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In this paper, we present a parallel harmonic-balance approach, applicable to the steady-state and envelope-following analyses of both driven and autonomous circuits. Our approach is centered on a naturally parallelizable preconditioning technique that speeds up the core computation in harmonic-balance-based analysis. As a coarse-grained parallel approach by algorithm construction, the proposed method facilitates parallel computing via the use of domain knowledge and simplifies parallel programming compared with fine-grained strategies. The proposed parallel preconditioning technique can be combined with more conventional parallel approaches such as parallel device model evaluation, parallel fast Fourier transform operation, and parallel matrix-vector product to further improve runtime efficiency. In our message-passing-interface-based implementation over a cluster of workstations and multithreading-based implementation on a shared-memory machine, favorable runtime speedups with respect to the conventional serial approaches and the serial implementations of the same parallel algorithms are achieved.