magpylib-material-response

Warning This package is experimental and in development phase, breaking API changes may happen at any time.

Magpylib-Material-Response adds the response of magnetic materials to Magpylib: the magnetization of soft-magnetic parts and the demagnetization of hard magnets. A solved model is a magpylib source like any other.

• solve_face_charge solves linear, uniform parts on their surface, with no volume mesh: cuboids, cylinders, cylinder segments, spheres and closed triangle meshes, such as CAD exports. It gets within 1 % of a finite-element reference faster than finite elements on every validation case where both get there.
• solve_cells cuts the parts into cells and solves for the polarization of every cell at once with the method of moments: for a part that saturates on a BHCurve, an anisotropic susceptibility, or one that varies inside a part. A dense direct solver, or matrix-free GMRES with FFT products on grids of identical cells; meshing helpers cut cuboids, cylinders and, through TetGen, any closed triangular surface into cells.
• solve_fem (the fem extra, NGSolve) solves the same model by finite elements, to check the other two, a saturating part too; study_cells, study_fem and compare give error bars by refining the mesh or the element order.

What drives a part is any other source in the model: magnets, currents and a UniformField. All of these are importable from the package itself.

Installation

pip install magpylib-material-response

Tetrahedral meshing of TriangularMesh magnets needs the optional TetGen, finite elements NGSolve:

pip install "magpylib-material-response[tetgen]"
pip install "magpylib-material-response[fem]"

Minimal examples

import magpylib as magpy
from magpylib_material_response import solve_face_charge

# a magnet on an iron plate, SI units (m, T)
magnet = magpy.magnet.Cuboid(polarization=(0, 0, 1.2), dimension=(0.01, 0.01, 0.005))
magnet.position = (0, 0, 0.0055)
plate = magpy.magnet.Cuboid(polarization=(0, 0, 0), dimension=(0.04, 0.04, 0.006))
plate.susceptibility = 1000  # soft iron; the magnet, with none, keeps its polarization

solved = solve_face_charge(magpy.Collection(magnet, plate))
print(
    magpy.getB(solved, (0, 0, 0.012))
)  # 205 mT above the magnet, 160 without the plate

import magpylib as magpy
from magpylib_material_response import solve_cells
from magpylib_material_response.meshing import mesh_Cuboid

# a magnet with finite susceptibility, demagnetizing itself
magnet = magpy.magnet.Cuboid(polarization=(0, 0, 1), dimension=(1e-3, 1e-3, 1e-3))
magnet.susceptibility = 0.3  # µr = 1.3

mesh_demag = solve_cells(mesh_Cuboid(magnet, target_elems=125))
print(magpy.getB(mesh_demag, (0, 0, 1.5e-3)))

import magpylib as magpy
import numpy as np
from magpylib_material_response import BHCurve, UniformField, solve_cells
from magpylib_material_response.meshing import mesh_Cuboid

# an iron cube saturating in an applied field, with a B-H curve in A/m and T
H = np.r_[0.0, np.geomspace(1e-2, 1e6, 200)]
mu0H = magpy.mu_0 * H
cube = magpy.magnet.Cuboid(polarization=(0, 0, 0), dimension=(0.01, 0.01, 0.01))
cube.susceptibility = BHCurve(H=H, B=1000 * mu0H / (1 + 1000 * mu0H / 1.6) + mu0H)

model = magpy.Collection(mesh_Cuboid(cube, (4, 4, 4)), UniformField(B=(0, 0, 1)))
solved = solve_cells(model)
print(magpy.getB(solved, (0, 0, 0.02)))  # the applied 1 T included

AI coding assistants: the package ships an Agent Skill, which uvx library-skills adds to a project.

See the documentation for a quickstart, worked examples, and the method description.