.1 * beta0_init)
if ls == 0:
beta0 = min(beta0 / gamma2, 1.0)
ls = 0
MainItEff = MainItEff + 1
beta = beta0 # /(0.999**MainIt)
theta = fc.Function(VF)
solver_V.solve(theta.vector(), -1.0 * shapeder)
# ------------------------------------
# Compute norm theta and grad(phi)
# ------------------------------------
mpi_comm = theta.function_space().mesh().mpi_comm()
arraytheta = theta.vector().get_local()
theta_gathered = mpi_comm.gather(arraytheta, root=0)
# parei aqui !!!!!
comm.Barrier()
if rank == 0:
set_trace()
theta_vec = theta.vector()[fc.vertex_to_dof_map(VF)]
theta1_mat = theta_vec[0:len(theta_vec):2].reshape(Nz, Nx)
theta2_mat = theta_vec[1:len(theta_vec):2].reshape(Nz, Nx)
norm_theta[MainItEff - 1] = np.sqrt(
theta1_mat.reshape(Nz * Nx).dot(theta1_mat.reshape(Nx * Nz)) +
theta2_mat.reshape(Nz * Nx).dot(theta2_mat.reshape(Nx * Nz)))
max_gnp = np.sqrt(fc.assemble(dot(grad(phi), grad(phi)) * dtotal))
print("Norm(grad(phi)) : {:.4e}".format(max_gnp))
print("L2-norm of theta : {:.4e}".format(
norm_theta[MainItEff - 1]))
print("Cost functional : {:.4e}".format(
Jevaltotal[MainItEff - 1]))
# ------------------------------------------------------------
# Update level set function using the descent direction theta
# ------------------------------------------------------------
phi_mat_old = phi_mat
hj_input = [
theta1_mat, theta2_mat, phi_mat, parameters, beta,
MainItEff - 1
]
phi_mat = hamiltonjacobi(*hj_input)
del (hj_input)
phi.vector()[:] = phi_mat.reshape(
(Nz) * (Nx))[fc.dof_to_vertex_map(V)]
ind = inside_shape(phi_mat)
ind_c = np.ones_like(phi_mat) - ind
vel_field_new = seism_vel[0] * ind + seism_vel[1] * ind_c
# ----------------
# Computing error
# ----------------
error_area = np.abs(chi1 - ind)
relative_error = np.sum(error_area) / np.sum(chi0)
print('relative error : {:.3f}%'.format(100 *
relative_error))
with open(path + "error.txt", "a") as text_file:
text_file.write(f'{MainIt} {np.round(relative_error,3):>3}\n')
# Plot actual phi function
if MainIt % 50 == 0:
plot_mat3D(parameters, 'phi_3D', phi_mat, MainIt)
plot_countour(parameters, 'phi_contour', phi_mat, MainIt)
phi_ind = '%03d_' % (MainIt)
np.save(parameters["path_phi"] + phi_ind + 'phi.npy', phi_mat)
# --------------------------------
# Reinitialize level set function
# --------------------------------
if np.mod(MainItEff, 10) == 0:
phi_mat = reinit(Nz, Nx, phi_mat)
# ====================================
# -------- Stopping criterion --------
# ====================================
if MainItEff > 5:
stop0 = stop_coeff * (Jevaltotal[1] - Jevaltotal[2])
stop1 = Jevaltotal[MainItEff - 2] - Jevaltotal[MainItEff - 1]
if stop1 < stop0:
stop_decision = stop_decision + 1
if stop_decision == stop_decision_limit:
MainIt = MainItMax + 1
print("stop0 : {:.4e}".format(stop0))
print("stop1 : {:.4e}".format(stop1))
print("Stopping step : {:d} of {:d}".format(
stop_decision, stop_decision_limit))
print("----------------------------------------------\n")
cont += 1
MainIt += 1
return None
w_DMI = D * fe.inner(m, fe.curl(m))
w_ani = -K * fe.inner(m, ea)**2
w = w_Zeeman + w_exchange + w_DMI + w_ani
return -1 / (mu0 * Ms) * fe.derivative(w * fe.dx, m)
m_init = fe.Constant((1, 0, 0))
m = fe.interpolate(m_init, V)
# Effective field
Heff_form = effective_field(m)
# Preassemble projection Matrix
Amat = fe.assemble(fe.dot(u, v) * fe.dx)
