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 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)