Efficient Parallel-in-Time Solution of Time-Periodic Problems Using a MultiHarmonic Coarse Grid Correction

This paper presents a highly parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the extension parareal method, known to accelerate sequential computations via parallelization fine grid. The proposed approach reduces complexity periodic by introducing simplified Newton algorithm, which allows an additional coarse In particular, at each iteration multiharmonic correction performed, converts block-cyclic system in time domain into block-diagonal frequency domain, thereby solving component parallel. convergence analysis method discussed one-dimensional model problem. introduced and several existing approaches are compared their application eddy current problem both linear models coaxial cable. Performance considered methods also illustrated three-dimensional transformer model.