def example3(Ms):
x0 = y0 = z0 = 0
x1 = 500
y1 = 10
z1 = 500
nx = 50
ny = 1
nz = 1
mesh = df.Box(x0, y0, z0, x1, y1, z1, nx, ny, nz)
sim = Sim(mesh, Ms, unit_length=1e-9)
sim.alpha = 0.01
sim.set_m((1, 0, 0.1))
H_app = Zeeman((0, 0, 5e5))
sim.add(H_app)
exch = fe.Exchange(13.0e-12)
sim.add(exch)
demag = Demag(solver="FK")
sim.add(demag)
llg = sim.llg
max_time = 1 * np.pi / (llg.gamma * 1e5)
ts = np.linspace(0, max_time, num=100)
for t in ts:
print t
sim.run_until(t)
df.plot(llg._m)
df.interactive()
def ring_down(m0=(1, 0.01, 0), pbc=None):
n = 49
assert n >= 1 and n % 2 == 1
Ms = 8.6e5
sim = Simulation(mesh, Ms, unit_length=1e-9, name='dy', pbc='1d')
sim.alpha = 1e-3
sim.set_m(m0)
sim.set_tol(1e-8, 1e-8)
parameters = {
'absolute_tolerance': 1e-10,
'relative_tolerance': 1e-10,
'maximum_iterations': int(1e5)
}
Ts = []
for i in range(-n / 2 + 1, n / 2 + 1):
Ts.append((10. * i, 0, 0))
demag = Demag(Ts=Ts)
demag.parameters['phi_1'] = parameters
demag.parameters['phi_2'] = parameters
sim.add(demag)
sim.add(Exchange(1.3e-11))
sim.schedule('save_ndt', every=2e-12)
sim.run_until(4e-9)
def test_zhangli():
#mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(100, 1, 1), 50, 1, 1)
mesh = df.IntervalMesh(50, 0, 100)
sim = Sim(mesh, Ms=8.6e5, unit_length=1e-9, kernel='llg_stt')
sim.set_m(init_m)
sim.add(UniaxialAnisotropy(K1=520e3, axis=[1, 0, 0]))
sim.add(Exchange(A=13e-12))
sim.alpha = 0.01
sim.llg.set_parameters(J_profile=init_J, speedup=50)
p0 = sim.m_average
sim.run_until(5e-12)
p1 = sim.m_average
print sim.integrator.stats()
print p0, p1
sim.run_until(1e-11)
p1 = sim.m_average
print sim.integrator.stats()
print p0, p1
assert p1[0] < p0[0]
assert abs(p0[0]) < 1e-15
assert abs(p1[0]) > 1e-3
def run_finmag(demagsolver):
"""Run the finmag simulation and store data in (demagsolvertype)averages.txt."""
