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 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_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 test_thin_film_demag_against_real_demag():
sim = Sim(
df.BoxMesh(df.Point(0, 0, 0), df.Point(500e-9, 500e-9, 1e-9), 50, 50,
1), Ms)
sim.set_m((0, 0, 1))
tfdemag = ThinFilmDemag()
sim.add(tfdemag)
H_tfdemag = tfdemag.compute_field().view().reshape((3, -1)).mean(1)
demag = Demag()
sim.add(demag)
H_demag = demag.compute_field().view().reshape((3, -1)).mean(1)
diff = np.abs(H_tfdemag - H_demag) / Ms
print "Standard Demag:\n", H_demag
print "ThinFilmDemag:\n", H_tfdemag
print "Difference relative to Ms:\n", diff
assert np.allclose(H_tfdemag, H_demag, atol=0.05 * Ms) # 5% of Ms
sim.set_m((1, 0, 0))
H_tfdemag = tfdemag.compute_field().view().reshape((3, -1)).mean(1)
H_demag = demag.compute_field().view().reshape((3, -1)).mean(1)
print "Running again, changed m in the meantime."
diff = np.abs(H_tfdemag - H_demag) / Ms
print "Standard Demag:\n", H_demag
print "ThinFilmDemag:\n", H_tfdemag
print "Difference relative to Ms:\n", diff
assert np.allclose(H_tfdemag, H_demag, atol=0.005 * Ms) # 0.5% of Ms
def test_current_time():
size = 20e-9
simplices = 4
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(size, size, size), simplices,
simplices, simplices)
Ms = 860e3
A = 13.0e-12
sim = Sim(mesh, Ms)
sim.set_m((1, 0, 0))
sim.add(Exchange(A))
sim.add(Demag())
t = 0.0
t_max = 1e-10
dt = 1e-12
while t <= t_max:
t += dt
sim.run_until(t)
# cur_t is equal to whatever time the integrator decided to probe last
assert not sim.integrator.cur_t == 0.0
# t is equal to our current simulation time
assert abs(sim.t - t) < epsilon
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 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 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 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_simulation(mesh):
sim = Sim(mesh, Ms=8.6e5, unit_length=1e-9)
sim.set_m((1, 0, 0))
sim.add(UniaxialAnisotropy(-1e5, (0, 0, 1), name='Kp'))
sim.add(UniaxialAnisotropy(1e4, (1, 0, 0), name='Kx'))
return sim
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 angles_after_a_nanosecond(initial_M, pins=[]):
sim = Sim(mesh, Ms)
sim.set_m(initial_M, L=length)
sim.add(Exchange(A))
sim.pins = pins
sim.run_until(1e-9)
m = vectors(sim.m)
angles = np.array([angle(m[i], m[i + 1]) for i in xrange(len(m) - 1)])
return angles
def create_sim(mesh):
Ms = 3.84e5 # A/m
A = 8.78e-12 # J/m
D = 1.58e-3 # J/m**2
sim = Sim(mesh, Ms, unit_length=1e-9)
sim.set_m((0, 0, 1))
sim.set_tol(reltol=1e-10, abstol=1e-10)
sim.add(Exchange(A))
sim.add(DMI(D))
return sim
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 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 compare_with_demag_from_initial_m(H_gen, m_init, atol=0, rtol=0):
sim = Sim(df.UnitCubeMesh(2, 2, 2), Ms, unit_length=1e-9)
sim.set_m(m_init)
demag = ThinFilmDemag()
sim.add(demag)
H_computed = demag.compute_field()
H_expected = H_gen(sim.m)
diff = np.abs(H_computed - H_expected)
print "Expected, with shape {}:\n".format(H_expected.shape), H_expected
print "Got, with shape {}:\n".format(H_computed.shape), H_computed
print "Difference:\n", diff
assert np.allclose(H_computed, H_expected, atol=atol, rtol=rtol)
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 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 create_simulation():
from finmag.util.meshes import ellipsoid
#mesh = df.IntervalMesh(10,0,30)
#mesh = df.RectangleMesh(0,0,10,2,5,1)
mesh = ellipsoid(30, 10, 10, maxh=3.0)
sim = Sim(mesh, Ms=8.6e5, unit_length=1e-9)
sim.set_m((1, 1, 1))
sim.add(Exchange(1.3e-11))
sim.add(UniaxialAnisotropy(-1e5, (0, 0, 1), name='Kp'))
sim.add(UniaxialAnisotropy(1e4, (1, 0, 0), name='Kx'))
return sim
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 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 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():
L = W = 12.5e-9
H = 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))
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 test_exchange_field_should_change_when_M_changes():
sim = Sim(mesh, Ms)
sim.set_m(df.Expression(('(2*x[0]-L)/L',
'sqrt(1 - ((2*x[0]-L)/L)*((2*x[0]-L)/L))',
'0'), L=length, degree=1))
exchange = Exchange(A)
sim.add(exchange)
# save the beginning value of M and the exchange field for comparison
# purposes
old_m = sim.m
old_H_ex = exchange.compute_field()
sim.run_until(1e-11)
# Capture the current value of the exchange field and m.
m = sim.m
H_ex = exchange.compute_field()
# We assert that the magnetisation has indeed changed since the beginning.
assert not np.array_equal(old_m, m)
assert not np.array_equal(old_H_ex, H_ex), "H_ex hasn't changed."
def run_simulation():
L = W = 12.5e-9
H = 5e-9
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(L, W, H), 5, 5, 2)
sim = Sim(mesh, Ms=860e3, name="finmag_validation")
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 # polarisation direction
phi = pi / 2
p = (sin(theta) * cos(phi), sin(theta) * sin(phi), cos(theta))
sim.set_stt(current_density=J, polarisation=0.4, thickness=H, direction=p)
sim.schedule("save_averages", every=5e-12)
sim.run_until(10e-9)
def run_finmag():
sim = Sim(mesh, Ms, unit_length=unit_length)
sim.alpha = 0.5
sim.set_m(init_m)
exchange = Exchange(13.0e-12)
sim.add(exchange)
dmi = DMI(4e-3)
sim.add(dmi)
dmi_direct = DMI(4e-3, method='direct', name='dmi_direct')
sim.add(dmi_direct)
df.plot(sim.m_field.f, title='m')
fun = df.interpolate(HelperExpression(), sim.S3)
df.plot(fun, title='exact')
df.plot(Field(sim.S3, dmi.compute_field()).f, title='dmi_petsc')
df.plot(Field(sim.S3, dmi_direct.compute_field()).f,
title='dmi_direct',
interactive=True)
maxh=2,
save_result=True,
filename='nanocylinder',
directory='mesh',
)
# Simulation and energies -----------------------------------------------------
# Bulk
A = 8.78e-12
D = 1.58e-3
Ms = 3.84e5
B = 0.4
initial_sk_diam = 20
sim = Sim(mesh, Ms=Ms, unit_length=1e-9, name="FeGe_cylinder")
# A linear model for the skyrmion profile
def m_init(pos):
x, y = pos[0], pos[1]
if (x**2 + y**2)**0.5 < initial_sk_diam:
r = (x**2 + y**2)**0.5
phi = np.arctan2(y, x) + 0.5 * np.pi
k = np.pi / initial_sk_diam
return (np.sin(k * r) * np.cos(phi), np.sin(k * r) * np.sin(phi),
-np.cos(k * r))
else:
return (0, 0, 1)