def __init__(self, Cg, m0, B0, R_E, c_squared):
self.Cg = Cg
self.m0 = m0
self.B0 = B0
self.R_E = R_E
self.c_squared = c_squared
self.nv = 40
self.nk = 45 # NB: keep odd to avoid blowups with y = 0!
self.nl = 8
self.lmin = 1.1
self.lmax = 7.0
self.logvmin = np.log(1e11)
self.logvmax = np.log(1e17)
# recall: k{hat}_min => theta_max and vice versa! Y/y = 33 => alpha ~= 4 degr.
self.khatmax = (33. * R_E * (B0 / self.lmin)**0.5)**0.2
self.khatmin = -self.khatmax
self.vk_mesh = d.RectangleMesh(
d.Point(self.logvmin, self.khatmin),
d.Point(self.logvmax, self.khatmax),
self.nv, self.nk
)
self.l_mesh = d.IntervalMesh(self.nl, self.lmin, self.lmax)
self.l_boundary = OneDWallExpression(degree=0).configure(0., self.lmax)
def burgers_spacedisc(N=10, nu=None, x0=0.0, xE=1.0, retfemdict=False,
condensemats=True):
mesh = dolfin.IntervalMesh(N, x0, xE)
V = dolfin.FunctionSpace(mesh, 'CG', 1)
u = dolfin.TrialFunction(V)
v = dolfin.TestFunction(V)
# boundaries and conditions
ugamma = dolfin.Expression('0', degree=1)
def _spaceboundary(x, on_boundary):
return on_boundary
diribc = dolfin.DirichletBC(V, ugamma, _spaceboundary)
mass = assemble(v*u*dx)
stif = assemble(nu*inner(nabla_grad(v), nabla_grad(u))*dx)
M = dts.mat_dolfin2sparse(mass)
A = dts.mat_dolfin2sparse(stif)
M, _, bcdict = dts.condense_velmatsbybcs(M, [diribc], return_bcinfo=True)
ininds = bcdict['ininds']
A, rhsa = dts.condense_velmatsbybcs(A, [diribc])
def burger_nonl(vvec, t):
v0 = expandvfunc(vvec, V=V, ininds=ininds)
bnl = assemble(0.5*v*((v0*v0).dx(0))*dx)
return bnl.array()[ininds]
if retfemdict:
return M, A, rhsa, burger_nonl, dict(V=V, diribc=diribc, ininds=ininds)
else:
return M, A, rhsa, burger_nonl
def test_zhangli():
#mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(100, 1, 1), 50, 1, 1)
mesh = df.IntervalMesh(50, 0, 100)
sim = Sim(mesh, Ms=8.6e5, unit_length=1e-9, kernel='llg_stt')
sim.set_m(init_m)
sim.add(UniaxialAnisotropy(K1=520e3, axis=[1, 0, 0]))
sim.add(Exchange(A=13e-12))
sim.alpha = 0.01
sim.llg.set_parameters(J_profile=init_J, speedup=50)
p0 = sim.m_average
sim.run_until(5e-12)
p1 = sim.m_average
print sim.integrator.stats()
print p0, p1
sim.run_until(1e-11)
p1 = sim.m_average
print sim.integrator.stats()
print p0, p1
assert p1[0] < p0[0]
assert abs(p0[0]) < 1e-15
assert abs(p1[0]) > 1e-3
def get_domain(self):
"""
Define the Finite Element domain for the problem
"""
# Finite Element Mesh in solid
self.ice_mesh = dolfin.IntervalMesh(self.n,self.w0,self.wf)
self.ice_V = dolfin.FunctionSpace(self.ice_mesh,'CG',1)
self.ice_coords = self.ice_V.tabulate_dof_coordinates().copy()
self.ice_idx_wall = np.argmin(self.ice_coords)
# Finite Element Mesh in solution
self.sol_mesh = dolfin.IntervalMesh(self.n,self.Rstar_center,self.Rstar)
self.sol_V = dolfin.FunctionSpace(self.sol_mesh,'CG',1)
self.sol_mesh.coordinates()[:] = np.log(self.sol_mesh.coordinates())
self.sol_coords = self.sol_V.tabulate_dof_coordinates().copy()
self.sol_idx_wall = np.argmax(self.sol_coords)
self.flags.append('get_domain')
def test_anisotropy():
mesh = df.IntervalMesh(1, 0, 1)
sim = Simulation(mesh, Ms, unit_length=1e-9)
sim.set_m((mx, my, mz))
sim.add(UniaxialAnisotropy(K1, axis=[1, 0, 0]))
expected = 2 * K1 / (mu0 * Ms) * mx
field = sim.effective_field()
assert abs(field[0] - expected) / Ms < 1e-15
def test_spatially_varying_anisotropy_axis(tmpdir, debug=False):
Ms = 1e6
A = 1.3e-11
K1 = 6e5
lb = bloch_parameter(A, K1)
unit_length = 1e-9
nx = 20
Lx = nx * lb / unit_length
mesh = df.IntervalMesh(nx, 0, Lx)
# anisotropy axis goes from (0, 1, 0) at x=0 to (1, 0, 0) at x=Lx
expr_a = df.Expression(("x[0] / sqrt(pow(x[0], 2) + pow(Lx-x[0], 2))",
"(Lx-x[0]) / sqrt(pow(x[0], 2) + pow(Lx-x[0], 2))",
"0"), Lx=Lx, degree=1)
