An isoparametric three-dimensional meshfree electromagnetic–thermal framework with implicit curie-transition modeling for remeshing-free induction heating

Accurate numerical simulation of induction heating remains challenging due to the simultaneous presence of localized electromagnetic skin effects, steep thermo-magnetic nonlinearities across the Curie transition, and severe nodal anisotropies encountered in three-dimensional configurations. While standard finite element methods handle temperature-dependent property variations on fixed meshes, severe directional refinement within thin boundary layers frequently induces element distortion and geometric locking. This work presents an isoparametric Element-Free Galerkin (EFG) framework for coupled non-linear transient electromagnetic–thermal analyses on stationary, highly stretched nodal clouds. Rather than regenerating meshes or explicitly tracking moving boundaries, the thermo-magnetic phase transition across the Curie temperature is captured implicitly through local constitutive updates ( μ r ( T ) , σ ( T ) ) evaluated directly at fixed background Gauss quadrature points. The core methodological contribution lies in mapping the Moving Least Squares (MLS) compact support from an anisotropic physical domain into an isotropic reference space, augmented with trace-scaled Tikhonov regularization, thereby eliminating the over-smoothing and moment-matrix ill-conditioning typical of standard MLS under severe directional refinement. The spatial discretization is first verified against the analytical Bessel J 1 benchmark under constant material properties, demonstrating sub-percent errors within the electromagnetic skin layer and super-convergent spatial behavior on graded nodal distributions. The coupled transient framework is subsequently validated on a fully three-dimensional non-axisymmetric benchmark featuring an off-axis induction coil and a lateral magnetic flux concentrator. The proposed isoparametric EFG scheme achieves close agreement with the reference hexahedral FEM solution, yielding a global nodal RMS temperature deviation below 1 K across the thermal cycle while maintaining a measured overall runtime ratio of 1.24 × relative to the reference FEM ( N nodes = 2400 ), with an asymptotic scaling factor approaching 1.40 × for finer discretizations. By resolving the MLS aspect-ratio limitation without increasing the polynomial basis or support size, this framework provides a robust, remeshing-free baseline for steep-gradient multiphysics modeling, laying the numerical foundation for future extensions toward explicit kinematic interface enrichment.