sim = Sim(mesh, Ms, unit_length=unit_length)
sim.alpha = 0.5
sim.set_m((1, 0, 1))
exchange = Exchange(13.0e-12)
sim.add(exchange)
demag = Demag(solver=demagsolver)
sim.add(demag)
fh = open(os.path.join(MODULE_DIR, demagsolver + "averages.txt"), "w")
fe = open(os.path.join(MODULE_DIR, demagsolver + "energies.txt"), "w")
# Progressbar
bar = pb.ProgressBar(maxval=60, \
widgets=[pb.ETA(), pb.Bar('=', '[', ']'), ' ', pb.Percentage()])
logger.info("Time integration")
times = np.linspace(0, 3.0e-10, 61)
#times = np.linspace(0, 3.0e-10, 100000)
for counter, t in enumerate(times):
bar.update(counter)
# Integrate
sim.run_until(t)
print counter
print("press return to continue")
_ = raw_input()
# Save averages to file
mx, my, mz = sim.m_average
fh.write(str(t) + " " + str(mx) + " " + str(my) + " " + str(mz) + "\n")
# Energies
E_e = exchange.compute_energy()
E_d = demag.compute_energy()
fe.write(str(E_e) + " " + str(E_d) + "\n")
# Energy densities
if counter == 10:
exch_energy = exchange.energy_density_function()
demag_energy = demag.demag.energy_density_function()
finmag_exch, finmag_demag = [], []
R = range(100)
for i in R:
finmag_exch.append(exch_energy([15, 15, i]))
finmag_demag.append(demag_energy([15, 15, i]))
# Store data
np.save(
os.path.join(MODULE_DIR,
"finmag%s_exch_density.npy" % demagsolver),
np.array(finmag_exch))
np.save(
os.path.join(MODULE_DIR,
"finmag%s_demag_density.npy" % demagsolver),
np.array(finmag_demag))
fh.close()
fe.close()
def run_simulation():
L = 3e-8
W = 1e-8
H = 1e-8
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(L, W, H), 10, 4, 4)
Ms = 0.86e6 # A/m
A = 1.3e-11 # J/m
sim = Sim(mesh, Ms)
sim.set_m(("2*x[0]/L - 1", "2*x[1]/W - 1", "1"), L=3e-8, H=1e-8, W=1e-8)
sim.alpha = 0.1
sim.add(Zeeman((Ms / 2, 0, 0)))
sim.add(Exchange(A))
t = 0
dt = 1e-11
tmax = 1e-9 # s
fh = open(os.path.join(MODULE_DIR, "averages.txt"), "w")
while t <= tmax:
mx, my, mz = sim.m_average
fh.write(str(t) + " " + str(mx) + " " + str(my) + " " + str(mz) + "\n")
t += dt
sim.run_until(t)
fh.close()
def run_sim_with_stt():
sim = Sim(mesh, Ms=8.6e5)
sim.set_m((1, 0.01, 0.01))
sim.alpha = 0.014
sim.gamma = 221017
H_app_mT = np.array([0.2, 0.2, 10.0])
H_app_SI = H_app_mT / (1000 * mu0)
sim.add(Zeeman(tuple(H_app_SI)))
sim.add(Exchange(1.3e-11))
sim.add(UniaxialAnisotropy(1e5, (0, 0, 1)))
I = 5e-5 # current in A
J = I / (L * W) # current density in A/m^2
theta = 40.0 * pi / 180
phi = pi / 2 # polarisation direction
p = (sin(theta) * cos(phi), sin(theta) * sin(phi), cos(theta))
sim.llg.use_slonczewski(J=J, P=0.4, d=5e-9, p=(0, 1, 0))
with open(averages_with, "w") as f:
dt = 5e-12
t_max = 10e-9
for t in np.arange(0, t_max, dt):
sim.run_until(t)
f.write("{} {} {} {}\n".format(t, *sim.m_average))
def relax_system():
Ms = 8.6e5
sim = Simulation(mesh, Ms, unit_length=1e-9, name = 'dy')
sim.alpha = 0.001
sim.set_m(np.load('m_000088.npy'))
#sim.set_tol(1e-6, 1e-6)
A = 1.3e-11
sim.add(Exchange(A))
parameters = {
'absolute_tolerance': 1e-10,
'relative_tolerance': 1e-10,
