A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation

  • A. Schmitt
  • M. Schreiber
  • P. Peixoto
  • M. Schäfer
Special Issue Parallel-in-Time Methods


This work focuses on the Parareal parallel-in-time method and its application to the viscous Burgers equation. A crucial component of Parareal is the coarse time stepping scheme, which strongly impacts the convergence of the parallel-in-time method. Three choices of coarse time stepping schemes are investigated in this work: explicit Runge–Kutta, implicit–explicit Runge–Kutta, and implicit Runge–Kutta with semi-Lagrangian advection. Manufactured solutions are used to conduct studies, which provide insight into the viability of each considered time stepping method for the coarse time step of Parareal. One of our main findings is the advantageous convergence behavior of the semi-Lagrangian scheme for advective flows.


Parareal Burgers’ equation Semi-Lagrangian Runge–Kutta Parallel-in-time 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Numerical Methods in Mechanical Engineering and Graduate School of Computational EngineeringTU DarmstadtDarmstadtGermany
  2. 2.University of ExeterExeterUK
  3. 3.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil

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