def compute_field(mesh, nx=1, ny=1, m0=(1, 0, 0), pbc=None):
Ms = 1e6
sim = Simulation(mesh, Ms, unit_length=1e-9, name='dy', pbc=pbc)
sim.set_m(m0)
parameters = {
'absolute_tolerance': 1e-10,
'relative_tolerance': 1e-10,
'maximum_iterations': int(1e5)
}
demag = Demag(macrogeometry=MacroGeometry(nx=nx, ny=ny))
demag.parameters['phi_1'] = parameters
demag.parameters['phi_2'] = parameters
sim.add(demag)
field = sim.llg.effective_field.get_dolfin_function('Demag')
# XXX TODO: Would be good to compare all the field values, not
# just the value at a single point! (Max, 25.7.2014)
return field(0, 0, 0) / Ms
def test_dmi_pbc2d_1D(plot=False):
def m_init_fun(p):
if p[0] < 10:
return [0.5, 0, 1]
else:
return [-0.5, 0, -1]
mesh = df.RectangleMesh(df.Point(0, 0), df.Point(20, 2), 10, 1)
m_init = vector_valued_function(m_init_fun, mesh)
Ms = 8.6e5
sim = Simulation(mesh, Ms, pbc='2d', unit_length=1e-9)
sim.set_m(m_init_fun)
A = 1.3e-11
D = 5e-3
sim.add(Exchange(A))
sim.add(DMI(D))
sim.relax(stopping_dmdt=0.0001)
if plot:
sim.m_field.plot_with_dolfin()
mx = [sim.m_field.probe([x + 0.5, 1])[0] for x in range(20)]
assert np.max(np.abs(mx)) < 1e-6
def test_compute_skyrmion_number_2d_pbc():
mesh = df.RectangleMesh(df.Point(0, 0), df.Point(100, 100), 40, 40)
Ms = 8.6e5
sim = Simulation(mesh, Ms, pbc='2d', unit_length=1e-9)
sim.set_m(init_skx_down)
sim.add(Exchange(1.3e-11))
sim.add(DMI(D=4e-3))
sim.add(Zeeman((0, 0, 0.45 * Ms)))
sim.do_precession = False
sim.relax(stopping_dmdt=1, dt_limit=1e-9)
#df.plot(sim.m_field.f)
#df.interactive()
print np.max(sim.m_field.as_array())
sky_num = compute_skyrmion_number_2d(sim.m_field.f)
print 'sky_num = %g' % sky_num
assert sky_num < -0.95 and sky_num > -1.0
def compute_field(n=1, m0=(1, 0, 0), pbc=None):
assert n >= 1 and n % 2 == 1
Ms = 1e6
sim = Simulation(mesh, Ms, unit_length=1e-9, name='dy', pbc=pbc)
sim.set_m(m0)
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.set_m((1, 0, 0))
field1 = sim.llg.effective_field.get_dolfin_function('Demag')
sim.set_m((0, 0, 1))
field2 = sim.llg.effective_field.get_dolfin_function('Demag')
return (field1(0, 0, 0) / Ms, field2(0, 0, 0) / Ms)
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_finmag():
# Setup
setupstart = time.time()
mesh = df.Box(0, 0, 0, 30, 30, 100, 15, 15, 50)
sim = Simulation(mesh, Ms=0.86e6, unit_length=1e-9)
sim.set_m((1, 0, 1))
demag = Demag("FK")
demag.parameters["poisson_solver"]["method"] = "cg"
demag.parameters["poisson_solver"]["preconditioner"] = "jacobi"
demag.parameters["laplace_solver"]["method"] = "cg"
demag.parameters["laplace_solver"]["preconditioner"] = "bjacobi"
sim.add(demag)
sim.add(Exchange(13.0e-12))
# Dynamics
dynamicsstart = time.time()
sim.run_until(3.0e-10)
endtime = time.time()
# Write output to results.txt
output = open(os.path.join(MODULE_DIR, "results.txt"), "a")
output.write("\nBackend %s:\n" % df.parameters["linear_algebra_backend"])
output.write("\nSetup: %.3f sec.\n" % (dynamicsstart - setupstart))
output.write("Dynamics: %.3f sec.\n\n" % (endtime - dynamicsstart))
output.write(str(default_timer))
output.close()
def test_differentiate_heff():
ns = [2, 2, 2]
mesh = df.BoxMesh(0, 0, 0, 1, 1, 1, *ns)
sim = Simulation(mesh, 1.2)
sim.set_m([1, 0, 0])
sim.add(Demag())
sim.add(Exchange(2.3 * mu0))
compute_H = compute_H_func(sim)
