Softmagnetic Composite
Google Colab Link
The demo can be run on Google Colab without any local installation. Use the following link to try it out.
[6]:
!pip install -q magnumnp numpy==1.22.4
Run Demo:
[7]:
from magnumnp import *
import torch
#SIZE_CUBE = 900e-9
#gap = 23.08 14.29 9.09 6.98 4.35
#Ni = 13 21 33 43 69
#N = 3*Ni + 1 = 40 64 100 130 208
N = 40
Timer.enable()
# initialize state
eps = 1e-15
Nx, Ny, Nz = 3, 3, 3
nx, ny, nz = N, N, N
dx, dy, dz = 900e-9 / (N-1), 900e-9 / (N-1), 900e-9 / (N-1)
mesh = Mesh((nx,ny,nz), (dx,dy,dz))
state = State(mesh)
state.m = state.Constant((0,0,1))
state.material = {"alpha": 1.0}
state.material["Ms"] = state.Constant([0.0001/constants.mu_0])
state.material["Ms"][nx%Nx:,ny%Ny:,nz%Nz:] = 1.5/constants.mu_0
state.material["A"] = state.Constant([0.])
state.material["A"][nx%Nx:,ny%Ny:,nz%Nz:] = 10e-12
state.material["Ku"] = state.Constant([0.])
state.material["Ku"][nx%Nx:,ny%Ny:,nz%Nz:] = 8e3
k_dir = state.Tensor(((1.688281290426342229e-01, -7.18775080428410873e-01, 6.744326850020654351e-01),
(-1.24488794472133734e-02, 8.827421556265807601e-01, 4.696927847862328309e-01),
(4.360199027887372986e-02, 9.960452028850761419e-01, -7.74133079860866157e-02),
(3.749512630383480816e-01, 6.881354883832631053e-01, -6.21193287128471327e-01),
(8.860065554198717219e-01, 2.300892602270045995e-01, -4.02555978816864223e-01),
(-7.89116308031293234e-02, -7.44290764462179010e-01, -6.63177361239280949e-01),
(1.534426618908853179e-01, 6.661409155280296757e-01, 7.298709681658244186e-01),
(3.629777351625293469e-02, 7.384491837339980380e-01, 6.733314745950575997e-01),
(-6.22338299750334056e-01, -4.54495719851937984e-01, -6.37282261874698607e-01),
(5.091810893444697061e-01, -7.86185846048253700e-01, 3.502091285608797122e-01),
(-7.42309465286212555e-01, 5.245654409560085440e-01, 4.169025736321682052e-01),
(2.976579786344664136e-01, 5.698206235530806074e-01, -7.65966177274703174e-01),
(6.783747177775549531e-02, -5.13898942407917780e-01, 8.551642850440059895e-01),
(-4.09811740153190107e-01, -6.51000036118079772e-01, -6.38947017057653221e-01),
(-4.35391566957816666e-01, 7.000228998401875069e-01, -5.66040743340399221e-01),
(-3.67275369838029608e-01, -9.06849357668608080e-01, -2.06719726214920074e-01),
(-7.24876157150795674e-01, 2.752762585295002173e-01, -6.31488351661607993e-01),
(7.999944917638109887e-01, -5.94809366836661745e-01, -7.88075521186358679e-02),
(-6.38660840611896762e-01, -7.30613237722315789e-01, -2.41488359002706959e-01),
(5.978837032381554284e-01, -9.09378167932159697e-02, 7.964078043810925989e-01),
(-9.29805720633694821e-01, -3.57570345696486047e-01, 8.720533100304592167e-02),
(4.682836169203208332e-01, -6.07627185281937154e-01, -6.41482390896564447e-01),
(7.309975652323822404e-01, 1.317784064962062851e-01, -6.69534921572915164e-01),
(-1.26449163913964823e-01, -9.90975538690972102e-01, -4.44757311530326326e-02),
(4.076648517742982869e-01, 5.753823407754260488e-01, 7.090448015123099745e-01),
(3.803260297965609382e-01, 9.217214425940288836e-01, 7.603744683751342825e-02),
(-7.25468075571367832e-01, 2.563257490022778362e-01, -6.38743439672923241e-01))).reshape(3,3,3,3)
k_dir = k_dir.repeat_interleave(nx//Nx,0).repeat_interleave(ny//Ny,1).repeat_interleave(nz//Nz,2)
state.material["Ku_axis"] = state.Constant([1,1,1])
state.material["Ku_axis"][nx%Nx:,ny%Ny:,nz%Nz:,:] = k_dir
write_vti(state.material, "data/material.vti", state)
# initialize field terms
demag = DemagFieldPBC()
exchange = ExchangeFieldPBC()
aniso = UniaxialAnisotropyField()
external = ExternalField(TimeInterpolator(state, {0.0e-9: [0.0, 0.0, 0.0],
1.0e-9: [0.0, 0.0, 0.0],
3.5e-9: [0.1/constants.mu_0, 0.0, 0.0],
8.5e-9: [-0.1/constants.mu_0, 0.0, 0.0],
13.5e-9: [0.1/constants.mu_0, 0.0, 0.0]}))
# perform integration
llg = LLGSolver([demag, exchange, aniso, external])
logger = ScalarLogger("data/m.dat", ['t', external.h, 'm'])
while state.t < 13.5e-9-eps:
llg.step(state, 1e-10)
logger << state
Timer.print_report()
