MagnetiCalc 1.12.0

MagnetiCalc calculates the magnetic flux density, vector potential, energy, self-inductance and magnetic dipole moment of arbitrary coils. Inside a VisPy / OpenGL-accelerated PyQt5 GUI, the static magnetic flux density (B-field) or the magnetic vector potential (A-field) is displayed in interactive 3D, using multiple metrics for highlighting this field's properties.

MagnetiCalc

What does MagnetiCalc do?

MagnetiCalc calculates the static magnetic flux density, vector potential, energy, self-inductance and magnetic dipole moment of arbitrary coils. Inside a VisPy / OpenGL-accelerated PyQt5 GUI, the magnetic flux density (-field, in units of Tesla) or the magnetic vector potential (-field, in units of Tesla-meter) is displayed in interactive 3D, using multiple metrics for highlighting the field properties.

Experimental feature: To calculate the energy and self-inductance of permeable (i.e. ferrous) materials, different core media can be modeled as regions of variable relative permeability; however, core saturation is currently not modeled, resulting in excessive flux density values.

Who needs MagnetiCalc?

MagnetiCalc does its job for hobbyists, students, engineers and researchers of magnetic phenomena. I designed MagnetiCalc from scratch, because I didn't want to mess around with expensive and/or overly complex simulation software whenever I needed to solve a magnetostatic problem.

How does it work?

The -field calculation is implemented using the Biot-Savart law [1], employing multiprocessing techniques; MagnetiCalc uses just-in-time compilation (JIT) and, if available, GPU-acceleration (CUDA) to achieve high-performance calculations. Additionally, the use of easily constrainable "sampling volumes" allows for selective calculation over grids of arbitrary shape and arbitrary relative permeabilities (experimental).

The shape of any wire is modeled as a 3D piecewise linear curve. Arbitrary loops of wire are sliced into differential current elements (), each of which contributes to the total resulting field (, ) at some fixed 3D grid point (), summing over the positions of all current elements ():

At each grid point, the field magnitude (or field angle in some plane) is displayed using colored arrows and/or dots; field color and alpha transparency are individually mapped using one of the various available metrics.

The coil's energy [2] and self-inductance [3] are calculated by summing the squared -field over the entire sampling volume; ensure that the sampling volume encloses a large, non-singular portion of the field:

Additionally, the scalar magnetic dipole moment [4] is calculated by summing over all current elements:

References

[1]: Jackson, Klassische Elektrodynamik, 5. Auflage, S. 204, (5.4).
[2]: Kraus, Electromagnetics, 4th Edition, p. 269, 6-9-1.
[3]: Jackson, Klassische Elektrodynamik, 5. Auflage, S. 252, (5.157).
[4]: Jackson, Klassische Elektrodynamik, 5. Auflage, S. 216, (5.54).

Screenshot

(Screenshot taken from the latest GitHub release.)

Installation

If you have trouble installing MagnetiCalc, make sure to file an issue so I can help you get it up and running!

Requirements:

• Python 3.6+

Tested with:

• Python 3.8 in Ubuntu 20.04
• Python 3.7 in Linux Mint 19.3
• Python 3.8.10 in Windows 10 (21H2)

Prerequisites

On some systems, it may be necessary to upgrade pip first: python3 -m pip install pip --upgrade

Note: Windows users need to type python instead of python3

Linux

The following dependencies must be installed first (Ubuntu 20.04):

sudo apt install python3-dev
sudo apt install libxcb-xinerama0 --reinstall

Windows

It is recommended to install Python 3.8.10. Installation will currently fail for Python 3.9+ due to missing dependencies.

On some systems, it may be necessary to install the latest Microsoft Visual C++ Redistributable first.

Option A: Automatic install via pip

This will install or upgrade MagnetiCalc (and its dependencies) to the user site-packages directory and start it from there.

Linux

python3 -m pip install magneticalc --upgrade
python3 -m magneticalc

Windows

python -m pip install --upgrade magneticalc
python -m magneticalc

Juptyer Notebook & Jupyter Lab

From within a Jupyter Notebook, MagnetiCalc can be installed (upgraded) and run like this:

import sys
!{sys.executable} -m pip install magneticalc --upgrade
!{sys.executable} -m magneticalc

Option B: Manual download

Note: Windows users need to type python instead of python3.

Install (upgrade) all dependencies to the user site-packages directory:

python3 -m pip install numpy numba scipy PyQt5 vispy qtawesome sty si-prefix h5py --upgrade

Use Git to clone the latest version of MagnetiCalc from GitHub:

git clone https://github.com/shredEngineer/MagnetiCalc

Enter the cloned directory and start MagnetiCalc:

cd MagnetiCalc
python3 -m magneticalc

Enabling CUDA Support

Tested in Ubuntu 20.04, using the NVIDIA CUDA 10.1 driver and NVIDIA GeForce GTX 1650 GPU.

Please refer to the Numba Installation Guide which includes the steps necessary to get CUDA up and running.

Data Import/Export and Python API

GUI

MagnetiCalc allows the following data to be imported/exported using the GUI:

• Import/export wire points from/to TXT file.
• Export -/ -fields, wire points and wire current to an HDF5 container for use in post-processing.