'maximum_iterations': int(1e5)
}
demag = Demag()
demag.parameters['phi_1'] = parameters
demag.parameters['phi_2'] = parameters
print demag.parameters
sim.add(demag)
sim.schedule('save_ndt', every=2e-12)
sim.schedule('save_vtk', every=2e-12, filename='vtks/m.pvd')
sim.schedule('save_m', every=2e-12, filename='npys/m.pvd')
sim.run_until(1e-9)
def run_simulation():
L = W = 12.5e-9
H = 2.5e-9
sim = Sim(mesh, Ms=8.6e5, unit_length=1e-9)
sim.set_m((1, 0.01, 0.01))
sim.alpha = 0.014
sim.gamma = 221017
H_app_mT = np.array([0.0, 0.0, 10.0])
H_app_SI = H_app_mT / (1000 * mu0)
sim.add(Zeeman(tuple(H_app_SI)))
sim.add(Exchange(1.3e-11))
I = 5e-5 # current in A
J = I / (L * W) # current density in A/m^2
theta = 40.0 * pi / 180
phi = pi / 2 # polarisation direction
p = (sin(theta) * cos(phi), sin(theta) * sin(phi), cos(theta))
sim.llg.use_slonczewski(J=J, P=0.4, d=H, p=p)
with open(averages_file, "w") as f:
dt = 10e-12
t_max = 10e-9
for t in np.arange(0, t_max, dt):
sim.run_until(t)
f.write("{} {} {} {}\n".format(t, *sim.m_average))
def macrospin(Ms=0.86e6,
m_init=(1, 0, 0),
H_ext=(0, 0, 1e6),
alpha=0.1,
name='macrospin'):
"""
Minimal mesh with two vertices (1 nm apart). No anisotropy,
exchange coupling or demag is present so that magnetic moments at
the two vertices behave identical under the influence of the
external field. (Ideally, we would only have a single vertex but
Dolfin doesn't support this.)
Default values for the arguments:
Ms = 0.86e6 (saturation magnetisation in A/m)
m_init = (1, 0, 0) (initial magnetisation pointing along the x-axis)
H_ext = (0, 0, 1e6) (external field in A/m)
alpha = 0.1 (Gilbert damping coefficient)
"""
mesh = df.UnitIntervalMesh(1)
sim = Simulation(mesh, Ms=Ms, unit_length=1e-9, name=name)
sim.alpha = alpha
sim.set_m(m_init)
sim.add(Zeeman(H_ext))
return sim
def setup_module(module=None):
# define the mesh
x_max = 20e-9 # m
simplexes = 10
mesh = IntervalMesh(simplexes, 0, x_max)
def m_gen(coords):
x = coords[0]
mx = min(1.0, 2.0 * x / x_max - 1.0)
my = np.sqrt(1.0 - mx**2)
mz = 0.0
return np.array([mx, my, mz])
Ms = 0.86e6
A = 1.3e-11
global sim
sim = Sim(mesh, Ms)
sim.alpha = 0.2
sim.set_m(m_gen)
sim.pins = [0, 10]
exchange = Exchange(A)
sim.add(exchange)
# Save H_exc and m at t0 for comparison with nmag
global H_exc_t0, m_t0
H_exc_t0 = exchange.compute_field()
m_t0 = sim.m
t = 0
t1 = 5e-10
dt = 1e-11
# s
av_f = open(os.path.join(MODULE_DIR, "averages.txt"), "w")
tn_f = open(os.path.join(MODULE_DIR, "third_node.txt"), "w")
global averages
averages = []
global third_node
third_node = []
while t <= t1:
mx, my, mz = sim.m_average
averages.append([t, mx, my, mz])
av_f.write(
str(t) + " " + str(mx) + " " + str(my) + " " + str(mz) + "\n")
mx, my, mz = h.components(sim.m)
m2x, m2y, m2z = mx[2], my[2], mz[2]
third_node.append([t, m2x, m2y, m2z])
tn_f.write(
str(t) + " " + str(m2x) + " " + str(m2y) + " " + str(m2z) + "\n")
t += dt
sim.run_until(t)
av_f.close()
tn_f.close()
def create_initial_state():
print "Creating initial relaxed state."
