2019/08/13 by Kulchytska-Ruchka, Iryna, Schöps, Sebastian
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1908.05245
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 the complexity of the periodic Parareal solution by introducing a 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 solving for each frequency component in parallel. The convergence analysis of the method is discussed for a one-dimensional model problem. The introduced algorithm and several existing solution approaches are compared via their application to the eddy current problem for both linear and nonlinear models of a coaxial cable. Performance of the considered methods is also illustrated for a three-dimensional transformer model.