A New Parareal Algorithm for Problems with Discontinuous Sources

Abstract

The Parareal algorithm allows to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal algorithm for ordinary differential equations which involve discontinuous right-hand sides. Such situations occur in various applications, e.g., when an electric device is supplied with a pulse-width-modulated signal. Our new Parareal algorithm uses a smooth input for the coarse problem with reduced dynamics. We derive error estimates that show how the input reduction influences the overall convergence rate of the algorithm. We support our theoretical results by numerical experiments, and also test our new Parareal algorithm in an eddy current simulation of an induction machine.

References in corpus (2)

• Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics
• Parallel-In-Time Simulation of Eddy Current Problems Using Parareal

Cited by in corpus (7)

• Accelerated Steady-State Torque Computation for Induction Machines using Parallel-In-Time Algorithms
• Multigrid-reduction-in-time for Eddy Current problems
• A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs
• A space-time finite element method for the eddy current approximation of rotating electric machines
• Wavelet-based Edge Multiscale Parareal Algorithm for Parabolic Equations with Heterogeneous Coefficients
• An efficient steady-state analysis of the eddy current problem using a parallel-in-time algorithm
• Weighted Relaxation for Multigrid Reduction in Time