Matrix-Free Nonlinear Finite-Element Solver Using Transmission-Line Modeling on GPU

The transmission-line modeling (TLM) used for nonlinear finite-element (FE) solution has a paramount feature that the admittance matrix is unchanged and only needs one-time factorization; and this feature becomes a drawback when the required number of TLM iterations increase due to the mismatch between the transmission-line impedance and the load. In this paper, a matrix-free TLM scheme is proposed to make use of the solved nonlinear reluctivities without employing any matrices at each timestep, thus substantially decreasing the number of required TLM iterations. The matrix-free solver is suitable for massively parallel processing and the design is implemented on the Tesla V100 graphics processing unit (GPU). A speedup of more than 27 times is obtained compared with a commercial FE package for different problem sizes while maintaining high accuracy.