# in theory, a discontinuous Galerkin (constant over the cell) is a good
# choice to represent material parameters. In this case though, the
# parameter varies linearly, so we use the usual CG.
V = df.VectorFunctionSpace(mesh, "CG", 1, dim=3)
a = Field(V, expr_a)
sim = Simulation(mesh, Ms, unit_length)
sim.set_m((1, 1, 0))
sim.add(UniaxialAnisotropy(K1, a))
sim.relax()
# probe the easy axis and the magnetisation along the interval
points = 100
xs = np.linspace(0, Lx, points)
axis_xs = np.zeros((points, 3))
m_xs = np.zeros((points, 3))
for i, x in enumerate(xs):
axis_xs[i] = a(x)
m_xs[i] = sim.m_field(x)
# we want to the magnetisation to follow the easy axis
# it does so, except at x=0, what is happening there?
diff = np.abs(m_xs - axis_xs)
assert diff.max() < 0.02
if debug:
old = os.getcwd()
os.chdir(tmpdir)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xs, axis_xs[:, 0], "b+", label="a_x")
ax.plot(xs, m_xs[:, 0], "r--", label="m_x")
ax.legend(loc="upper left")
ax.set_ylim((0, 1.05))
ax.set_xlabel("x (nm)")
plt.savefig('spatially_varying_easy_axis.png')
plt.close()
sim.m_field.save_pvd('spatially_varying_easy_axis.pvd')
os.chdir(old)
def build_mesh(self):
r"""
Build the mesh:
(1) check that the input parameters for the mesh are valid (the function performing the test must be
defined in the child mesh class)
(2) set the mesh transformation. Depending on whether `r\_rm=None` or `r\_rm=float`, the transformation
will be the baseline transformation (as defined in the child mesh class)
or its updated form declustering mesh points at `r\_rm`
(3) create a starting linear mesh, in particular, compute its extrema by using the Newton method
(4) obtain a nonlinear mesh by applying the transformation defined at (2)
(5) apply additional linear refinement if required
(6) check that the obtained mesh points are not closer than the user-set tolerance of
:math:`\mathrm{too\_fine}\times\mathrm{DOLFIN\_EPS}`.