# Check that H_eff is linear without Zeeman
np.random.seed(1)
m1 = fnormalise(np.random.randn(*sim.m.shape))
m2 = fnormalise(np.random.randn(*sim.m.shape))
# TODO: need to use a non-iterative solver here to increase accuracy
assert np.max(
np.abs(compute_H(m1) + compute_H(m2) - compute_H(m1 + m2))) < 1e-6
# Add the zeeman field now
sim.add(Zeeman([2.5, 3.5, 4.3]))
# Check that both fd2 and fd4 give the same result
assert np.max(
np.abs(
differentiate_fd4(compute_H, m1, m2) -
differentiate_fd2(compute_H, m1, m2))) < 1e-10
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 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_scipy_advance_time():
mesh = df.UnitIntervalMesh(10)
sim = Simulation(mesh, Ms=1, unit_length=1e-9, integrator_backend="scipy")
sim.set_m((1, 0, 0))
sim.advance_time(1e-12)
sim.advance_time(2e-12)
sim.advance_time(2e-12)
sim.advance_time(2e-12)
def test_anisotropy():
mesh = df.IntervalMesh(1, 0, 1)
sim = Simulation(mesh, Ms, unit_length=1e-9)
sim.set_m((mx, my, mz))
sim.add(UniaxialAnisotropy(K1, axis=[1, 0, 0]))
expected = 2 * K1 / (mu0 * Ms) * mx
field = sim.effective_field()
assert abs(field[0] - expected) / Ms < 1e-15
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 test_spatially_varying_anisotropy_axis(tmpdir, debug=False):
Ms = 1e6
A = 1.3e-11
K1 = 6e5
lb = bloch_parameter(A, K1)
unit_length = 1e-9
nx = 20
Lx = nx * lb / unit_length
mesh = df.IntervalMesh(nx, 0, Lx)
# anisotropy axis goes from (0, 1, 0) at x=0 to (1, 0, 0) at x=Lx
expr_a = df.Expression(("x[0] / sqrt(pow(x[0], 2) + pow(Lx-x[0], 2))",
"(Lx-x[0]) / sqrt(pow(x[0], 2) + pow(Lx-x[0], 2))",
"0"), Lx=Lx, degree=1)
# in theory, a discontinuous Galerkin (constant over the cell) is a good
# choice to represent material parameters. In this case though, the
# parameter varies linearly, so we use the usual CG.
V = df.VectorFunctionSpace(mesh, "CG", 1, dim=3)
a = Field(V, expr_a)
sim = Simulation(mesh, Ms, unit_length)
sim.set_m((1, 1, 0))
sim.add(UniaxialAnisotropy(K1, a))
sim.relax()
# probe the easy axis and the magnetisation along the interval
points = 100
xs = np.linspace(0, Lx, points)
axis_xs = np.zeros((points, 3))
m_xs = np.zeros((points, 3))
for i, x in enumerate(xs):
axis_xs[i] = a(x)
m_xs[i] = sim.m_field(x)
# we want to the magnetisation to follow the easy axis
# it does so, except at x=0, what is happening there?
diff = np.abs(m_xs - axis_xs)
assert diff.max() < 0.02
if debug:
old = os.getcwd()
os.chdir(tmpdir)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xs, axis_xs[:, 0], "b+", label="a_x")
ax.plot(xs, m_xs[:, 0], "r--", label="m_x")
ax.legend(loc="upper left")
ax.set_ylim((0, 1.05))
ax.set_xlabel("x (nm)")
plt.savefig('spatially_varying_easy_axis.png')
plt.close()
sim.m_field.save_pvd('spatially_varying_easy_axis.pvd')
os.chdir(old)
def run_simulation(plot=False):
mu0 = 4.0 * np.pi * 10**-7 # vacuum permeability N/A^2
Ms = 1.0e6 # saturation magnetisation A/m
A = 13.0e-12 # exchange coupling strength J/m
Km = 0.5 * mu0 * Ms**2 # magnetostatic energy density scale kg/ms^2
lexch = (A / Km)**0.5 # exchange length m
unit_length = 1e-9
K1 = Km
L = lexch / unit_length
nx = 10
Lx = nx * L
ny = 1
Ly = ny * L
nz = 30
Lz = nz * L
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(Lx, Ly, Lz), nx, ny, nz)
