Resumen de Nonlinear model order reduction for the fast solution of induction heating problems in time-domain
Lorenzo Codecasa, Federico Moro, Piergiorgio Alotto
Purpose – This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.
Design/methodology/approach – A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection.
Findings – The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem.
Research limitations/implications – Only linear magnetic materials are considered in the present formulation.
Practical implications – The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method.
Originality/value – The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.
