def test_differentiate_heff():
ns = [2, 2, 2]
mesh = df.BoxMesh(0, 0, 0, 1, 1, 1, *ns)
sim = Simulation(mesh, 1.2)
sim.set_m([1, 0, 0])
sim.add(Demag())
sim.add(Exchange(2.3 * mu0))
compute_H = compute_H_func(sim)
# Check that H_eff is linear without Zeeman
np.random.seed(1)
m1 = fnormalise(np.random.randn(*sim.m.shape))
m2 = fnormalise(np.random.randn(*sim.m.shape))
# TODO: need to use a non-iterative solver here to increase accuracy
assert np.max(
np.abs(compute_H(m1) + compute_H(m2) - compute_H(m1 + m2))) < 1e-6
# Add the zeeman field now
sim.add(Zeeman([2.5, 3.5, 4.3]))
# Check that both fd2 and fd4 give the same result
assert np.max(
np.abs(
differentiate_fd4(compute_H, m1, m2) -
differentiate_fd2(compute_H, m1, m2))) < 1e-10
def setup():
"""
Create a cuboid mesh representing a magnetic material and two
dolfin.Functions defined on this mesh:
m -- unit magnetisation (linearly varying across the sample)
Ms_func -- constant function representing the saturation
magnetisation Ms
*Returns*
A triple (m_space, m, Ms_func), where m_space is the
VectorFunctionSpace (of type "continuous Lagrange") on which the
magnetisation m is defined and m, Ms_funct are as above.
"""
m_space = df.VectorFunctionSpace(mesh, "CG", 1)
m = Field(m_space, value=df.Expression(("1e-9", "x[0]/10", "0"), degree=1))
m.set_with_numpy_array_debug(fnormalise(m.get_numpy_array_debug()))
Ms_space = df.FunctionSpace(mesh, "DG", 0)
Ms_func = df.interpolate(df.Constant(Ms), Ms_space)
return m_space, m, Ms_func
def use_slonczewski(self, J, P, d, p, Lambda=2, epsilonprime=0.0, with_time_update=None):
"""
Activates the computation of the Slonczewski spin-torque term in the LLG.
*Arguments*
J is the current density in A/m^2 as a number, dolfin function,
dolfin expression or Python function. In the last case the
current density is assumed to be spatially constant but can
vary with time. Thus J=J(t) should be a function expecting a
single variable t (the simulation time) and return a number.
Note that a time-dependent current density can also be given
as a dolfin Expression, but a python function should be much
more efficient.
P is the polarisation (between 0 and 1). It is defined as P = (x-y)/(x+y),
where x and y are the fractions of spin up/down electrons).
d is the thickness of the free layer in m.
p is the direction of the polarisation as a triple (is automatically normalised to unit length).
- Lambda: the Lambda parameter in the Slonczewski/Xiao spin-torque term
- epsilonprime: the strength of the secondary spin transfer term
- with_time_update:
A function of the form J(t), which accepts a time step `t`
as its only argument and returns the new current density.
N.B.: For efficiency reasons, the return value is currently
assumed to be a number, i.e. J is assumed to be spatially
constant (and only varying with time).
"""
self.do_slonczewski = True
self.fun_slonczewski_time_update = with_time_update
self.Lambda = Lambda
self.epsilonprime = epsilonprime
if isinstance(J, df.Expression):
J = df.interpolate(J, self.S1)
if not isinstance(J, df.Function):
func = df.Function(self.S1)
func.assign(df.Constant(J))
J = func
self.J = J.vector().array()
assert P >= 0.0 and P <= 1.0
self.P = P
self.d = d
polarisation = df.Function(self.S3)
polarisation.assign(df.Constant((p)))
# we use fnormalise to ensure that p has unit length
self.p = helpers.fnormalise(
polarisation.vector().array()).reshape((3, -1))
def m_average(self):
self._m.vector().set_local(helpers.fnormalise(self.M))
mx = df.assemble(df.dot(self._m, df.Constant([1, 0, 0])) * df.dx)
my = df.assemble(df.dot(self._m, df.Constant([0, 1, 0])) * df.dx)
mz = df.assemble(df.dot(self._m, df.Constant([0, 0, 1])) * df.dx)
volume = df.assemble(df.Constant(1)*df.dx, mesh=self.mesh)
return np.array([mx, my, mz])/volume
def compute_scalar_potential_native_gcr(mesh,
m_expr=df.Constant([1, 0, 0]),
Ms=1.0):
gcrdemag = Demag("GCR")
V = df.VectorFunctionSpace(mesh, "Lagrange", 1)
m = Field(V, value=m_expr)
m.set_with_numpy_array_debug(helpers.fnormalise(m.get_numpy_array_debug()))
gcrdemag.setup(m, Ms, unit_length=1)
phi1 = gcrdemag.compute_potential()
normalise_phi(phi1, mesh)
return phi1
def compute_scalar_potential_llg(mesh, m_expr=df.Constant([1, 0, 0]), Ms=1.):
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
m = Field(S3, value=m_expr)
m.set_with_numpy_array_debug(helpers.fnormalise(m.get_numpy_array_debug()))
demag = Demag()
demag.setup(m, Field(df.FunctionSpace(mesh, 'DG', 0), Ms), unit_length=1)
phi = demag.compute_potential()
normalise_phi(phi, mesh)
return phi
def set_m(self, value, **kwargs):
"""
Set the magnetisation (scaled automatically).