API

Documentation: API, MagnetiCalc_Data

The API class provides basic functions for importing/exporting data programmatically:

• Generate a wire shape using NumPy and export it to a TXT file:

  from magneticalc import API
  import numpy as np
  
  wire = [
      (np.cos(a), np.sin(a), np.sin(16 * a))
      for a in np.linspace(0, 2 * np.pi, 200)
  ]
  
  API.export_wire("MyWire.txt", wire)
  

• Import an HDF5 file containing an -field (which needs to be generated using the GUI first) and plot it using Matplotlib.

  from magneticalc import API
  import matplotlib.pyplot as plt
  
  data = API.import_hdf5("MagnetiCalc_Export_A.hdf5")
  axes = data.get_axes()
  a_field = data.get_a_field()
  
  ax = plt.figure(figsize=(10, 10), dpi=150).add_subplot(projection="3d")
  ax.quiver(*axes, *a_field, length=5e5, normalize=False, linewidth=2)
  plt.show()
  

  The data is wrapped in a MagnetiCalc_Data object which provides convenience functions for accessing, transforming and reshaping the data:

  • .get_dimension() returns the sampling volume dimension as a 3-tuple.
  • .get_axes(reduce=True) returns the axis ticks of the sampling volume.
  • .get_axes_list() returns a list of all 3D points of the sampling volume.
  • .get_a_field_list() returns a list of all 3D vectors of the -Field.
  • .get_a_field(as_3d=True) returns a 3D field for each component of the -Field, indexed over the reduced axes.

License

Copyright © 2020–2021, Paul Wilhelm, M. Sc. <[e-mail]>

ISC License

Permission to use, copy, modify, and/or distribute this software for any purpose with or without fee is hereby granted, provided that the above copyright notice and this permission notice appear in all copies.

THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

Contribute

You are invited to contribute to MagnetiCalc in any way you like! :)

If this software has been helpful to you in some way or another, please let me and others know!

ToDo

General

• Ensure consistent PyQt5 look and feel in Windows and Linux. (Dynamically adjust dialogs.)
• Move from INI format to HDF5 format for storing project data; make auto-generated MagnetiCalc.ini a global settings file instead. (Retain option to import old MagnetiCalc.ini files.)
• Add a global settings dialog for some selection of options currently hard-coded in various classes.

Functional

• Add an overlay for vector metrics, like gradient or curvature (derived from the fundamental - and -fields).
• Add a list of objects, for wires and permeability classes (constraints), with a transformation pipeline for each object; move the Wire widget to a dedicated dialog window instead. (Add support for multiple wires, study mutual induction.)
• Highlight permeability classes with in the 3D view.
• Add support for multiple current values and animate the resulting fields.
• Add support for modeling of core material saturation and hysteresis effects (Landau–Lifshitz–Gilbert equation).
• Provide a means to emulate permanent magnets.

Usability

• Add more example projects to examples/.
• Move variations of each wire preset (e.g. the number of turns) into an individual sub-menu; alternatively, provide a dialog for parametric generation.
• Add stationary coordinate system and ruler in the bottom left corner.
• Add support for selective display over a portion of the metric range, enabling a kind of iso-contour display.

Known Bugs

• Fix issue where the points of a sampling volume with fractional resolution are not always spaced equidistantly for some sampling volume dimensions.
• Fix calculation of divergence right at the sampling volume boundary.
• Fix delayed GUI start-up when loading "complex" files.
• Fix missing scaling of VisPy markers when zooming.
• Fix unnecessary shading of VisPy markers.

Code Quality

• Add debug output where it is missing.
• Add type hints where they are missing.
• Use my QtWidgets2 wrapper everywhere.
• Use the @property decorator for accessing data where applicable.
• Merge sparse *_Types.py modules with higher-level classes if possible.

Design

• Replace plain QMessageBox dialogs with nice-looking custom dialogs where possible.

Video

A very short demo of MagnetiCalc in action:

Links

If you want to comment on the project or see additional info, please visit my personal website: https://paulwilhelm.de/magneticalc/

Appendix: Metrics

Metric	Symbol	Description
Magnitude		Magnitude in space
Magnitude X		Magnitude in X-direction
Magnitude Y		Magnitude in Y-direction
Magnitude Z		Magnitude in Z-direction
Magnitude XY		Magnitude in XY-plane
Magnitude XZ		Magnitude in XZ-plane
Magnitude YZ		Magnitude in YZ-plane
Divergence		Divergence
Divergence +		Positive Divergence
Divergence –		Negative Divergence
Log Magnitude		Logarithmic Magnitude in space
Log Magnitude X		Logarithmic Magnitude in X-direction
Log Magnitude Y		Logarithmic Magnitude in Y-direction
Log Magnitude Z		Logarithmic Magnitude in Z-direction
Log Magnitude XY		Logarithmic Magnitude in XY-plane
Log Magnitude XZ		Logarithmic Magnitude in XZ-plane
Log Magnitude YZ		Logarithmic Magnitude in YZ-plane
Log Divergence		Logarithmic Divergence
Log Divergence +		Positive Logarithmic Divergence
Log Divergence –		Negative Logarithmic Divergence
Angle XY		Field angle in XY-plane
Angle XZ		Field angle in XZ-plane
Angle YZ		Field angle in YZ-plane