2023-05-08 12:31:43 magnum.np:INFO [State] running on device: cpu (dtype = float64)
2023-05-08 12:31:43 magnum.np:INFO [Mesh] 40x40x40 (size= 2.30769e-08 x 2.30769e-08 x 2.30769e-08)
2023-05-08 12:31:43 magnum.np:INFO [LLGSolver] using RKF45 solver (atol = 1e-05)
2023-05-08 12:31:48 magnum.np:INFO [LLG] step: dt= 1e-10 t=1e-10
2023-05-08 12:31:50 magnum.np:INFO [LLG] step: dt= 1e-10 t=2e-10
2023-05-08 12:31:52 magnum.np:INFO [LLG] step: dt= 1e-10 t=3e-10
2023-05-08 12:31:55 magnum.np:INFO [LLG] step: dt= 1e-10 t=4e-10
2023-05-08 12:31:58 magnum.np:INFO [LLG] step: dt= 1e-10 t=5e-10
2023-05-08 12:32:02 magnum.np:INFO [LLG] step: dt= 1e-10 t=6e-10
2023-05-08 12:32:05 magnum.np:INFO [LLG] step: dt= 1e-10 t=7e-10
2023-05-08 12:32:07 magnum.np:INFO [LLG] step: dt= 1e-10 t=8e-10
2023-05-08 12:32:10 magnum.np:INFO [LLG] step: dt= 1e-10 t=9e-10
2023-05-08 12:32:12 magnum.np:INFO [LLG] step: dt= 1e-10 t=1e-09
2023-05-08 12:32:14 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.1e-09
2023-05-08 12:32:17 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.2e-09
2023-05-08 12:32:19 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.3e-09
2023-05-08 12:32:23 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.4e-09
2023-05-08 12:32:26 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.5e-09
2023-05-08 12:32:30 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.6e-09
2023-05-08 12:32:33 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.7e-09
2023-05-08 12:32:36 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.8e-09
2023-05-08 12:32:41 magnum.np:INFO [LLG] step: dt= 1e-10 t=1.9e-09
2023-05-08 12:32:45 magnum.np:INFO [LLG] step: dt= 1e-10 t=2e-09
2023-05-08 12:32:48 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.1e-09
2023-05-08 12:32:52 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.2e-09
2023-05-08 12:32:55 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.3e-09
2023-05-08 12:32:59 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.4e-09
2023-05-08 12:33:03 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.5e-09
2023-05-08 12:33:07 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.6e-09
2023-05-08 12:33:12 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.7e-09
2023-05-08 12:33:17 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.8e-09
2023-05-08 12:33:21 magnum.np:INFO [LLG] step: dt= 1e-10 t=2.9e-09
2023-05-08 12:33:25 magnum.np:INFO [LLG] step: dt= 1e-10 t=3e-09
2023-05-08 12:33:29 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.1e-09
2023-05-08 12:33:33 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.2e-09
2023-05-08 12:33:37 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.3e-09
2023-05-08 12:33:43 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.4e-09
2023-05-08 12:33:46 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.5e-09
2023-05-08 12:33:49 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.6e-09
2023-05-08 12:33:51 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.7e-09
2023-05-08 12:33:55 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.8e-09
2023-05-08 12:33:57 magnum.np:INFO [LLG] step: dt= 1e-10 t=3.9e-09
2023-05-08 12:34:00 magnum.np:INFO [LLG] step: dt= 1e-10 t=4e-09
2023-05-08 12:34:02 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.1e-09
2023-05-08 12:34:05 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.2e-09
2023-05-08 12:34:08 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.3e-09
2023-05-08 12:34:10 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.4e-09
2023-05-08 12:34:12 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.5e-09
2023-05-08 12:34:14 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.6e-09
2023-05-08 12:34:16 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.7e-09
2023-05-08 12:34:19 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.8e-09
2023-05-08 12:34:21 magnum.np:INFO [LLG] step: dt= 1e-10 t=4.9e-09
2023-05-08 12:34:23 magnum.np:INFO [LLG] step: dt= 1e-10 t=5e-09
