Cuboids demagnetization#
The following example demonstrates how to create magnetic sources with different susceptibilities using the Magpylib library. It defines three cuboid magnets with varying susceptibilities and positions, creates a collection of these magnets, and computes their magnetic field responses using different levels of meshing. The results are then compared to a Finite Element Method (FEM) analysis to evaluate the performance of the Magpylib-Material-Response approach. The comparison is presented in two separate plots, one showing the magnetic field values and the other showing the difference between the Magpylib results and the FEM reference data. The code demonstrates that even with a low number of mesh elements, the Magpylib results quickly approach the reference FEM values.
Define magnetic sources with their susceptibilities#
import json
import magpylib as magpy
import numpy as np
import pandas as pd
import plotly.express as px
from loguru import logger
from magpylib_material_response.data import get_dataset
from magpylib_material_response.demag import apply_demag
from magpylib_material_response.meshing import mesh_all
if magpy.__version__.split(".")[0] != "5":
raise RuntimeError(
f"Magpylib version must be >=5, (installed: {magpy.__version__})"
)
magpy.defaults.display.backend = "plotly"
# some low quality magnets with different susceptibilities
cube1 = magpy.magnet.Cuboid(polarization=(0, 0, 1), dimension=(0.001, 0.001, 0.001))
cube1.move((-0.0015, 0, 0))
cube1.susceptibility = 0.3 # µr=1.3
cube1.style.label = f"Cuboid, susceptibility={cube1.susceptibility}"
cube2 = magpy.magnet.Cuboid(polarization=(0.9, 0, 0), dimension=(0.001, 0.001, 0.001))
cube2.rotate_from_angax(-45, "y").move((0, 0, 0.0002))
cube2.susceptibility = 1.0 # µr=2.0
cube2.style.label = f"Cuboid, susceptibility={cube2.susceptibility}"
mx = 0.6 * np.sin(np.deg2rad(30))
my = 0.6 * np.cos(np.deg2rad(30))
cube3 = magpy.magnet.Cuboid(polarization=(mx, my, 0), dimension=(0.001, 0.001, 0.002))
cube3.move((0.0016, 0, 0.0005)).rotate_from_angax(30, "z")
cube3.susceptibility = 0.5 # µr=1.5
cube3.style.label = f"Cuboid, susceptibility={cube3.susceptibility}"
# collection of all cells
coll = magpy.Collection(cube1, cube2, cube3, style_label="No demag")
sensor = magpy.Sensor(
position=np.linspace((-0.004, 0, -0.001), (0.004, 0, -0.001), 301)
)
magpy.show(*coll, sensor)
# example of meshed Collection
coll_meshed = mesh_all(
coll, target_elems=50, per_child_elems=False, style_label="No demag - meshed"
)
coll_meshed.show()
Compute material response - demagnetization#
# apply demagnetization with varying number of cells
colls = [coll]
for target_elems in [1, 2, 8, 16, 32, 64, 128, 256]:
with logger.contextualize(target_elems=target_elems):
coll_meshed = mesh_all(
coll, target_elems=target_elems, per_child_elems=True, min_elems=1
)
coll_demag = apply_demag(
coll_meshed,
style={"label": f"Coll_demag ({len(coll_meshed.sources_all):3d} cells)"},
)
colls.append(coll_demag)
2024-04-21 at 10:18:49 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag ( 3 cells) with 3 cells - Counter({'Cuboid': 3})
2024-04-21 at 10:18:49 | SUCCESS | timelog | {'target_elems': 1} ✅ Demagnetization of Coll_demag ( 3 cells) with 3 cells - Counter({'Cuboid': 3}) done 🕑 1.002sec
2024-04-21 at 10:18:50 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag ( 6 cells) with 6 cells - Counter({'Cuboid': 6})
2024-04-21 at 10:18:51 | SUCCESS | timelog | {'target_elems': 2} ✅ Demagnetization of Coll_demag ( 6 cells) with 6 cells - Counter({'Cuboid': 6}) done 🕑 1.002sec