sim = Sim(mesh, Ms=Ms, unit_length=1e-9)
sim.set_m(m_gen)
sim.alpha = 0.5
sim.add(Exchange(1.3e-11))
sim.add(Demag())
sim.relax()
np.savetxt(initial_m_file, sim.m)
def test_deviations_over_alpha_and_tol(number_of_alphas=5, do_plot=False):
alphas = numpy.linspace(0.01, 1.00, number_of_alphas)
max_deviationss = []
for rtol_power_of_ten in rtols_powers_of_ten:
rtol = pow(10, rtol_power_of_ten)
print "#### New series for rtol={0}. ####".format(rtol)
# One entry in this array corresponds to the maximum deviation between
# the analytical solution and the computed solution for one value of alpha.
max_deviations = []
for alpha in alphas:
print "Solving for alpha={0}.".format(alpha)
sim = Simulation(mesh, 1, unit_length=1e-9)
sim.alpha = alpha
sim.set_m((1, 0, 0))
sim.add(Zeeman((0, 0, 1e5)))
ts = numpy.linspace(0, 1e-9, num=50)
ys = odeint(sim.llg.solve_for,
sim.llg._m_field.get_numpy_array_debug(),
ts,
rtol=rtol,
atol=rtol)
# One entry in this array corresponds to the deviation between the two
# solutions for one particular moment during the simulation.
deviations = []
M_analytical = make_analytic_solution(1e5, alpha, sim.gamma)
for i in range(len(ts)):
M_computed = numpy.mean(ys[i].reshape((3, -1)), 1)
M_ref = M_analytical(ts[i])
# The difference of the two vectors has 3 components. The
# deviation is the average over these components.
deviation = numpy.mean(numpy.abs(M_computed - M_ref))
assert deviation < TOLERANCE
deviations.append(deviation)
# This represents the addition of one point to the graph.
max_deviations.append(numpy.max(deviations))
# This represents one additional series in the graph.
max_deviationss.append(max_deviations)
if do_plot:
for i in range(len(rtols_powers_of_ten)):
label = r"$rtol=1\cdot 10^{" + str(rtols_powers_of_ten[i]) + r"}$"
plt.plot(alphas, max_deviationss[i], ".", label=label)
plt.legend()
plt.title(r"Influence of $\alpha$ and rtol on the Deviation")
plt.ylabel("deviation")
plt.xlabel(r"$\alpha$")
plt.ylim((0, 1e-6))
plt.savefig(os.path.join(MODULE_DIR, "deviation_over_alpha_rtols.pdf"))
def run_simulation(stop_when_mx_eq_zero):
"""
Runs the simulation using field #1 from the problem description.
Stores the average magnetisation components regularly, as well as the
magnetisation when the x-component of the average magnetisation crosses
the value 0 for the first time.
"""
mesh = from_geofile(os.path.join(MODULE_DIR, "bar.geo"))
sim = Simulation(mesh, Ms, name="dynamics", unit_length=1e-9)
sim.alpha = alpha
sim.gamma = gamma
sim.set_m(np.load(m_0_file))
sim.add(Demag())
sim.add(Exchange(A))
"""
Conversion between mu0 * H in mT and H in A/m.
mu0 * H = 1 mT
= 1 * 1e-3 T
= 1 * 1e-3 Vs/m^2
divide by mu0 with mu0 = 4pi * 1e-7 Vs/Am
gives H = 1 / 4pi * 1e4 A/m
with the unit A/m which is indeed what we want.
Consequence:
Just divide the value of mu0 * H in Tesla
by mu0 to get the value of H in A/m.
"""
Hx = -24.6e-3 / mu0
Hy = 4.3e-3 / mu0
Hz = 0
sim.add(Zeeman((Hx, Hy, Hz)))
def check_if_crossed(sim):
mx, _, _ = sim.m_average
if mx <= 0:
print "The x-component of the spatially averaged magnetisation first crossed zero at t = {}.".format(
sim.t)
np.save(m_at_crossing_file, sim.m)
