def run_test(self, backend, method, nsteps=40000):
llg = setup_domain_wall_cobalt(node_count=NODE_COUNT)
integrator = llg_integrator(llg,
llg.m_field,
backend,
method=method,
nsteps=nsteps)
t = datetime.now()
integrator.advance_time(END_TIME)
dt = datetime.now() - t
print "backend=%s, method=%s: elapsed time=%s, n_rhs_evals=%s, error=%g" % (
backend, method, dt, integrator.n_rhs_evals,
domain_wall_error(llg.m_field.as_array(), NODE_COUNT))
def run_test(backend, method, mode='onego', nsteps=40000):
llg = setup_domain_wall_cobalt(node_count=NODE_COUNT)
integrator = llg_integrator(llg,
llg.m_field,
backend,
method=method,
nsteps=nsteps)
t = datetime.now()
if mode == 'onego':
END_TIME = END_TIME1 + END_TIME2
elif mode == 'twogoes' or mode == 'twogoesreinit':
END_TIME = END_TIME1
else:
raise ValueError(
"Can only understand 'onego', 'twogoes', twogoesreinit'.")
integrator.advance_time(END_TIME)
dt = datetime.now() - t
print "backend=%s, method=%s: elapsed time=%s, n_rhs_evals=%s, error=%g" % (
backend, method, dt, integrator.n_rhs_evals,
domain_wall_error(integrator.m, NODE_COUNT))
if mode == 'onego':
return integrator
if mode == 'twogoesreinit':
# check that rhs counter goes back to zero
print "re-initialising"
integrator.reinit()
assert integrator.n_rhs_evals == 0
else:
print "Not re-initialising"
integrator.advance_time(END_TIME2)
print "backend=%s, method=%s: elapsed time=%s, n_rhs_evals=%s, error=%g" % (
backend, method, dt, integrator.n_rhs_evals,
domain_wall_error(integrator.m, NODE_COUNT))
print("second call to integrator.n_rhs_evals ={}".format(
integrator.n_rhs_evals))
return integrator
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()
# Create mesh
mu = 1e-9
mesh = Mesh("coarse_bar.xml.gz")
#mesh = Mesh("bar.xml.gz")
# Setup LLG
llg = LLG(mesh, unit_length=mu)
llg.Ms = 0.86e6
llg.A = 13.0e-12
llg.alpha = 0.5
llg.set_m((1, 0, 1))
llg.setup(use_exchange=True, use_dmi=False, use_demag=True, demag_method="FK")
# Set up time integrator
integrator = llg_integrator(llg, llg.m)
dt = 5e-12
######
# After ten time steps, plot the energy density
# from z=0 to z=100 through the center of the body.
######
# Integrate
integrator.run_until(dt * 10)
exch = llg.exchange.energy_density_function()
demag = llg.demag.energy_density_function()
finmag_exch, finmag_demag = [], []
R = range(100)
for i in R:
finmag_exch.append(exch([15, 15, i]))
def compute_domain_wall_cobalt(end_time=1e-9):
llg = setup_domain_wall_cobalt()
integrator = llg_integrator(llg, llg.m_field)
integrator.advance_time(end_time)
return np.linspace(0, LENGTH, NODE_COUNT), llg.m.reshape((3, -1))
def test_external_field_depends_on_t():
tfinal = 0.3 * 1e-9
dt = 0.001e-9
simplices = 2
L = 10e-9
mesh = df.IntervalMesh(simplices, 0, L)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
GHz = 1e9
omega = 100 * GHz
llg = LLG(S1, S3)
llg.set_m(df.Constant((1, 0, 0)))
#This is the time dependent field
H_app_expr = df.Expression(("0.0", "0.0", "H0*sin(omega*t)"),
H0=1e5,
omega=omega,
t=0.0,
degree=1)
H_app = TimeZeeman(H_app_expr)
Ms_field = Field(df.FunctionSpace(mesh, 'DG', 0), 8.6e5)
H_app.setup(llg.m_field, Ms=Ms_field)
#define function that updates that expression, and the field object
def update_H_ext(t):
print "update_H_ext being called for t=%g" % t
H_app.update(t)
llg.effective_field.add(H_app, with_time_update=update_H_ext)
#nothing special from here, just setting up time integration
integrator = llg_integrator(llg, llg.m_field)
#to gather data for later analysis
mlist = []
tlist = []
hext = []
#time loop
times = np.linspace(0, tfinal, tfinal / dt + 1)
for t in times:
integrator.advance_time(t)
print "Integrating time: %g" % t
mlist.append(llg.m_average)
tlist.append(t)
hext.append(H_app.H((0)))
#only plotting and data analysis from here on
mx = [tmp[0] for tmp in mlist]
my = [tmp[1] for tmp in mlist]
mz = [tmp[2] for tmp in mlist]
pylab.plot(tlist, mx, label='m_x')
pylab.plot(tlist, my, label='m_y')
pylab.plot(tlist, mz, label='m_z')
pylab.xlabel('time [s]')
pylab.legend()
pylab.savefig(os.path.join(MODULE_DIR, 'results.png'))
pylab.close()
#if max_step is not provided, or chosen too large,
#the external field appears not smooth in this plot.
#What seems to happen is that the ode integrator
#returns the solution without calling the rhs side again
#if we request very small time steps.
#This is only for debugging.
pylab.plot(tlist, hext, '-x')
pylab.ylabel('external field [A/m]')
pylab.xlabel('time [s]')
pylab.savefig(os.path.join(MODULE_DIR, 'hext.png'))
pylab.close()
#Then try to fit sinusoidal curve through results
def sinusoidalfit(t, omega, phi, A, B):
return A * np.cos(omega * t + phi) + B
#if scipy available
try:
import scipy.optimize
except ImportError:
print "Couldn't import scipy.optimize, skipping test"
else:
popt, pcov = scipy.optimize.curve_fit(sinusoidalfit,
np.array(tlist),
np.array(my),
p0=(omega * 1.04, 0., 0.1, 0.2))
#p0 is the set of parameters with which the fitting
#routine starts
print "popt=", popt
fittedomega, fittedphi, fittedA, fittedB = popt
f = open(os.path.join(MODULE_DIR, "fittedresults.txt"), "w")
print >> f, "Fitted omega : %9g" % (fittedomega)
print >> f, "Rel error in omega fit : %9g" % (
(fittedomega - omega) / omega)
print >> f, "Fitted phi : %9f" % (fittedphi)
print >> f, "Fitted Amplitude (A) : %9f" % (fittedA)
print >> f, "Fitted Amp-offset (B) : %9f" % (fittedB)
pylab.plot(tlist, my, label='my - simulated')
pylab.plot(tlist,
sinusoidalfit(np.array(tlist), *popt),
'-x',
label='m_y - fit')
pylab.xlabel('time [s]')
pylab.legend()
pylab.savefig(os.path.join(MODULE_DIR, 'fit.png'))
deviation = np.sqrt(
sum((sinusoidalfit(np.array(tlist), *popt) - my)**2)) / len(tlist)
print >> f, "stddev=%g" % deviation
f.close()
assert (fittedomega - omega) / omega < 1e-4
assert deviation < 5e-4