A Reduced Magnetic Vector Potential Approach with Higher-Order Splines

TL;DR

This paper introduces a high-order isogeometric method for magnetoquasistatic eddy-current problems that improves accuracy and efficiency by avoiding coil meshing and supporting complex winding paths.

Contribution

It generalizes the reduced magnetic vector potential approach with high-order splines, enabling better accuracy and practical implementation in electromagnetic simulations.

Findings

Achieves optimal convergence rates in numerical tests.

Identifies key requirements for practical high-order accuracy.

Supports arbitrary winding paths without coil meshing.

Abstract

This work presents a high-order isogeometric formulation for magnetoquasistatic eddy-current problems based on a decomposition into Biot-Savart-driven source fields and finite-element reaction fields. Building upon a recently proposed surface-only Biot-Savart evaluation, we generalize the reduced magnetic vector potential framework to the quasistatic regime and introduce a consistent high-order spline discretization. The resulting method avoids coil meshing, supports arbitrary winding paths, and enables high-order field approximation within a reduced computational domain. Beyond establishing optimal convergence rates, the numerical investigation identifies the requirements necessary to recover high-order accuracy in practice, including geometric regularity of the enclosing interface, accurate kernel quadrature, and compatible trace spaces for the source-reaction coupling.