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Investigation of the time integration methods on the parareal method for field computation of eddy currents problems

In this paper, we investigate the influence of time integration methods on the performance of the Parareal method for the computation of eddy current problems. Parareal is a method that allows parallelization in time domain. The time interval is split into many smaller time intervals (as many as the number of available CPUs) with a fine time grid and solved in parallel allowing to capture the finescale details of the solution. An approximation of initial conditions for these fine problems is obtained by solving a cheap, time-dependent problem defined on a coarse grid for the entire time interval. The method has been successfully implemented for the problem of eddy currents using the implicit backward Euler method. In this paper we will investigate the influence of the time stepping methods on the convergence and the complexity of the Parareal algorithm.