SummaryWe present a fast time‐domain multiphysics simulation framework that combines full‐wave electromagnetism (EM) and carrier transport in semiconductor devices (technology computer‐aided design (TCAD)) for radio frequency (RF) and mixed‐signal modules. The proposed framework features a division of linear and nonlinear components in the EM–TCAD coupled system. The linear portion is extracted and handled independently with high efficiency by a matrix exponential approach assisted with Krylov subspace method. The nonlinear component is treated by ordinary Newton's method yet with a much sparser Jacobian matrix that leads to substantial speedup in solving the linear system of equations. More convenient error management and adaptive control are also available through the linear and nonlinear decoupling. Furthermore, a new form of system formulation is developed to further enhance the efficiency of the proposed framework by reducing the stiffness of EM–TCAD systems via special equation and variable transforms. Copyright © 2015 John Wiley & Sons, Ltd.