# 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:

- 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}

}

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