The Parareal Algorithm

  • Staff G
  • 17

    Readers

    Mendeley users who have this article in their library.
  • N/A

    Citations

    Citations of this article.

Abstract

A short introduction to the parareal algorithm is made on basis of [17]. Then, for the autonomous differential equation, a theorem for the stability property of the algorithm is derived. The theorem states that G∆T must be strong A-stable with limz→−∞ |R(z)| ≤ 1 , in order for the algorithm to 2 be stable for all n, k. Several test problems involving periodic solutions, semidiscretized parabolic PDE’s, stiffness and nonlinearity are calculated using different implicit Runge-Kutta schemes with different order and stabiliy properties. Using the theta-method, the property limz→−∞ |R(z)| ≤ 1 2 is tested, and the results verifies the theorem. Instabilities in the two different heat-equation test problems are predicted using the theorem. Different formulations of the system, for which the coarse propagator G∆T operates, are tested. Substantial differences is found, and explenations are discussed.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

There are no full text links

Authors

  • Gunnar a Staff

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free