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This paper illustrates the application of an alternating direction implicit (ADI) technique for the pseudospectral time-domain (PSTD) algorithm. A lumped element finite-difference time-domain (FDTD) simulator is developed to the wide-band modeling of microwave and millimeter wave integrated circuit. Three-dimensional ADI- PSTD scheme is adopted to describe the circuit passive part, whereas numerical device simulation techniques are employed for the active semiconductor devices. To achieve very accurate results, the short-open calibration technique has been modeled the interconnections. The resulting scheme allows for accurate mixed-mode simulation, which inherently accounts for propagation and radiative effects. Comparisons with the FDTD approach and an approach based on strong splitting demonstrate the potential of the method to substantially reduce the cost of simulating linear waves in dispersive materials.