2024-04-21 at 10:18:52 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag ( 24 cells) with 24 cells - Counter({'Cuboid': 24})
2024-04-21 at 10:18:52 | SUCCESS | timelog | {'target_elems': 8} ✅ Demagnetization of Coll_demag ( 24 cells) with 24 cells - Counter({'Cuboid': 24}) done 🕑 1.004sec
2024-04-21 at 10:18:53 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag ( 52 cells) with 52 cells - Counter({'Cuboid': 52})
2024-04-21 at 10:18:53 | SUCCESS | timelog | {'target_elems': 16} ✅ Demagnetization of Coll_demag ( 52 cells) with 52 cells - Counter({'Cuboid': 52}) done 🕑 1.006sec
2024-04-21 at 10:18:54 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag (102 cells) with 102 cells - Counter({'Cuboid': 102})
2024-04-21 at 10:18:54 | SUCCESS | timelog | {'target_elems': 32} ✅ Demagnetization of Coll_demag (102 cells) with 102 cells - Counter({'Cuboid': 102}) done 🕑 1.012sec
2024-04-21 at 10:18:55 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag (191 cells) with 191 cells - Counter({'Cuboid': 191})
2024-04-21 at 10:18:56 | SUCCESS | timelog | {'target_elems': 64} ✅ Demagnetization of Coll_demag (191 cells) with 191 cells - Counter({'Cuboid': 191}) done 🕑 1.026sec
2024-04-21 at 10:18:57 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag (378 cells) with 378 cells - Counter({'Cuboid': 378})
2024-04-21 at 10:18:57 | SUCCESS | timelog | {'target_elems': 128} ✅ Demagnetization of Coll_demag (378 cells) with 378 cells - Counter({'Cuboid': 378}) done 🕑 1.081sec
2024-04-21 at 10:18:58 | INFO | run | {} ℹ️ Start Demagnetization of Coll_demag (754 cells) with 754 cells - Counter({'Cuboid': 754})
2024-04-21 at 10:18:58 | INFO | run | {} ℹ️ Start Demagnetization tensor calculation
2024-04-21 at 10:18:59 | SUCCESS | timelog | {'target_elems': 256} ✅ Demagnetization tensor calculation done 🕑 2.245sec
2024-04-21 at 10:19:01 | SUCCESS | timelog | {'target_elems': 256} ✅ Demagnetization of Coll_demag (754 cells) with 754 cells - Counter({'Cuboid': 754}) done 🕑 3.288sec
Compare with FEM analysis#
# compute field before demag
B_no_demag_df = magpy.getB(coll_meshed, sensor, output="dataframe")
B_cols = ["Bx", "By", "Bz"]
def get_FEM_dataframe(sim):
res = sim["results"][0]
df = B_no_demag_df.copy()
for Bk in B_cols:
df[Bk] = res["value"].get(Bk, np.nan)
df["computation"] = res["computation"]
return df
def get_magpylib_dataframe(collection, sensors):
df = magpy.getB(collection, sensors, output="dataframe")
df["computation"] = collection.style.label
return df
sim_ANSYS = get_dataset("FEMdata_test_cuboids")
df = pd.concat(
[
get_FEM_dataframe(sim_ANSYS),
*[get_magpylib_dataframe(c, sensor) for c in colls],
]
).sort_values(["computation", "path"])
df["Distance [m]"] = sensor.position[df["path"]][:, 0]
df["Distance [m]"] -= df["Distance [m]"].min()
px_kwargs = dict(
x="Distance [m]",
y=B_cols,
facet_col="variable",
color="computation",
line_dash="computation",
height=400,
facet_col_spacing=0.05,
labels={**{Bk: f"{Bk} [T]" for Bk in B_cols}, "value": "value [T]"},
)
fig1 = px.line(
df,
title="Methods comparison",
**px_kwargs,
)
fig1.update_yaxes(matches=None, showticklabels=True)
df_diff = df.copy()
ref = sim_ANSYS["results"][0]["computation"]
for st in df_diff["computation"].unique():
df_diff.loc[df_diff["computation"] == st, B_cols] -= df.loc[
df["computation"] == ref, B_cols
].values
fig2 = px.line(
df_diff,
title=f"Methods comparison - diff vs {ref}",
**px_kwargs,
)
fig2.update_yaxes(matches=None, showticklabels=True)
display(fig1, fig2)
As shown above, already with a low number of mesh elements, the result is approaching the reference FEM values and improves while refining the mesh.