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In this work, the authors developed a fast electromagnetics-based nonlinear-linear co-simulation algorithm based on a recently developed time-domain orthogonal finite-element reduction-recovery method (OrFE-RR). In this method, the linear part and the nonlinear part are naturally decoupled due to the diagonal matrix in the single surface system. Meanwhile, as the devices are usually not connected to the same mesh element, the devices are also decoupled. Thus, the linear part and the nonlinear devices can be solved separately with the coupling accounted in the right hand side. This method neither generates large dense matrix nor requires a staggered marching iteration. Hence, it is capable of simulating large-scale integrated circuits that consist of both linear network and nonlinear devices.