# When this function returns True, it means this event is done
# and doesn't need to be triggered anymore.
# When we return False, it means we want to stop the simulation.
return not stop_when_mx_eq_zero
sim.schedule(check_if_crossed, every=1e-12)
sim.schedule('save_averages', every=10e-12, at_end=True)
sim.schedule('save_vtk', every=10e-12, at_end=True, overwrite=True)
sim.run_until(2.0e-9)
return sim.t
def excite_system():
Ms = 8.6e5
sim = Simulation(mesh, Ms, pbc='1d', unit_length=1e-9)
sim.alpha = 0.0001
sim.set_m(np.load('relaxed.npy'))
alpha_expr = AlphaExpression()
alpha_mult = df.interpolate(alpha_expr, sim.llg.S1)
sim.spatial_alpha(0.0001, alpha_mult)
#df.plot(alpha_mult)
#df.interactive()
#xs=find_skyrmion_center(sim.llg._m)
#
#assert(1==2)
A = 1.3e-11
D = 4e-3
sim.add(Exchange(A))
sim.add(DMI(D))
sim.add(Zeeman((0, 0, 0.4 * Ms)))
GHz = 1e9
omega = 50 * 2 * np.pi * GHz
def time_fun(t):
return np.sinc(omega * (t - 50e-12))
h0 = 1e3
kc = 1.0 / 45.0
H0 = MyExpression(h0, kc)
sim.add(TimeZeemanPython(H0, time_fun))
xs = find_skyrmion_center(sim.llg._m)
ts = np.linspace(0, 8e-9, 4001)
np.save('xs.npy', xs)
sim.create_integrator()
sim.integrator.integrator.set_scalar_tolerances(1e-8, 1e-8)
index = 0
for t in ts:
sim.run_until(t)
np.save('data/m_%d.npy' % index, sim.llg.m)
index += 1
def test_spatially_varying_alpha_using_Simulation_class():
"""
test that I can change the value of alpha through the property sim.alpha
and that I get an df.Function back.
"""
length = 20
simplices = 10
mesh = df.IntervalMesh(simplices, 0, length)
sim = Simulation(mesh, Ms=1, unit_length=1e-9)
sim.alpha = 1
expected_alpha = np.ones(simplices + 1)
assert np.array_equal(sim.alpha.vector().array(), expected_alpha)
def run_simulation():
print "Running simulation of STT dynamics."
sim = Sim(mesh, Ms=Ms, unit_length=1e-9)
sim.set_m(np.loadtxt(initial_m_file))
sim.alpha = 0.01
sim.add(Exchange(1.3e-11))
sim.add(Demag())
sim.llg.use_slonczewski(J=0.1e12, P=0.4, d=10e-9, p=(0, 1, 0))
with open(averages_file, "w") as f:
dt = 5e-12
t_max = 10e-9
for t in np.arange(0, t_max, dt):
sim.run_until(t)
f.write("{} {} {} {}\n".format(t, *sim.m_average))
def relax_system(mesh):
sim = Sim(mesh, Ms=8.0e5, unit_length=1e-9)
sim.gamma = 2.211e5
sim.alpha = 1
sim.add(Exchange(A=13e-12))
sim.add(Demag())
sim.set_m(init_m)
sim.relax(stopping_dmdt=0.01)
np.save('m0.npy', sim.m)
df.plot(sim._m)
def test_uniform_external_field():
TOLERANCE = 3.5e-10
mesh = df.UnitCubeMesh(2, 2, 2)
sim = Sim(mesh, Ms)
sim.set_m((1, 0, 0))
sim.add(Zeeman((0, Ms, 0)))
sim.alpha = 1.0
sim.run_until(1e-9)
m = sim.m.reshape((3, -1)).mean(-1)
expected_m = np.array([0, 1, 0])
diff = np.abs(m - expected_m)
