VECTOR-CASE

Vectorized Efficient C Tool for Analytical Series Expansion of Mutual Inductance for Circular Coils with Rectangular Cross-Section in Coaxial Configuration

Introduction

This is the code that accompanies the paper "Calculation of mutual inductance of two coaxial thick coils with rectangular cross-section by using cylindrical multipole expansion", by Filip Vučič, and Davor Dobrota. The paper available at IEEE Xplore (https://ieeexplore.ieee.org/document/10856207), and can be cited as (preprint):

@ARTICLE{10856207,
  author={Vučić, Filip and Dobrota, Davor},
  journal={IEEE Transactions on Magnetics}, 
  title={Calculation of mutual inductance of two coaxial thick coils with rectangular cross section by using cylindrical multipole expansion}, 
  year={2025},
  volume={},
  number={},
  pages={1-1},
  doi={10.1109/TMAG.2025.3535634}}

The code is meant to be a header-only C library. This makes it easy to include in other projects, and to use in conjunction with other libraries as well as from other languages. For an example of this, see how to use the code from Python.

Use

Base use-case

The code is written in C, and is intended to be used as header-only library. The code is vectorized, and is intended to be used with SSE, AVX, or AVX-512 instruction sets. To enable them, uncomment the appropriate line in src/settings.h or pass an appropriate definition to the compiler by some other means.

One can generate lookup tables for the sums using the functions found in generate_lookup_tables.py

Python

There is also an implementation of the method in Python, using the Decimal class to achieve adaptive precision.

There is a demonstration of how the methods from the header files can be used in Python bz means of the CFFI library. Additionally one might consider using cppyy, but at a potential loss of performance due to more limited control of the compiler and compilation flags.

Mathematica and implementation of external method

Finally, an implementation of method by Župan et al ( T. Župan, Ž. Štih, and B. Trkulja, “Fast and precise method for inductance calculation of coaxial circular coils with rectangular cross section using the one-dimensional integration of elementary functions applicable to superconducting magnets,” IEEE Transactions on Applied Superconductivity, vol. 24, no. 2, pp. 81–89, 2014.) is implemented in C (but does not converge with Gauss-Legendre) and Mathematica.