"""
# check input parameters are valid
self.check_params()
# define transformation - either baseline or with point removal at r_rm
if self.r_rm is None:
if self.adjust_transition:
transform = self.baseline_transform_w_adjusted_xs()
else:
transform = self.baseline_transform()
else:
transform = self.transform_with_declustering()
self.T, self.Tprime, self.Tprimeprime, self.small_r_Tm1, self.large_r_Tm1 = transform
# extrema of starting mesh - find using the Newton method
x_min_0 = self.small_r_Tm1(self.r_min) # initial guess
F_min = lambda x: self.T(x) - self.r_min
self.x_min = sopt.newton(F_min, x_min_0, self.Tprime, tol=self.Ntol)
x_max = self.large_r_Tm1(self.r_max)
F_max = lambda x: self.T(x) - self.r_max
self.x_max = sopt.newton(F_max, x_max, self.Tprime, tol=self.Ntol)
# create starting linear mesh from x_min to x_max
self.mesh = d.IntervalMesh(self.num_cells, self.x_min, self.x_max)
x_mesh = self.mesh.coordinates()[:, 0]
# apply transform and get a refined radial mesh
T = np.vectorize(self.T)
refined_mesh = T(x_mesh)
self.mesh.coordinates()[:, 0] = refined_mesh[:]
# apply optional linear refinement if required
if self.linear_refine:
self.apply_linear_refinement()
# check that points are not closer than user-set tolerance
self.check_mesh()
def set_mesh(self):
dx, xmax = self.dx, self.xmax
nel = int(xmax/dx) # Number of elements
mesh = d.IntervalMesh(nel, 0, xmax)
self.mesh = mesh
# to output
self.cells = {'line': mesh.cells()}
xyz = mesh.coordinates()
self.xyzio = np.zeros([xyz.shape[0], 3])
self.xyzio[:,0] = xyz.flatten()
def test_llb(do_plot=False):
#mesh = df.BoxMesh(0, 0, 0, 2, 2, 2, 1, 1, 1)
mesh = df.IntervalMesh(1,0,2)
Ms = 8.6e5
sim = LLB(mesh)
sim.alpha = 0.5
sim.beta = 0.0
sim.M0 = Ms
sim.set_M((Ms,0,0))
sim.set_up_solver(reltol=1e-7, abstol=1e-7)
sim.add(Exchange(1.3e-11,chi=1e-7))
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
steps = 100
dt = 1e-12; ts = np.linspace(0, steps * dt, steps+1)
precession_coeff = sim.gamma
mz_ref = []
mz = []
real_ts=[]
for t in ts:
print t,sim.Ms
sim.run_until(t)
real_ts.append(sim.t)
mz_ref.append(np.tanh(precession_coeff * sim.alpha * H0 * sim.t))
#mz.append(sim.M[-1]/Ms) # same as m_average for this macrospin problem
mz.append(sim.m[-1])
mz=np.array(mz)
if do_plot:
ts_ns = np.array(real_ts) * 1e9
plt.plot(ts_ns, mz, "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_sllg.png"))
print("Deviation = {}, total value={}".format(
np.max(np.abs(mz - mz_ref)),
mz_ref))
assert np.max(np.abs(mz - mz_ref)) < 2e-7
def setup_finmag():
mesh = df.IntervalMesh(xn, x0, x1)
coords = np.array(zip(*mesh.coordinates()))
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
m = Field(S3)
m.set_with_numpy_array_debug(m_gen(coords).flatten())
exchange = Exchange(A)
exchange.setup(m, Field(df.FunctionSpace(mesh, 'DG', 0), Ms))
H_exc = df.Function(S3)
H_exc.vector()[:] = exchange.compute_field()
return dict(m=m, H=H_exc, table=start_table())
def setup_module(module=None):
x_max = 100e-9 # m
simplexes = 50
mesh = dolfin.IntervalMesh(simplexes, 0, x_max)
def m_gen(coords):
x = coords[0]
mx = min(1.0, x / x_max)
mz = 0.1
my = np.sqrt(1.0 - (0.99 * mx**2 + mz**2))
return np.array([mx, my, mz])
K1 = 520e3 # J/m^3
Ms = 0.86e6
sim = Sim(mesh, Ms)
sim.alpha = 0.2
sim.set_m(m_gen)
anis = UniaxialAnisotropy(K1, (0, 0, 1))
sim.add(anis)
# Save H_anis and m at t0 for comparison with nmag
global H_anis_t0, m_t0
H_anis_t0 = anis.compute_field()
m_t0 = sim.m
av_f = open(os.path.join(MODULE_DIR, "averages.txt"), "w")
tn_f = open(os.path.join(MODULE_DIR, "third_node.txt"), "w")
t = 0
t_max = 3e-10
dt = 5e-12
# s
while t <= t_max:
mx, my, mz = sim.m_average
averages.append([t, mx, my, mz])
av_f.write(
str(t) + " " + str(mx) + " " + str(my) + " " + str(mz) + "\n")
mx, my, mz = h.components(sim.m)
m2x, m2y, m2z = mx[2], my[2], mz[2]
third_node.append([t, m2x, m2y, m2z])
tn_f.write(
str(t) + " " + str(m2x) + " " + str(m2y) + " " + str(m2z) + "\n")
t += dt
sim.run_until(t)
av_f.close()
tn_f.close()
def test_spatially_varying_alpha_using_Simulation_class():
"""
test that I can change the value of alpha through the property sim.alpha
and that I get an df.Function back.