2023-05-08 12:34:26 magnum.np:INFO [LLG] step: dt= 1e-10 t=5.1e-09
2023-05-08 12:34:29 magnum.np:INFO [LLG] step: dt= 1e-10 t=5.2e-09
2023-05-08 12:34:32 magnum.np:INFO [LLG] step: dt= 1e-10 t=5.3e-09
2023-05-08 12:34:35 magnum.np:INFO [LLG] step: dt= 1e-10 t=5.4e-09
2023-05-08 12:34:37 magnum.np:INFO [LLG] step: dt= 1e-10 t=5.5e-09
2023-05-08 12:34:40 magnum.np:INFO [LLG] step: dt= 1e-10 t=5.6e-09
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File ~/git/magnum.np/magnumnp/common/timer.py:236, in timedmethod.<locals>.timed(*args, **kwargs)
235 with Timer("%s.%s" % (args[0].__class__.__name__, method.__name__)):
--> 236 return method(*args, **kwargs)
File ~/git/magnum.np/magnumnp/solvers/llg.py:49, in LLGSolver.step(self, state, dt, **kwargs)
47 @timedmethod
48 def step(self, state, dt, **kwargs):
---> 49 self._solver.step(state, dt, **kwargs)
50 logging.info_blue("[LLG] step: dt= %g t=%g" % (dt, state.t))
File ~/git/magnum.np/magnumnp/solvers/ode_solvers/rkf45.py:92, in RKF45.step(self, state, dt, rtol, atol, **llg_args)
91 while state.t < t1:
---> 92 _m1, _t1, err = self._try_step(state, **llg_args)
93 dt_opt = state._tensor(self._optimal_stepsize(err, atol or self._atol))
File ~/git/magnum.np/magnumnp/solvers/ode_solvers/rkf45.py:52, in RKF45._try_step(self, state, **llg_args)
51 f, m, t, dt = self._f_wrapper, state.m, state.t, self._dt
---> 52 k1 = dt * f(state, t, m, **llg_args)
53 k2 = dt * f(state, t + 1./ 4.*dt, m + 1./ 4.*k1, **llg_args)
File ~/git/magnum.np/magnumnp/solvers/ode_solvers/rkf45.py:45, in RKF45._f_wrapper(self, state, t, m, **llg_args)
44 state.m = m
---> 45 f = self._f(state, **llg_args)
46 state.t = t0
File ~/git/magnum.np/magnumnp/solvers/llg.py:36, in LLGSolver.dm(self, state, alpha, no_precession)
34 alpha_prime = alpha * gamma_prime
---> 36 h = sum([term.h(state) for term in self._terms])
38 dm = -alpha_prime * torch.linalg.cross(state.m, torch.linalg.cross(state.m, h))
File ~/git/magnum.np/venv/lib/python3.8/site-packages/torch/_tensor.py:1295, in Tensor.__torch_function__(cls, func, types, args, kwargs)
1294 with _C.DisableTorchFunctionSubclass():
-> 1295 ret = func(*args, **kwargs)
1296 if func in get_default_nowrap_functions():
KeyboardInterrupt:
The above exception was the direct cause of the following exception:
KeyboardInterrupt Traceback (most recent call last)
Cell In[7], line 81
78 logger = ScalarLogger("data/m.dat", ['t', external.h, 'm'])
80 while state.t < 13.5e-9-eps:
---> 81 llg.step(state, 1e-10)
82 logger << state
84 Timer.print_report()
File ~/git/magnum.np/magnumnp/common/timer.py:236, in timedmethod.<locals>.timed(*args, **kwargs)
233 @wraps(method)
234 def timed(*args, **kwargs):
235 with Timer("%s.%s" % (args[0].__class__.__name__, method.__name__)):
--> 236 return method(*args, **kwargs)
File ~/git/magnum.np/magnumnp/common/timer.py:103, in Timer.__exit__(self, e_typ, e_val, trcbak)
101 def __exit__(self, e_typ, e_val, trcbak):
102 if all((e_typ, e_val, trcbak)):
--> 103 raise e_typ from e_val
105 if not Timer._options['active']: return self
107 if Timer._options['skip'] <= self._data['calls']:
KeyboardInterrupt:
Plot Results
[ ]:
from os import path
if not path.isdir("ref"):
!mkdir ref
!wget -P ref https://gitlab.com/magnum.np/magnum.np/raw/main/demos/softmagnetic_composite/ref/m_ref.dat
[5]:
import matplotlib.pyplot as plt
import numpy as np
data = np.loadtxt("data/m.dat")
ref = np.loadtxt("ref/m_ref.dat")
fig, ax = plt.subplots(figsize=(7,5))
cycle = plt.rcParams['axes.prop_cycle'].by_key()['color']
ax.plot(data[:,1]*4*np.pi*1e-7, data[:,4], '-', color = cycle[2], label = "magnum.np")
ax.plot(ref[:,1]*4*np.pi*1e-7, ref[:,4], '-', color = cycle[2], linewidth = 6, alpha = 0.4, label = "magnum.af")
ax.set_xlim([-0.1,0.1])
ax.set_ylim([-1,1])
ax.set_title("SMC Demo")
ax.set_xlabel("External Field $\mu$$_0$ H$^{ext}$$_x$ [T]")
ax.set_ylabel("Reduced Magnetization m [1]")
ax.legend(ncol=3)
ax.grid()
fig.savefig("data/results.png")
IOStream.flush timed out