A Reduced Magnetic Vector Potential Approach with Higher-Order Splines

2026-02-26

AI Summary

This work proposes a reduced-dimensional magnetic vector potential framework that eliminates the need for volumetric coil discretization in magneto-quasistatic eddy current problems. Addressing the limitations of conventional approaches—which require explicit coil modeling, struggle with arbitrary winding geometries, and suffer from restricted high-order accuracy—the method couples a Biot–Savart source field with a finite element reaction field. The source field is computed via surface integration over the coil boundary, while high-order spline discretizations from isogeometric analysis enable both domain reduction and accurate field approximation under quasistatic conditions. This study extends reduced-dimensional vector potential formulations to eddy current scenarios for the first time, accommodating arbitrary winding configurations and guaranteeing optimal convergence rates. Numerical experiments highlight the critical roles of trace-space compatibility, exact kernel integration, and geometric regularity in achieving high-order accuracy.

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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.

Problem

• magnetoquasistatic
• eddy-current
• high-order accuracy
• reduced magnetic vector potential
• isogeometric analysis

Innovation

• isogeometric analysis
• reduced magnetic vector potential
• high-order splines
• eddy-current problems
• Biot-Savart law