"""
length = 20
simplices = 10
mesh = df.IntervalMesh(simplices, 0, length)
sim = Simulation(mesh, Ms=1, unit_length=1e-9)
sim.alpha = 1
expected_alpha = np.ones(simplices + 1)
assert np.array_equal(sim.alpha.vector().array(), expected_alpha)
def test_unconstrained_newton_solver(self):
L, nelem = 1, 201
mesh = dl.IntervalMesh(nelem, -L, L)
Vh = dl.FunctionSpace(mesh, "CG", 2)
forcing = dl.Constant(1)
dirichlet_bcs = [dl.DirichletBC(Vh, dl.Constant(0.0), on_any_boundary)]
bc0 = dl.DirichletBC(Vh, dl.Constant(0.0), on_any_boundary)
uh = dl.TrialFunction(Vh)
vh = dl.TestFunction(Vh)
F = dl.inner((1 + uh**2) * dl.grad(uh),
dl.grad(vh)) * dl.dx - forcing * vh * dl.dx
u = dl.Function(Vh)
F = dl.action(F, u)
parameters = {
"symmetric": True,
"newton_solver": {
# "relative_tolerance": 1e-8,
"report": True,
"linear_solver": "cg",
"preconditioner": "petsc_amg"
}
}
dl.solve(F == 0, u, dirichlet_bcs, solver_parameters=parameters)
# dl.plot(uh)
# plt.show()
u_newton = dl.Function(Vh)
F = dl.inner((1 + uh**2) * dl.grad(uh),
dl.grad(vh)) * dl.dx - forcing * vh * dl.dx
F = dl.action(F, u_newton)
# Compute Jacobian
J = dl.derivative(F, u_newton, uh)
unconstrained_newton_solve(
F,
J,
u_newton,
dirichlet_bcs=dirichlet_bcs,
bc0=bc0,
# linear_solver='PETScLU',opts=dict())
linear_solver=None,
opts=dict())
error = dl.errornorm(u, u_newton, mesh=mesh)
assert error < 1e-15
def test_method_of_computing_the_average_matters():
length = 20e-9 # m
simplices = 10
mesh = df.IntervalMesh(simplices, 0, length)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
llg = LLG(S1, S3)
llg.set_m((
'(2*x[0]-L)/L',
'sqrt(1 - ((2*x[0]-L)/L)*((2*x[0]-L)/L))',
'0'), L=length)
average1 = llg.m_average
average2 = np.mean(components(llg.m_numpy), axis=1)
diff = np.abs(average1 - average2)
assert diff.max() > 5e-2
def run_dolfin():
import dolfin as df
x_array = np.linspace(-49.5, 49.5, 100)
mesh = df.IntervalMesh(100, -50, 50)
Delta = np.sqrt(A / K)
xi = 2 * A / D
Delta_s = Delta * 1e9
V = df.FunctionSpace(mesh, "Lagrange", 1)
u = df.TrialFunction(V)
v = df.TestFunction(V)
u_ = df.Function(V)
F = -df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx - \
(0.5 / Delta_s**2) * df.sin(2 * u) * v * df.dx
F = df.action(F, u_)
J = df.derivative(F, u_, u)
# the boundary condition is from equation (8)
theta0 = np.arcsin(Delta / xi)
ss = 'x[0]<0? %g: %g ' % (-theta0, theta0)
u0 = df.Expression(ss)
def u0_boundary(x, on_boundary):
return on_boundary
bc = df.DirichletBC(V, u0, u0_boundary)
problem = df.NonlinearVariationalProblem(F, u_, bcs=bc, J=J)
solver = df.NonlinearVariationalSolver(problem)
solver.solve()
u_array = u_.vector().array()
mx_df = []
for x in x_array:
mx_df.append(u_(x))
return mx_df
def mesh1d(left, right, meshres):
mesh = dolfin.IntervalMesh(meshres, left, right)
# Construct of the facet markers:
boundary = (dolfin.MeshFunction("size_t", mesh,
mesh.topology().dim() - 1, 0), {})
#boundary[0].set_all(0)
for f in dolfin.facets(mesh):
if dolfin.near(f.midpoint()[0], left):
boundary[0][f] = 1 # left
boundary[1]['inner'] = 1
elif dolfin.near(f.midpoint()[0], right):
boundary[0][f] = 2 # right
