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_sim_ode(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')
sim.alpha = alpha
sim.set_m((1, 0, 0))
sim.set_tol(1e-12, 1e-14)
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
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.advance_time(t)
mm = sim.m.copy()
mm.shape = (3, -1)
mx, my, mz = mm[:, 0] # same as m_average for this macrospin problem
mzs.append(mz)
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
assert np.max(length_error) < 1e-9
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))
