C-Coil: A High Performance Computing Approach for Magnetostatic Circular Coil Calculations

Accurate computation of magnetostatic coupling between non-coaxial circular coils remains prohibitively expensive when millions of configurations must be evaluated for design-space exploration. We propose a novel approach based on numerical methods to improve performance by 5 to 7 orders of magnitude while matching the accuracy of state-of-the-art semi-analytical methods. While other approaches strive to reduce the number of integration directions in the six-fold integral to 2 or 4, we propose a five-fold integral with simple-to-evaluate integrands. In place of the filament method, we employ the Gauss-Legendre quadrature due to its exponential convergence and find that numerical integration can be quicker than analytic integral evaluation. Furthermore, to tackle the complexity of allocating the computational resources to each of the five integration directions, we propose a heuristic that leads to 2 orders of magnitude lower computation time or 2 to 4 orders of magnitude higher accuracy. We also provide an implementation of our approach in C-Coil, an open-source C++ library with Python bindings that can also be used in MATLAB.