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The recent multi/many-core CPUs or GPUs have provided an ideal parallel computing platform to accelerate the time-consuming analysis of radio-frequency/millimeter-wave (RF/MM) integrated circuit (IC). This paper develops a structured shooting algorithm that can fully take advantage of parallelism in periodic steady state (PSS) analysis. Utilizing periodic structure of the state matrix of RF/MM-IC simulation, a cyclic-block-structured shooting-Newton method has been parallelized and mapped onto recent GPU platforms. We first present the formulation of the parallel cyclic-block-structured shooting-Newton algorithm, called periodic Arnoldi shooting method. Then we will present its parallel implementation details on GPU. Results from several industrial examples show that the structured parallel shooting-Newton method on Tesla's GPU can lead to speedups of more than 20× compared to the state-of-the-art implicit GMRES methods under the same accuracy on the CPU.