boundary[1]['outer'] = 2
# Definition of measures and normal vector:
n = dolfin.FacetNormal(mesh)
dx = dolfin.Measure("dx", mesh)
ds = dolfin.Measure("ds", subdomain_data=boundary[0])
return (mesh, boundary, n, dx, ds)
def test_spatially_varying_alpha_using_LLG_class():
"""
no property magic here - llg.alpha is a df.Function at heart and can be
set with any type using llg.set_alpha()
"""
length = 20
simplices = 10
mesh = df.IntervalMesh(simplices, 0, length)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, 3)
llg = LLG(S1, S3)
llg.set_alpha(1)
expected_alpha = np.ones(simplices + 1)
print "Got:\n", llg.alpha.vector().array()
print "Expected:\n", expected_alpha
assert np.array_equal(llg.alpha.vector().array(), expected_alpha)
def test_non_uniform_external_field():
TOLERANCE = 1e-9
length = 10e-9
vertices = 5
mesh = df.IntervalMesh(vertices, 0, length)
sim = Sim(mesh, Ms)
sim.set_m((1, 0, 0))
# applied field
# (0, -H, 0) for 0 <= x <= a
# (0, +H, 0) for a < x <= length
H_expr = df.Expression(("0", "H*(x[0]-a)/fabs(x[0]-a)", "0"), a=length / 2, H=Ms / 2, degree=1)
sim.add(Zeeman(H_expr))
sim.alpha = 1.0
sim.run_until(1e-9)
m = sim.m.reshape((3, -1)).mean(-1)
expected_m = np.array([0, 0, 0])
diff = np.abs(m - expected_m)
assert np.max(diff) < TOLERANCE
def test_get_interaction_list():
# has bar mini example Demag and Exchange?
s = finmag.example.barmini()
lst = s.get_interaction_list()
assert 'Exchange' in lst
assert 'Demag' in lst
assert len(lst) == 2
# Let's remove one and ceck again
s.remove_interaction('Exchange')
assert s.get_interaction_list() == ['Demag']
# test simulation with no interaction
s2 = finmag.sim_with(mesh=dolfin.IntervalMesh(10, 0, 1),
m_init=(1, 0, 0),
Ms=1,
demag_solver=None,
unit_length=1e-8)
assert s2.get_interaction_list() == []
def setup_domain_wall_cobalt(node_count=NODE_COUNT,
A=A_Co,
Ms=Ms_Co,
K1=K1_Co,
length=LENGTH,
do_precession=True):
mesh = df.IntervalMesh(node_count - 1, 0, length)
S1 = df.FunctionSpace(mesh, "Lagrange", 1)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
llg = LLG(S1, S3)
llg.set_m(
np.array([initial_m(xi, node_count)
for xi in xrange(node_count)]).T.reshape((-1, )))
exchange = Exchange(A)
llg.effective_field.add(exchange)
anis = UniaxialAnisotropy(K1, (0, 0, 1))
llg.effective_field.add(anis)
llg.pins = [0, node_count - 1]
return llg
def test_anisotropy_energy_density():
"""
Written in sperical coordinates, the equation for the
anisotropy energy density reads
E/V = K*sin^2(theta),
where theta is the angle between the magnetisation and
the easy axis. With a magnetisation pointing 45 degrees
between the x- and z-axis, and using the z-axis as the
easy axis, theta becomes pi/4. sin^2(pi/4) evaluates
to 1/2, and with K set to 1 in this simple test case,
we expect the energy density to be 1/2 at every node.
"""
# 5 simplices between 0 and 1 nm.
mesh = df.IntervalMesh(5, 0, 1e-9)
V = df.VectorFunctionSpace(mesh, "CG", 1, dim=3)
# Initial magnetisation 45 degress between x- and z-axis.
m_vec = df.Constant((1 / np.sqrt(2), 0, 1 / np.sqrt(2)))
m = Field(V, value=m_vec)
# Easy axis in z-direction.
a = df.Constant((0, 0, 1))