LU = fe.LUSolver()
LU.set_operator(Amat)
def compute_dmdt(m):
"""Convenience function that does all in one go"""
# Assemble RHS
b = fe.assemble(Heff_form)
# Project onto Heff
LU.solve(Heff.vector(), b)
LLG = -gamma / (1 + alpha * alpha) * fe.cross(m, Heff) - alpha * gamma / (
1 + alpha * alpha) * fe.cross(m, fe.cross(m, Heff))
CFL = 5.0
dt = CFL * hsize * hsize
T = 2.0
frequencySave = 100
# weak form
Left = u/dt * uT * fn.dx + v/dt * vT * fn.dx \
+ c1 * fn.inner(fn.grad(u), fn.grad(uT)) * fn.dx \
+ c2 * fn.inner(fn.grad(v), fn.grad(vT)) * fn.dx
Right = uold * uT/dt * fn.dx + vold * vT/dt * fn.dx \
+ d * (a - uold + uold * uold * vold) * uT * fn.dx \
+ d * (b - uold * uold * vold) * vT * fn.dx
AA = fn.assemble(Left)
solver = fn.LUSolver(AA)
solver.parameters["reuse_factorization"] = True
# time loop
inc = 0
while (t <= T):
print "t =", t
# solve
BB = fn.assemble(Right)
solver.solve(Sol.vector(), BB)
# output to file
u, v = Sol.split()
def construct_solver(bilinear_form, boundary_conditions):
matrix = fenics.assemble(bilinear_form)
apply_boundary_conditions(matrix, boundary_conditions)
return fenics.LUSolver(matrix)
#Tiempos intermedio entre tn y tn+1 utilizando modelo alfa generalizado
def avg(x_old, x_new, alpha):
return alpha * x_old + (1 - alpha) * x_new
#Formulación variacional
a_new = update_a(du, u_old, v_old, a_old, ufl=True)
v_new = update_v(a_new, u_old, v_old, a_old, ufl=True)
res = m(avg(a_old, a_new, alpha_m), w) + c(avg(v_old, v_new, alpha_f), w) + k(
avg(u_old, du, alpha_f), w) - Wext(w)
a_form = fnc.lhs(res)
L_form = fnc.rhs(res)
#Solvers (veremos luego)
K, res = fnc.assemble_system(a_form, L_form, bc)
solver = fnc.LUSolver(K, 'default') #"mumps")
solver.parameters["symmetric"] = True
# We now initiate the time stepping loop. We will keep track of the beam vertical tip
# displacement over time as well as the different parts of the system total energy. We
# will also compute the stress field and save it, along with the displacement field, in
# a ``XDMFFile``.
# The option `flush_ouput` enables to open the result file before the loop is finished,
# the ``function_share_mesh`` option tells that only one mesh is used for all functions
# of a given time step (displacement and stress) while the ``rewrite_function_mesh`` enforces
# that the same mesh is used for all time steps. These two options enables writing the mesh
# information only once instead of :math:`2N_{steps}` times::
# Time-stepping
time = np.linspace(0, T, Nsteps + 1)
u_tip = np.zeros((Nsteps + 1, ))
# Compare timing of fenics solve vs scipy solve
import scipy.sparse.linalg as spla
t = time()
solve_A_scipy = spla.factorized(A_scipy)
scipy_factorization_time = time() - t
print('scipy_factorization_time=', scipy_factorization_time)
t = time()
x_numpy = solve_A_scipy(b_numpy)
scipy_solve_time = time() - t
print('scipy_solve_time=', scipy_solve_time)
t = time()
solve_A_fenics = fenics.LUSolver(A_fenics)
fenics_factorization_time = time() - t
print('fenics_factorization_time=', fenics_factorization_time)
x = fenics.Function(V)
t = time()
solve_A_fenics.solve(x.vector(), b_fenics)
fenics_first_solve_time = time() - t
print('fenics_first_solve_time=', fenics_first_solve_time)
x2 = fenics.Function(V)
t = time()
solve_A_fenics.solve(x2.vector(), b_fenics)
fenics_second_solve_time = time() - t
