Author:

Keywords:

time-parallel time-integration, parareal, convergence analysis, shooting, multigrid, deferred correction, partial-differential equations, initial-value problems, multigrid method, boundary-value, algorithms, discretization, pdes, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, BOUNDARY-VALUE, ALGORITHMS, DISCRETIZATION, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0802 Computation Theory and Mathematics, Numerical & Computational Mathematics, 4901 Applied mathematics, 4903 Numerical and computational mathematics

Abstract:

The parareal algorithm is a method to solve time-dependent problems parallel in time: it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time. In this paper the relation of the parareal algorithm to space-time multigrid and multiple shooting methods is first briefly discussed. The focus of the paper is on new convergence results that show superlinear convergence of the algorithm when used on bounded time intervals, and linear convergence for unbounded intervals.