# These are 1 just to simplify the analytical solution.
K = 1
Ms = 1
anis = UniaxialAnisotropy(K, a)
anis.setup(m, Field(df.FunctionSpace(mesh, 'DG', 0), Ms))
density = anis.energy_density()
deviation = np.abs(density - 0.5)
print "Anisotropy energy density (expect array of 0.5):"
print density
print "Max deviation: %g" % np.max(deviation)
assert np.all(deviation < TOL), \
"Max deviation %g, should be zero." % np.max(deviation)
def one_dimensional_problem():
x_min = 0
x_max = 100e-9
x_n = 100000
dolfin_mesh = df.IntervalMesh(x_n, x_min, x_max)
oommf_mesh = mesh.Mesh((20, 1, 1), size=(x_max, 1e-12, 1e-12))
def m_gen(rs):
xs = rs[0]
return np.array(
[xs / x_max,
np.sqrt(1 - (xs / x_max)**2),
np.zeros(len(xs))])
return compare_anisotropy(m_gen,
Ms,
K1, (1, 1, 1),
dolfin_mesh,
oommf_mesh,
dims=1,
name="1D")
def __init__(self,
t_end,
start_cells,
perc,
do_step=None,
do_step_adj=None,
get_dwr_est=None,
j=None):
## time discretization
self.mesh = dol.IntervalMesh(int(start_cells), 0, int(t_end))
## percentage of cells to refine in a single refinement step
self.perc = perc
## end time
self.t_end = t_end
self.do_step = do_step
self.do_step_adj = do_step_adj
## dwr estimate function
self.get_dwr_est = get_dwr_est
self.j = j
## time discretization
self.times = []
def instantiate(self, N, dtype, regular_mesh=None):
"""
Return a pair (A, None), where A is a matrix representing the
action on a vector v given by the right-hand side of the
linearised LLG equation (without damping):
A*v = dv/dt = -gamma * m_0 x H_exchange(v)
"""
if not iseven(N):
raise ValueError("N must be even. Got: {}".format(N))
# XXX TODO: Actually, we shouldn't store these values in 'self'
# because we can always re-instantiate the problem,
# right?
self.N = N
self.dtype = dtype
if regular_mesh == None:
regular_mesh = self.regular_mesh
self.K = N // 2
if regular_mesh:
mesh = df.IntervalMesh(self.K - 1, self.xmin, self.xmax)
else:
mesh = irregular_interval_mesh(self.xmin, self.xmax, self.K)
#raise NotImplementedError()
V = df.VectorFunctionSpace(mesh, 'CG', 1, dim=3)
v = Field(V)
self.exch = Exchange(A=self.A_ex)
Ms_field = Field(df.FunctionSpace(mesh, 'DG', 0), self.Ms)
self.exch.setup(v, Ms_field, unit_length=self.unit_length)
C_2Kx2K = LinearOperator(
shape=(N, N),
matvec=self.compute_action_rhs_linearised_LLG_2K,
dtype=dtype)
C_2Kx2K_dense = as_dense_array(C_2Kx2K)
return C_2Kx2K_dense, None
def __init__(self, odcoo, gamma=1e-3, alphau=1e-6, ystar=None):
if ystar is None:
self.ystarx = dolfin.Expression('-0.1*sin(5*3.14*t)', t=0)
self.ystary = dolfin.Expression('0.1*sin(5*3.14*t)', t=0)
# self.ystarx = dolfin.Expression('-0.0', t=0)
# self.ystary = dolfin.Expression('0.0', t=0)
# if t, then add t=0 to both comps !!1!!11
else:
self.ystarx = ystar[0]
self.ystary = ystar[1]
self.NU, self.NY = 4, 4
self.R = None
# regularization parameter
self.alphau = alphau
# weighting of the penalization of the terminal value
self.gamma = gamma
self.V = None
self.W = None
self.ymesh = dolfin.IntervalMesh(self.NY - 1, odcoo['ymin'],
odcoo['ymax'])
self.Y = dolfin.FunctionSpace(self.ymesh, 'CG', 1)
def test_1d():
print "1D problem..."
for x_n in [1e1, 1e2, 1e3, 1e4, 1e5, 1e6]:
dolfin_mesh = df.IntervalMesh(int(x_n), 0, x_max)
oommf_mesh = mesh.Mesh((int(x_n), 1, 1), size=(x_max, 1e-12, 1e-12))
res = compare_anisotropy(m_gen,
1.0,
K1, (1, 1, 1),
dolfin_mesh,
oommf_mesh,
dims=1,
name="1D")
vertices[0].append(dolfin_mesh.num_vertices())
mean_rdiffs[0].append(np.mean(res["rel_diff"]))
max_rdiffs[0].append(np.max(res["rel_diff"]))
def linear(x, a, b):
return a * x + b
xs = np.log(vertices[0])
ys = np.log(mean_rdiffs[0])
popt, pcov = curve_fit(linear, xs, ys)
assert popt[0] < -1.0
def simple_mesh(Ld, N, ext_bnd_id=1):
"""
Returns a mesh for a given list, Ld, containing the size of domain in each
spatial direction, and the corresponding number of cell divisions N.
