Efficient Parallel-in-Time Solution of Time-Periodic Problems Using a Multi-Harmonic Coarse Grid Correction
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This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of (nonlinear) time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential computations via parallelization on the fine grid. The proposed approach reduces complexity of the periodic Parareal solution by introducing a special simplified Newton algorithm, which allows an additional parallelization on the coarse grid. In particular, at each Newton iteration a multi-harmonic correction is performed, which converts the block-cyclic periodic system in the time domain into a block-diagonal system in the frequency domain, thereby allowing separate solution for each frequency component in parallel. Comparison of the introduced algorithm and several existing solution approaches is illustrated via their application to the eddy current problem for both linear and nonlinear models of a coaxial cable.
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