Coupling the Parareal Algorithm with the Waveform Relaxation Method for the Solution of Differential Algebraic Equations

In this paper, a coupling strategy of the Parareal algorithm with the Waveform Relaxation method is presented for the parallel solution of differential algebraic equations. The classical Waveform Relaxation (in space) method and the Para real (in time) method are first recalled, followed by the introduction of a coupled Para real-Waveform Relaxation method recently introduced for the solution of partial differential equations. Here, this coupled method is extended to the solution of differential algebraic equations. Numerical experiments, performed on parallel multicores architectures, illustrate the impressive performances of this new method.