"""
d = len(N)
mesh_types = [df.RectangleMesh, df.BoxMesh]
if d == 1:
mesh = df.IntervalMesh(N[0], 0.0, Ld[0])
else:
mesh = mesh_types[d - 2](df.Point(*np.zeros(len(Ld))), df.Point(*Ld),
*N)
facet_func = df.FacetFunction('size_t', mesh)
facet_func.set_all(0)
class ExtBnd(df.SubDomain):
def inside(self, x, on_boundary):
return on_boundary
bnd = ExtBnd()
bnd.mark(facet_func, ext_bnd_id)
return mesh, facet_func
def __init__(self,
tfml_file,
system_name='magma',
p_name='Pressure',
f_name='Porosity',
c_name='c',
n_name='n',
m_name='m',
d_name='d',
N_name='N',
h_squared_name='h_squared',
x0_name='x0'):
"""read the tfml_file and use libspud to populate the internal parameters
c: wavespeed
n: permeability exponent
m: bulk viscosity exponent
d: wave dimension
N: number of collocation points
x0: coordinate wave peak
h_squared: the size of the system in compaction lengths
squared (h/delta)**2
"""
# initialize libspud and extract parameters
libspud.clear_options()
libspud.load_options(tfml_file)
# get model dimension
self.dim = libspud.get_option("/geometry/dimension")
self.system_name = system_name
# get solitary wave parameters
path = "/system::" + system_name + "/coefficient::"
scalar_value = "/type::Constant/rank::Scalar/value::WholeMesh/constant"
vector_value = "/type::Constant/rank::Vector/value::WholeMesh/constant::dim"
c = libspud.get_option(path + c_name + scalar_value)
n = int(libspud.get_option(path + n_name + scalar_value))
m = int(libspud.get_option(path + m_name + scalar_value))
d = float(libspud.get_option(path + d_name + scalar_value))
N = int(libspud.get_option(path + N_name + scalar_value))
self.h = np.sqrt(
libspud.get_option(path + h_squared_name + scalar_value))
self.x0 = np.array(libspud.get_option(path + x0_name + vector_value))
self.swave = SolitaryWave(c, n, m, d, N)
self.rmax = self.swave.r[-1]
self.tfml_file = tfml_file
# check that d <= dim
assert (d <= self.dim)
# sort out appropriate index for calculating distance r
if d == 1:
self.index = [self.dim - 1]
else:
self.index = range(0, int(d))
# check that the origin point is the correct dimension
assert (len(self.x0) == self.dim)
#read in information for constructing Function space and dolfin objects
# get the mesh parameters and reconstruct the mesh
meshtype = libspud.get_option("/geometry/mesh/source[0]/name")
if meshtype == 'UnitSquare':
number_cells = libspud.get_option(
"/geometry/mesh[0]/source[0]/number_cells")
diagonal = libspud.get_option(
"/geometry/mesh[0]/source[0]/diagonal")
mesh = df.UnitSquareMesh(number_cells[0], number_cells[1],
diagonal)
elif meshtype == 'Rectangle':
x0 = libspud.get_option(
"/geometry/mesh::Mesh/source::Rectangle/lower_left")
x1 = libspud.get_option(
"/geometry/mesh::Mesh/source::Rectangle/upper_right")
number_cells = libspud.get_option(
"/geometry/mesh::Mesh/source::Rectangle/number_cells")
diagonal = libspud.get_option(
"/geometry/mesh[0]/source[0]/diagonal")
mesh = df.RectangleMesh(x0[0], x0[1], x1[0], x1[1],
number_cells[0], number_cells[1], diagonal)
elif meshtype == 'UnitCube':
number_cells = libspud.get_option(
"/geometry/mesh[0]/source[0]/number_cells")
mesh = df.UnitCubeMesh(number_cells[0], number_cells[1],
number_cells[2])
elif meshtype == 'Box':
x0 = libspud.get_option(
"/geometry/mesh::Mesh/source::Box/lower_back_left")
x1 = libspud.get_option(
"/geometry/mesh::Mesh/source::Box/upper_front_right")
