def check_energy_for_m(m, E_expected):
"""
Helper function to compare the computed energy for a given
magnetisation with an expected analytical value.
"""
m_field = Field(S3)
m_field.set(df.Constant(m))
H_ext = Zeeman(H * np.array([1, 0, 0]))
H_ext.setup(m_field, Ms, unit_length=unit_length)
E_computed = H_ext.compute_energy()
assert np.allclose(E_computed, E_expected, atol=0, rtol=1e-12)
def check_energies(m=None, theta=None):
"""
Helper function to compare the computed energy for a given
magnetisation with an expected analytical value. The argument
theta is the angle between the magnetisation vector and the
x-axis.
"""
# Exactly one of m, theta must be given
assert ((m is None or theta is None)
and not (m is None and theta is None))
if m is None:
if theta is None:
raise ValueError("Exactly one of m, theta must be given.")
theta_rad = theta * pi / 180.
m = (cos(theta_rad), sin(theta_rad), 0)
else:
if theta != None:
raise ValueError("Exactly one of m, theta must be given.")
m = m / np.linalg.norm(m)
m_field = Field(S3)
m_field.set(df.Constant(m))
H_ext = Zeeman(H * np.array([1, 0, 0]))
H_ext.setup(m_field,
Field(df.FunctionSpace(mesh, 'DG', 0), Ms),
unit_length=unit_length)
#E_analytical_1 = -mu0 * Ms * H * volume_1 * cos(theta_rad)
E_analytical_1 = -mu0 * Ms * H * volume_1 * np.dot(m, [1, 0, 0])
E_analytical_2 = -mu0 * Ms * H * volume_2 * np.dot(m, [1, 0, 0])
E_analytical_total = E_analytical_1 + E_analytical_2
E_computed_1 = H_ext.compute_energy(dx=dx_disk_1)
E_computed_2 = H_ext.compute_energy(dx=dx_disk_2)
E_computed_total = H_ext.compute_energy(dx=df.dx)
# Check that the sum of the computed energies for disk #1 and #2 equals
# the total computed energy
assert np.allclose(E_computed_1 + E_computed_2,
E_computed_total,
atol=0,
rtol=1e-12)
# Check that the computed energies are within the tolerance of the
# analytical expressions
assert np.allclose(E_computed_1, E_analytical_1, atol=0, rtol=RTOL)
assert np.allclose(E_computed_2, E_analytical_2, atol=0, rtol=RTOL)
assert np.allclose(E_computed_total,
E_analytical_total,
atol=0,
rtol=RTOL)
def test_dmdt_computation_with_oommf():
# set up finmag
llg = LLG(S1, S3)
llg.set_m((-3, -2, 1))
Ms = llg.Ms.vector().array()[0]
Ms = float(Ms)
h = Ms / 2
H_app = (h / np.sqrt(3), h / np.sqrt(3), h / np.sqrt(3))
zeeman = Zeeman(H_app)
zeeman.setup(llg.m_field, llg.Ms, 1)
llg.effective_field.add(zeeman)
dmdt_finmag = df.Function(llg.S3)
dmdt_finmag.vector()[:] = llg.solve(0)
# set up oommf
msh = mesh.Mesh((nL, nW, nH), size=(L, W, H))
m0 = msh.new_field(3)
m0.flat[0] += -3
m0.flat[1] += -2
m0.flat[2] += 1
m0.flat /= np.sqrt(m0.flat[0] * m0.flat[0] + m0.flat[1] * m0.flat[1] +
m0.flat[2] * m0.flat[2])
dmdt_oommf = oommf_dmdt(m0, Ms, A=0, H=H_app, alpha=0.5,
gamma_G=llg.gamma).flat
# extract finmag data for comparison with oommf
dmdt_finmag_like_oommf = msh.new_field(3)
for i, (x, y, z) in enumerate(msh.iter_coords()):
dmdt_x, dmdt_y, dmdt_z = dmdt_finmag(x, y, z)
dmdt_finmag_like_oommf.flat[0, i] = dmdt_x
dmdt_finmag_like_oommf.flat[1, i] = dmdt_y
dmdt_finmag_like_oommf.flat[2, i] = dmdt_z
# compare
difference = np.abs(dmdt_finmag_like_oommf.flat - dmdt_oommf)
relative_difference = difference / np.max(
np.sqrt(dmdt_oommf[0]**2 + dmdt_oommf[1]**2 + dmdt_oommf[2]**2))
print "comparison with oommf, dm/dt, relative difference:"
print stats(relative_difference)
assert np.max(relative_difference) < TOLERANCE
return difference, relative_difference
