1 research outputs found
Efficient Parallel-in-Time Solution of Time-Periodic Problems Using a Multi-Harmonic 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
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