assert np.max(diff) < TOLERANCE
def setup_module(module=None):
x_max = 100e-9 # m
simplexes = 50
mesh = dolfin.IntervalMesh(simplexes, 0, x_max)
def m_gen(coords):
x = coords[0]
mx = min(1.0, x / x_max)
mz = 0.1
my = np.sqrt(1.0 - (0.99 * mx**2 + mz**2))
return np.array([mx, my, mz])
K1 = 520e3 # J/m^3
Ms = 0.86e6
sim = Sim(mesh, Ms)
sim.alpha = 0.2
sim.set_m(m_gen)
anis = UniaxialAnisotropy(K1, (0, 0, 1))
sim.add(anis)
# Save H_anis and m at t0 for comparison with nmag
global H_anis_t0, m_t0
H_anis_t0 = anis.compute_field()
m_t0 = sim.m
av_f = open(os.path.join(MODULE_DIR, "averages.txt"), "w")
tn_f = open(os.path.join(MODULE_DIR, "third_node.txt"), "w")
t = 0
t_max = 3e-10
dt = 5e-12
# s
while t <= t_max:
mx, my, mz = sim.m_average
averages.append([t, mx, my, mz])
av_f.write(
str(t) + " " + str(mx) + " " + str(my) + " " + str(mz) + "\n")
mx, my, mz = h.components(sim.m)
m2x, m2y, m2z = mx[2], my[2], mz[2]
third_node.append([t, m2x, m2y, m2z])
tn_f.write(
str(t) + " " + str(m2x) + " " + str(m2y) + " " + str(m2z) + "\n")
t += dt
sim.run_until(t)
av_f.close()
tn_f.close()
def excite_system():
Ms = 8.0e5
sim = Simulation(mesh, Ms, unit_length=1e-9, name='dy')
sim.alpha = 0.001
sim.set_m((1, 0, 0))
sim.set_tol(1e-6, 1e-6)
A = 1.3e-11
sim.add(Exchange(A))
sim.add(Zeeman(varying_field))
sim.schedule('save_ndt', every=2e-12)
sim.run_until(0.5e-9)
def run_finmag():
"""Run the finmag simulation and store data in averages.txt."""
sim = Sim(mesh, Ms, unit_length=unit_length)
sim.alpha = 0.5
sim.set_m((1, 0, 1))
exchange = Exchange(13.0e-12)
sim.add(exchange)
demag = Demag(solver="FK")
sim.add(demag)
fh = open(os.path.join(MODULE_DIR, "averages.txt"), "w")
fe = open(os.path.join(MODULE_DIR, "energies.txt"), "w")
logger.info("Time integration")
times = np.linspace(0, 3.0e-10, 61)
for counter, t in enumerate(times):
# Integrate
sim.run_until(t)
# Save averages to file
mx, my, mz = sim.m_average
fh.write(str(t) + " " + str(mx) + " " + str(my) + " " + str(mz) + "\n")
# Energies
E_e = exchange.compute_energy()
E_d = demag.compute_energy()
fe.write(str(E_e) + " " + str(E_d) + "\n")
# Energy densities
if counter == 10:
exch_energy = exchange.energy_density_function()
demag_energy = demag.energy_density_function()
finmag_exch, finmag_demag = [], []
R = range(100)
for i in R:
finmag_exch.append(exch_energy([15, 15, i]))
finmag_demag.append(demag_energy([15, 15, i]))
# Store data
np.save(os.path.join(MODULE_DIR, "finmag_exch_density.npy"),
np.array(finmag_exch))
np.save(os.path.join(MODULE_DIR, "finmag_demag_density.npy"),
np.array(finmag_demag))
fh.close()
fe.close()
def setup_sim(self, m0):
Hz = [8e4, 0, 0] # A/m
A = 1.3e-11 # J/m
Ms = 800e3 # A/m
alpha = 1.