There are several ways to use this function. Either you provide
a 3-tuple of numbers, which will get cast to a dolfin.Constant, or
a dolfin.Constant directly.
Then a 3-tuple of strings (with keyword arguments if needed) that will
get cast to a dolfin.Expression, or directly a dolfin.Expression.
You can provide a numpy.ndarray of nodal values of shape (3*n,),
where n is the number of nodes.
Finally, you can pass a function (any callable object will do) which
accepts the coordinates of the mesh as a numpy.ndarray of
shape (3, n) and returns the magnetisation like that as well.
You can call this method anytime during the simulation. However, when
providing a numpy array during time integration, the use of
the attribute m instead of this method is advised for performance
reasons and because the attribute m doesn't normalise the vector.
"""
if isinstance(value, tuple):
if isinstance(value[0], str):
# a tuple of strings is considered to be the ingredient
# for a dolfin expression, whereas a tuple of numbers
# would signify a constant
val = df.Expression(value, degree=1, **kwargs)
else:
val = df.Constant(value)
new_m = df.interpolate(val, self.S3)
elif isinstance(value, (df.Constant, df.Expression)):
new_m = df.interpolate(value, self.S3)
elif isinstance(value, (list, np.ndarray)):
new_m = df.Function(self.S3)
new_m.vector()[:] = value
elif hasattr(value, '__call__'):
coords = np.array(zip(*self.S3.mesh().coordinates()))
new_m = df.Function(self.S3)
new_m.vector()[:] = value(coords).flatten()
else:
raise AttributeError
new_m.vector()[:] = h.fnormalise(new_m.vector().array())
self._m.vector()[:] = new_m.vector()[:]
tmp = df.assemble(
self._Ms_cell *
df.dot(df.TestFunction(self.S3), df.Constant([1, 1, 1])) * df.dx)
self._Ms.vector().set_local(tmp / self.vol)
self._M.vector().set_local(self.Ms * self.m)
self.prepare_solver()
def set_m(self, value, normalise=True, **kwargs):
"""
Set the magnetisation (if `normalise` is True, it is automatically
normalised to unit length).
`value` can have any of the forms accepted by the function
'finmag.util.helpers.vector_valued_function' (see its
docstring for details).
You can call this method anytime during the simulation. However, when
providing a numpy array during time integration, the use of
the attribute m instead of this method is advised for performance
reasons and because the attribute m doesn't normalise the vector.
"""
m0 = helpers.vector_valued_function(value, self.S3, normalise=False, **kwargs).vector().array()[self.v2d_xxx]
if np.any(np.isnan(m0)):
raise ValueError("Attempting to initialise m with NaN(s)")
if normalise:
m0 = helpers.fnormalise(m0)
self._m_field.set_with_ordered_numpy_array_xxx(m0)
C = 1.3e-11 # J/m exchange constant
Ms = 8.6e5 # A/m saturation magnetisation
t = 0 # s
H_app = (0, 0, 0)
H_app = interpolate(Constant(H_app), V)
pins = []
# Defaults overwrite from spinwave program
Ms = 1e6
alpha = 0.02
m0_tuple = (("1", "5 * pow(cos(pi * (x[0] * pow(10, 9) - 11) / 6), 3) \
* pow(cos(pi * x[1] * pow(10, 9) / 6), 3)", "0"))
M = interpolate(Expression(m0_tuple), V)
M.vector()[:] = h.fnormalise(M.vector().array())
m_arr = M.vector().array()
for i in xrange(nb_nodes):
x, y, z = mesh.coordinates()[i]
mx = 1
my = 0
mz = 0
if 8e-9 < x < 14e-9 and -3e-9 < y < 3e-9:
pass
else:
m_arr[i] = mx
m_arr[i + nb_nodes] = my
m_arr[i + 2 * nb_nodes] = mz
M.vector()[:] = m_arr
def m(self):
mh = helpers.fnormalise(self.M)
self._m.vector().set_local(mh)
return mh