Hyperbolic Basis Functions for Time-Transient Analysis of Eddy Currents in Conductive and Magnetic Thin Sheets

TL;DR

This paper introduces a novel finite-element method using hyperbolic basis functions derived from steady-state solutions to efficiently model the time-transient behavior of eddy currents in thin conductive and magnetic sheets, improving accuracy and computational efficiency.

Contribution

The paper proposes a new time-domain finite-element approach utilizing hyperbolic basis functions based on steady-state solutions, enabling better modeling of transient eddy currents in thin sheets.

Findings

Good agreement with standard finite element solutions.

Effective in both harmonic and time-dependent simulations.

Applicable to linear and nonlinear magnetic materials.

Abstract

This paper presents a new time-domain finite-element approach for modelling thin sheets with hyperbolic basis functions derived from the well-known steady-state solution of the linear flux diffusion equation. The combination of solutions at different operating frequencies permits the representation of the time-evolution of field quantities in the magnetic field formulation. This approach is here applied to solve a planar shielding problem in harmonic and time-dependent simulations for materials with either linear or nonlinear characteristics. Local and global quantities show good agreement with the reference solutions obtained by the standard finite element method on a complete and representative discretization of the region exposed to a time-varying magnetic field.