mesh = df.BoxMesh(0, 0, 0, *(self.box_size + self.box_divisions))
sim = Simulation(mesh, Ms)
sim.alpha = alpha
sim.set_m(m0)
sim.add(Demag())
sim.add(Exchange(A))
sim.add(Zeeman(Hz))
return sim
def test_negative_uniform_external_field():
TOLERANCE = 1e-10
mesh = df.UnitCubeMesh(2, 2, 2)
sim = Sim(mesh, Ms)
sim.set_m((1, 0.1, 0)) # slightly misaligned
sim.add(Zeeman((-1.0 * Ms, 0, 0)))
sim.alpha = 1.0
sim.run_until(1e-9)
m = sim.m.reshape((3, -1)).mean(-1)
print "Average magnetisation ({:.2g}, {:.2g}, {:.2g}).".format(*m)
expected_m = np.array([-1, 0, 0])
diff = np.abs(m - expected_m)
TOLERANCE = 1e-5
assert np.max(diff) < TOLERANCE
def compare_with_analytic_solution(alpha=0.5, max_t=1e-9):
"""
Compares the C/dolfin/odeint solution to the analytical one.
"""
print "Running comparison with alpha={0}.".format(alpha)
# define 3d mesh
x0 = y0 = z0 = 0
x1 = y1 = z1 = 10e-9
nx = ny = nz = 1
mesh = dolfin.BoxMesh(dolfin.Point(x0, x1, y0), dolfin.Point(y1, z0, z1),
nx, ny, nz)
sim = Simulation(mesh, Ms=1)
sim.alpha = alpha
sim.set_m((1, 0, 0))
sim.add(Zeeman((0, 0, 1e6)))
# plug in an integrator with lower tolerances
sim.set_tol(abstol=1e-12, reltol=1e-12)
ts = numpy.linspace(0, max_t, num=100)
ys = numpy.array([(sim.advance_time(t), sim.m.copy())[1] for t in ts])
tsfine = numpy.linspace(0, max_t, num=1000)
m_analytical = make_analytic_solution(1e6, alpha, sim.gamma)
save_plot(ts, ys, tsfine, m_analytical, alpha)
TOLERANCE = 1e-6 # tolerance on Ubuntu 11.10, VM Hans, 25/02/2012
rel_diff_maxs = list()
for i in range(len(ts)):
m = numpy.mean(ys[i].reshape((3, -1)), axis=1)
m_ref = m_analytical(ts[i])
diff = numpy.abs(m - m_ref)
diff_max = numpy.max(diff)
rel_diff_max = numpy.max(diff / numpy.max(m_ref))
rel_diff_maxs.append(rel_diff_max)
print "t= {0:.3g}, diff_max= {1:.3g}.".format(ts[i], diff_max)
msg = "Diff at t= {0:.3g} too large.\nAllowed {1:.3g}. Got {2:.3g}."
assert diff_max < TOLERANCE, msg.format(ts[i], TOLERANCE, diff_max)
print "Maximal relative difference: "
print numpy.max(numpy.array(rel_diff_maxs))
def with_current(mesh):
sim = Sim(mesh, Ms=8.0e5, unit_length=1e-9, name='stt')
sim.gamma = 2.211e5
sim.alpha = 0.1
sim.set_m(np.load('m0.npy'))
sim.add(Exchange(A=13e-12))
sim.add(Demag())
sim.set_zhangli(init_J, 1.0, 0.05)
sim.schedule('save_ndt', every=5e-11)
#sim.schedule('save_vtk', every=5e-11)
sim.schedule(spin_length, every=5e-11)
sim.run_until(8e-9)
df.plot(sim._m)
def t_test_sim_ode_parallel(do_plot=False):
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(2, 2, 2), 1, 1, 1)
sim = Sim(mesh, 8.6e5, unit_length=1e-9, pbc='2d', parallel=True)
sim.alpha = alpha
sim.set_m((1, 0, 0))
sim.set_tol(1e-10, 1e-14)
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
