Parareal in time approximation of the Korteveg‐deVries‐Burgers' equations
Sidi MahmoudKaber, Yvon Maday · PAMM · 2007
Abstract The parareal in time algorithm is a predictor corrector method that allows to get parallelisation through the time. It consists in segmenting the interval of time integration into slabs, then propose iteratively seed values at the left hand side of each of the slabs. The derivation of the seed values is done sequentially and involves propagator that should mimic the equation to be solved but should be very cheap and parallel accurate propagations of each seed value over each slab. Various approaches have been proposed to get the coarse propagator, in this paper, we use the averaging approach developed by Barenblatt and Chorin for the Korteveg‐deVries‐Burgers' equations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)