# Anisotropy easy axis is (0, 0, 1) in the lower half of the film and
# (1, 0, 0) in the upper half. This is a toy model of the exchange spring
# systems that Bob Stamps is working on.
boundary = Lz / 2.0
expr_a = df.Expression(("x[2] <= b ? 0 : 1", "0", "x[2] <= b ? 1 : 0"),
b=boundary,
degree=1)
V = df.VectorFunctionSpace(mesh, "DG", 0, dim=3)
a = Field(V, expr_a)
sim = Simulation(mesh, Ms, unit_length)
sim.set_m((1, 0, 1))
sim.add(UniaxialAnisotropy(K1, a))
sim.add(Exchange(A))
sim.relax()
if plot:
points = 200
zs = np.linspace(0, Lz, points)
axis_zs = np.zeros((points, 3)) # easy axis probed along z-axis
m_zs = np.zeros((points, 3)) # magnetisation probed along z-axis
for i, z in enumerate(zs):
axis_zs[i] = a((Lx / 2.0, Ly / 2.0, z))
m_zs[i] = sim.m_field((Lx / 2.0, Ly / 2.0, z))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(zs, axis_zs[:, 0], "-o", label="a_x")
ax.plot(zs, axis_zs[:, 2], "-x", label="a_z")
ax.plot(zs, m_zs[:, 0], "-", label="m_x")
ax.plot(zs, m_zs[:, 2], "-", label="m_z")
ax.set_xlabel("z (nm)")
ax.legend(loc="upper left")
plt.savefig(os.path.join(MODULE_DIR, "profile.png"))
sim.m_field.save_pvd(os.path.join(MODULE_DIR, 'exchangespring.pvd'))
def example_simulation():
Ms = 8.6e5
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(40, 20, 20), 10, 5, 5)
example = Simulation(mesh, Ms, name="sim_with_scheduling")
example.set_m((0.1, 1, 0))
example.add(Exchange(13.0e-12))
example.add(Demag())
example.add(Zeeman((Ms/2, 0, 0)))
return example
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 cubic_anisotropy(K1=520e3, K2=0, K3=0):
mesh = df.RectangleMesh(df.Point(0, 0), df.Point(50, 2), 20, 1)
sim = Simulation(mesh, Ms, unit_length=1e-9)
sim.set_m(m_init)
sim.add(
CubicAnisotropy(K1=K1,
K2=K2,
K3=K3,
u1=(1, 0, 0),
u2=(0, 1, 0),
assemble=False))
field1 = sim.effective_field()
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 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_compute_main():
Ms = 1700e3
A = 2.5e-6 * 1e-5
Hz = [10e3 * Oersted_to_SI(1.), 0, 0]
mesh = df.BoxMesh(0, 0, 0, 50, 50, 10, 6, 6, 2)
mesh = df.BoxMesh(0, 0, 0, 5, 5, 5, 1, 1, 1)
print mesh
# Find the ground state
sim = Simulation(mesh, Ms)
sim.set_m([1, 0, 0])
sim.add(Demag())
sim.add(Exchange(A))
sim.add(Zeeman(Hz))
sim.relax()
def test_compute_A():
Ms = 1700e3
A = 2.5e-6 * 1e-5
Hz = [10e3 * Oersted_to_SI(1.), 0, 0]
mesh = df.BoxMesh(0, 0, 0, 5, 5, 5, 2, 2, 2)
sim = Simulation(mesh, Ms)
sim.set_m([1, 0, 0])
sim.add(Demag())
# sim.add(Exchange(A))
# sim.add(Zeeman(Hz))
sim.relax()
print mesh
A0, m0 = compute_A(sim)
print A0[:3, :3]
print m0
def run_simulation(do_precession):
Ms = 0.86e6
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(30e-9, 30e-9, 100e-9), 6, 6,
20)
sim = Simulation(mesh, Ms)
sim.set_m((1, 0, 1))
sim.do_precession = do_precession
sim.add(Demag())
sim.add(Exchange(13.0e-12))
averages = []
for t in ts:
sim.run_until(t)
averages.append(sim.m_average)
return np.array(averages)
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 relax_system(mesh=mesh):
Ms = 8.6e5
sim = Simulation(mesh, Ms, pbc='1d', unit_length=1e-9, name='relax')
sim.set_m(m_init_skyrmion)
A = 1.3e-11
D = 4e-3
sim.add(Exchange(A))
sim.add(DMI(D))
sim.add(Zeeman((0, 0, 0.4 * Ms)))
#sim.run_until(1e-9)
#sim.schedule('save_vtk', at_end=True)
#sim.schedule(plot_m, every=1e-10, at_end=True)
sim.relax()
df.plot(sim.llg._m)
np.save('relaxed.npy', sim.m)
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()
def move_skyrmion(mesh):
Ms = 8.6e5
sim = Simulation(mesh, Ms, pbc='2d',unit_length=1e-9, kernel='llg_stt')
sim.set_m(np.load('m0.npy'))
sim.add(Exchange(1.3e-11))
sim.add(DMI(D = 4e-3))
sim.add(Zeeman((0,0,0.45*Ms)))
sim.alpha=0.01
sim.llg.set_parameters(J_profile=init_J, speedup=50)
ts = np.linspace(0, 5e-9, 101)
for t in ts:
sim.run_until(t)
print t
#p = df.plot(sim.llg._m)
sim.save_vtk(filename='nonlocal/v1e7_.pvd')
df.plot(sim.llg._m).write_png("vortex")
def move_skyrmion(mesh):
Ms = 8.6e5
sim = Simulation(mesh, Ms, pbc='2d', unit_length=1e-9)
sim.set_m(np.load('m0.npy'))
sim.add(Exchange(1.3e-11))
sim.add(DMI(D=4e-3))
sim.add(Zeeman((0, 0, 0.45 * Ms)))
sim.alpha = 0.01
sim.set_zhangli(init_J, 1.0, 0.01)
ts = np.linspace(0, 10e-9, 101)
for t in ts:
sim.run_until(t)
print t
#p = df.plot(sim.llg._m)
sim.save_vtk(filename='vtks/v1e7_.pvd')
df.plot(sim.llg._m).write_png("vortex")