def example2(Ms):
x0 = y0 = z0 = 0
x1 = 500
y1 = 10
z1 = 100
nx = 50
ny = 1
nz = 1
mesh = df.Box(x0, y0, z0, x1, y1, z1, nx, ny, nz)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
llb = LLB(S1, S3)
llb.alpha = 0.01
llb.beta = 0.0
llb.M0 = Ms
llb.set_M((Ms, 0, 0))
llb.set_up_solver(jacobian=False)
llb.chi = 1e-4
H_app = Zeeman((0, 0, 5e5))
H_app.setup(S3, llb._M, Ms=1)
llb.interactions.append(H_app)
exchange = Exchange(13.0e-12, 1e-2)
exchange.chi = 1e-4
exchange.setup(S3, llb._M, Ms, unit_length=1e-9)
llb.interactions.append(exchange)
demag = Demag("FK")
demag.setup(S3, llb._M, Ms=1)
llb.interactions.append(demag)
max_time = 1 * np.pi / (llb.gamma * 1e5)
ts = np.linspace(0, max_time, num=100)
for t in ts:
print t
llb.run_until(t)
df.plot(llb._M)
df.interactive()
def example1(Ms=8.6e5):
x0 = y0 = z0 = 0
x1 = y1 = z1 = 10
nx = ny = nz = 1
mesh = df.Box(x0, x1, y0, y1, z0, z1, nx, ny, nz)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
vis = df.Function(S3)
llb = LLB(S1, S3)
llb.alpha = 0.01
llb.beta = 0.0
llb.M0 = Ms
llb.set_M((Ms, 0, 0))
llb.set_up_solver(jacobian=False)
llb.chi = 1e-4
H_app = Zeeman((0, 0, 1e5))
H_app.setup(S3, llb._M, Ms=1)
llb.interactions.append(H_app)
exchange = Exchange(13.0e-12, 1e-2)
exchange.chi = 1e-4
exchange.setup(S3, llb._M, Ms, unit_length=1e-9)
llb.interactions.append(exchange)
max_time = 2 * np.pi / (llb.gamma * 1e5)
ts = np.linspace(0, max_time, num=100)
mlist = []
Ms_average = []
for t in ts:
llb.run_until(t)
mlist.append(llb.M)
vis.vector()[:] = mlist[-1]
Ms_average.append(llb.M_average)
df.plot(vis)
time.sleep(0.00)
print 'llb times', llb.call_field_times
save_plot(ts, Ms_average, 'Ms_%g-time.png' % Ms)
df.interactive()
def example1_sundials(Ms):
x0 = y0 = z0 = 0
x1 = y1 = z1 = 10
nx = ny = nz = 1
mesh = df.Box(x0, x1, y0, y1, z0, z1, nx, ny, nz)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
vis = df.Function(S3)
llb = LLB(S1, S3)
llb.alpha = 0.00
llb.set_m((1, 1, 1))
llb.Ms = Ms
H_app = Zeeman((0, 0, 1e5))
H_app.setup(S3, llb._m, Ms=Ms)
llb.interactions.append(H_app)
exchange = BaryakhtarExchange(13.0e-12, 1e-2)
exchange.setup(S3, llb._m, llb._Ms)
llb.interactions.append(exchange)
integrator = llg_integrator(llb, llb.M, abstol=1e-10, reltol=1e-6)
max_time = 2 * np.pi / (llb.gamma * 1e5)
ts = np.linspace(0, max_time, num=50)
mlist = []
Ms_average = []
for t in ts:
integrator.advance_time(t)
mlist.append(integrator.m.copy())
llb.M = mlist[-1]
vis.vector()[:] = mlist[-1]
Ms_average.append(llb.M_average)
df.plot(vis)
time.sleep(0.0)
print llb.count
save_plot(ts, Ms_average, 'Ms_%g-time-sundials.png' % Ms)
df.interactive()
def example1(Ms=8.6e5):
x0 = y0 = z0 = 0
x1 = y1 = z1 = 10
nx = ny = nz = 1
mesh = df.Box(x0, x1, y0, y1, z0, z1, nx, ny, nz)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
vis = df.Function(S3)
llb = LLB(S1, S3, rtol=1e-6, atol=1e-10)
llb.Ms = Ms
llb.alpha = 0.0
llb.set_m((1, 1, 1))
H_app = Zeeman((0, 0, 1e5))
H_app.setup(S3, llb._m, Ms=Ms)
llb.interactions.append(H_app)
exchange = BaryakhtarExchange(13.0e-12, 1e-5)
exchange.setup(S3, llb._m, llb._Ms)
llb.interactions.append(exchange)
max_time = 2 * np.pi / (llb.gamma * 1e5)
ts = np.linspace(0, max_time, num=100)
mlist = []
Ms_average = []
for t in ts:
llb.run_until(t)
mlist.append(llb.M)
vis.vector()[:] = mlist[-1]
Ms_average.append(llb.M_average)
df.plot(vis)
time.sleep(0.00)
print llb.count
save_plot(ts, Ms_average, 'Ms_%g-time.png' % Ms)
df.interactive()