# sim.add(Exchange(1.3e-11))
dt = 1e-12
ts = np.linspace(0, 500 * dt, 100)
precession_coeff = sim.gamma / (1 + alpha**2)
mz_ref = np.tanh(precession_coeff * alpha * H0 * ts)
mzs = []
length_error = []
for t in ts:
sim.run_until(t)
mm = sim.m.copy()
# mm.shape=(3,-1)
# mx,my,mz = mm[:,0] # same as m_average for this macrospin problem
mzs.append(mm[-1])
#length = np.sqrt(mx**2+my**2+mz**2)
# length_error.append(abs(length-1.0))
if do_plot:
ts_ns = ts * 1e9
plt.plot(ts_ns, mzs, "b.", label="computed")
plt.plot(ts_ns, mz_ref, "r-", label="analytical")
plt.xlabel("time (ns)")
plt.ylabel("mz")
plt.title("integrating a macrospin")
plt.legend()
plt.savefig(os.path.join(MODULE_DIR, "test_sim_ode.png"))
print("Deviation = {}, total value={}".format(np.max(np.abs(mzs - mz_ref)),
mz_ref))
assert np.max(np.abs(mzs - mz_ref)) < 1e-9
def test_non_uniform_external_field():
TOLERANCE = 1e-9
length = 10e-9
vertices = 5
mesh = df.IntervalMesh(vertices, 0, length)
sim = Sim(mesh, Ms)
sim.set_m((1, 0, 0))
# applied field
# (0, -H, 0) for 0 <= x <= a
# (0, +H, 0) for a < x <= length
H_expr = df.Expression(("0", "H*(x[0]-a)/fabs(x[0]-a)", "0"), a=length / 2, H=Ms / 2, degree=1)
sim.add(Zeeman(H_expr))
sim.alpha = 1.0
sim.run_until(1e-9)
m = sim.m.reshape((3, -1)).mean(-1)
expected_m = np.array([0, 0, 0])
diff = np.abs(m - expected_m)
assert np.max(diff) < TOLERANCE
def run_sim_without_stt():
sim = Sim(mesh, Ms=8.6e5)
sim.set_m((1, 0.01, 0.01))
sim.alpha = 0.014
sim.gamma = 221017
H_app_mT = np.array([0.2, 0.2, 10.0])
H_app_SI = H_app_mT / (1000 * mu0)
sim.add(Zeeman(tuple(H_app_SI)))
sim.add(Exchange(1.3e-11))
sim.add(UniaxialAnisotropy(1e5, (0, 0, 1)))
with open(averages_without, "w") as f:
dt = 5e-12
t_max = 10e-9
for t in np.arange(0, t_max, dt):
sim.run_until(t)
f.write("{} {} {} {}\n".format(t, *sim.m_average))
def run_simulation(verbose=False):
mesh = from_geofile('bar.geo')
sim = Simulation(mesh, Ms=0.86e6, unit_length=1e-9, name="finmag_bar")
sim.set_m((1, 0, 1))
sim.set_tol(1e-6, 1e-6)
sim.alpha = 0.5
sim.add(Exchange(13.0e-12))
sim.add(Demag())
sim.schedule('save_averages', every=5e-12)
sim.schedule("eta", every=10e-12)
sim.run_until(3e-10)
print timer
if verbose:
print "The RHS was evaluated {} times, while the Jacobian was computed {} times.".format(
sim.integrator.stats()['nfevals'],
timer.get("sundials_jtimes", "LLG").calls)
def relax(mesh):
Ms = 8.6e5
sim = Simulation(mesh, Ms, pbc='2d',unit_length=1e-9)
sim.set_m(m_init_fun)
sim.add(Exchange(1.3e-11))
sim.add(DMI(D = 4e-3))
sim.add(Zeeman((0,0,0.45*Ms)))
sim.alpha = 0.5
ts = np.linspace(0, 1e-9, 101)
for t in ts:
sim.run_until(t)
p = df.plot(sim.llg._m)
sim.save_vtk()
df.plot(sim.llg._m).write_png("vortex")
df.interactive()
