skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT)

Abstract

We solve the linear advection equation, $$\mathcal{u_{t} - au_{x} = f}$$ on the domain [0, 1.0] × [0, $$\mathcal{t_{f}}$$], with zero Dirichlet conditions in space. The initial condition in time is a sine-hump over the first half of the spatial domain. Solving even this simple problem scalably with a parallel-in-time method has so far proven elusive. We will focus on the multigrid reduction in time method (MGRIT), which is equivalent to the earlier parareal method, in a two-grid setting with F-relaxation.

Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1438750
Report Number(s):
LLNL-TR-750825
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Schroder, J. B. On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT). United States: N. p., 2018. Web. doi:10.2172/1438750.
Schroder, J. B. On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT). United States. doi:10.2172/1438750.
Schroder, J. B. Wed . "On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT)". United States. doi:10.2172/1438750. https://www.osti.gov/servlets/purl/1438750.
@article{osti_1438750,
title = {On the Use of Artificial Dissipation for Hyperbolic Problems and Multigrid Reduction in Time (MGRIT)},
author = {Schroder, J. B.},
abstractNote = {We solve the linear advection equation, $\mathcal{u_{t} - au_{x} = f}$ on the domain [0, 1.0] × [0, $\mathcal{t_{f}}$], with zero Dirichlet conditions in space. The initial condition in time is a sine-hump over the first half of the spatial domain. Solving even this simple problem scalably with a parallel-in-time method has so far proven elusive. We will focus on the multigrid reduction in time method (MGRIT), which is equivalent to the earlier parareal method, in a two-grid setting with F-relaxation.},
doi = {10.2172/1438750},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2018},
month = {5}
}

Technical Report:

Save / Share: