def test_anisotropy_energy_analytical(fixt):
"""
Compare one UniaxialAnisotropy energy with the corresponding analytical result.
The magnetisation is m = (0, sqrt(1 - x^2), x) and the easy axis still
a = (0, 0, 1). The squared dot product in the energy integral thus gives
dot(a, m)^2 = x^2. Integrating x^2 gives (x^3)/3 and the analytical
result with the constants we have chosen is 1 - 1/3 = 2/3.
"""
mesh = df.UnitCubeMesh(1, 1, 1)
functionspace = df.VectorFunctionSpace(mesh, "Lagrange", 1)
K1 = 1
Ms = Field(df.FunctionSpace(mesh, 'DG', 0), 1)
a = df.Constant((0, 0, 1))
m = Field(functionspace)
m.set(df.Expression(("0", "sqrt(1 - pow(x[0], 2))", "x[0]"), degree=1))
anis = UniaxialAnisotropy(K1, a)
anis.setup(m, Ms)
E = anis.compute_energy()
expected_E = float(2) / 3
print "With m = (0, sqrt(1-x^2), x), expecting E = {}. Got E = {}.".format(
expected_E, E)
#assert abs(E - expected_E) < TOLERANCE
assert np.allclose(E, expected_E, atol=1e-14, rtol=TOLERANCE)
def test_anisotropy_energy_simple_configurations(fixt, m, expected_E):
"""
Test some parallel and orthogonal configurations of m and a.
"""
mesh = df.UnitCubeMesh(1, 1, 1)
functionspace = df.VectorFunctionSpace(mesh, "Lagrange", 1)
K1 = 1
Ms = Field(df.FunctionSpace(mesh, 'DG', 0), 1)
a = df.Constant((0, 0, 1))
m_field = Field(functionspace)
m_field.set(df.Constant(m))
anis = UniaxialAnisotropy(K1, a)
anis.setup(m_field, Ms)
E = anis.compute_energy()
print "With m = {}, expecting E = {}. Got E = {}.".format(m, expected_E, E)
#assert abs(E - expected_E) < TOLERANCE
assert np.allclose(E, expected_E, atol=1e-14, rtol=TOLERANCE)
def run_simulation(lfactor, m_init, m_init_name=""):
L = lfactor * lexch
divisions = int(round(lfactor * 2)) # that magic number influences L
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(L, L, L), divisions,
divisions, divisions)
exchange = Exchange(A)
anisotropy = UniaxialAnisotropy(K1, [0, 0, 1])
demag = Demag()
sim = Simulation(mesh, Ms)
sim.set_m(m_init)
sim.add(exchange)
sim.add(anisotropy)
sim.add(demag)
sim.relax()
# Save average magnetisation.
mx, my, mz = sim.m_average
with open(os.path.join(MODULE_DIR, "data_m.txt"), "a") as f:
t = time.asctime()
f.write("{} {} {} {} {} {}\n".format(m_init_name, lfactor, mx, my, mz,
t))
# Save energies.
# We could call sim.total_energy, but we want the individual contributions.
e_exc = exchange.compute_energy() / (sim.Volume * Km)
e_anis = anisotropy.compute_energy() / (sim.Volume * Km)
e_demag = demag.compute_energy() / (sim.Volume * Km)
e_total = e_exc + e_anis + e_demag # relative total energy density
with open(os.path.join(MODULE_DIR, "data_energies.txt"), "a") as f:
t = time.asctime()
f.write("{} {} {} {} {} {} {}\n".format(m_init_name, lfactor, e_total,
e_exc, e_anis, e_demag, t))
return e_total
