A New Parareal Algorithm for Problems with Discontinuous Sources

We recently proposed a new Parareal algorithm for problems with discontinuous sources which are common in electrical engineering, e.g., when an electric device is supplied with a pulse-width-modulated signal. Our algorithm uses a smooth input for the coarse problem with reduced dynamics. In the new arXiv preprint 1803.05503 preprint an error estimates is derived that shows how the input reduction influences the overall convergence rate of the algorithm. The theoretical results are supported by numerical experiments, including an eddy current simulation of an induction machine.

New paper on Waveform Relaxation for Multiscale Problems

jcp Our paper on Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems (Innocent Niyonzima, Christophe Geuzaine, Sebastian Schöps) has been accepted by JCP:
This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton–Raphson scheme. The resolution of many mesoscale problems per Gauss point allows to compute the homogenized constitutive law and its derivative by finite differences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauss point. Continue reading →