A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation
Schmitt, AS; Schreiber, M; Peixoto, PSP; et al.Schäfer, MS
Date: 6 June 2018
Journal
Computing and Visualization in Science
Publisher
Springer Verlag
Publisher DOI
Abstract
This work focuses on the Parareal parallelin-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: ...
This work focuses on the Parareal parallelin-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 semiLagrangian
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.
Computer Science
Faculty of Environment, Science and Economy
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