A Self-Adaptive Model-Order Reduction Algorithm for Nonlinear Eddy-Current Problems Based on Quadratic–Bilinear Modeling

The finite-element time-domain simulation of nonlinear eddy-current problems requires the iterative solution of a large, sparse system of equations at every time-step. Model-order reduction is a powerful tool for reducing the computational effort for this task. In this paper, an adaptive order-reduction methodology with error control is proposed. In contrast to previous approaches, it treats the nonlinearity without simplification, by rewriting the original equations as a quadratic-bilinear system.