Analysis of a Krylov subspace enhanced parareal algorithm for linear problems 25

Abstract. The parareal algorithm is a numerical method to integrate evolution prob-lems on parallel computers. The performance of the algorithm is well understood for diusive problems, and it can have spectacular performance when applied to certain non-linear problems. Its convergence properties are however less favorable for hyperbolic problems. We present and analyze in this paper a variant of the parareal algorithm, re-cently proposed in the PITA framework for systems of second order ordinary dierential equations. 1