A 3-D Hybrid Cell Method for Induction Heating Problems

A novel hybrid approach for solving induction heating problems is presented. The electrothermal problem is discretized by the cell method (CM) and coupled to the boundary element method to avoid the air region meshing. The interface coupling is obtained by introducing a new topological framework for the CM, which is the augmented dual grid. The main advantage is that the electromagnetic hybrid formulation for computing time-harmonic eddy currents results in a partly dense indefinite linear system, which is solved by a fast TFQMR iterative method. The transient thermal problem, weakly coupled to the electrical one, is solved by the $\theta $ method under convection and radiation boundary conditions. The hybrid approach shows to be very accurate by comparison with third-order 2-D FEM on an axisymmetric test case. The applicability of the method then extends to full 3-D models with limited computing resources.