number_cells = libspud.get_option(
"/geometry/mesh::Mesh/source::Box/number_cells")
mesh = df.BoxMesh(x0[0], x0[1], x0[2], x1[0], x1[1], x1[2],
number_cells[0], number_cells[1],
number_cells[2])
elif meshtype == 'UnitInterval':
number_cells = libspud.get_option(
"/geometry/mesh::Mesh/source::UnitInterval/number_cells")
mesh = df.UnitIntervalMesh(number_cells)
elif meshtype == 'Interval':
number_cells = libspud.get_option(
"/geometry/mesh::Mesh/source::Interval/number_cells")
left = libspud.get_option(
"/geometry/mesh::Mesh/source::Interval/left")
right = libspud.get_option(
"/geometry/mesh::Mesh/source::Interval/right")
mesh = df.IntervalMesh(number_cells, left, right)
elif meshtype == 'File':
mesh_filename = libspud.get_option(
"/geometry/mesh::Mesh/source::File/file")
print "tfml_file = ", self.tfml_file, "mesh_filename=", mesh_filename
mesh = df.Mesh(mesh_filename)
else:
df.error("Error: unknown mesh type " + meshtype)
#set the functionspace for n-d solitary waves
path = "/system::" + system_name + "/field::"
p_family = libspud.get_option(path + p_name +
"/type/rank/element/family")
p_degree = libspud.get_option(path + p_name +
"/type/rank/element/degree")
f_family = libspud.get_option(path + f_name +
"/type/rank/element/family")
f_degree = libspud.get_option(path + f_name +
"/type/rank/element/degree")
pe = df.FiniteElement(p_family, mesh.ufl_cell(), p_degree)
ve = df.FiniteElement(f_family, mesh.ufl_cell(), f_degree)
e = pe * ve
self.functionspace = df.FunctionSpace(mesh, e)
#work out the order of the fields
for i in xrange(
libspud.option_count("/system::" + system_name + "/field")):
name = libspud.get_option("/system::" + system_name + "/field[" +
` i ` + "]/name")
if name == f_name:
self.f_index = i
if name == p_name:
self.p_index = i
import numpy as np
import dolfin as df
from finmag import Simulation as Sim
from finmag.energies import Exchange
from finmag.util.helpers import vectors, angle
TOLERANCE = 8e-7
# define the mesh
length = 20e-9 # m
simplexes = 10
mesh = df.IntervalMesh(simplexes, 0, length)
Ms = 8.6e5
A = 1.3e-11
# initial configuration of the magnetisation
left_right = '2*x[0]/L - 1'
up_down = 'sqrt(1 - (2*x[0]/L - 1)*(2*x[0]/L - 1))'
possible_orientations = [
(left_right, up_down, '0'), # (left_right, '0', up_down),
(up_down, '0', left_right)] # , (up_down, left_right, '0'),
#('0', left_right, up_down)] , ('0', up_down, left_right)]
def angles_after_a_nanosecond(initial_M, pins=[]):
sim = Sim(mesh, Ms)
sim.set_m(initial_M, L=length)
sim.add(Exchange(A))
sim.pins = pins
sim.run_until(1e-9)
) # or x[0] > 1.0 - dl.DOLFIN_EPS
def pde_varf(u, m, p):
return dl.inner(dl.nabla_grad(u),
dl.nabla_grad(p)) * dl.dx + u * p * dl.dx - m * p * dl.dx
# return u * p * dl.dx - m * p * dl.dx
# create mesh
dl.set_log_active(False)
sep = "\n" + "#" * 80 + "\n"
nx = 256
mesh = dl.IntervalMesh(dl.mpi_comm_self(), nx, 0., 1.)
# define function space
Vh2 = dl.FunctionSpace(mesh, 'Lagrange', 1)
Vh1 = dl.FunctionSpace(mesh, 'Lagrange', 1)
Vh = [Vh2, Vh1, Vh2]
ndofs = [Vh[STATE].dim(), Vh[PARAMETER].dim(), Vh[ADJOINT].dim()]
if rank == 0:
print(sep, "Set up the mesh and finite element spaces", sep)
print(
"Number of dofs: STATE={0}, PARAMETER={1}, ADJOINT={2}".format(*ndofs))
# define boundary conditions and PDE
u_bdr = dl.Expression("1-x[0]", degree=1)
u_bdr0 = dl.Constant(0.0)
