### A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.

- Publication Date:

- Report Number(s):
- LA-UR-16-23169

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-06NA25396

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 326; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Research Org:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org:
- USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC-21); USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Mathematics; Magnetic Fusion Energy

- OSTI Identifier:
- 1331283

- Alternate Identifier(s):
- OSTI ID: 1359312

```
Chacon, Luis, and Stanier, Adam John.
```*A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model*. United States: N. p.,
Web. doi:10.1016/j.jcp.2016.09.007.

```
Chacon, Luis, & Stanier, Adam John.
```*A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model*. United States. doi:10.1016/j.jcp.2016.09.007.

```
Chacon, Luis, and Stanier, Adam John. 2016.
"A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model". United States.
doi:10.1016/j.jcp.2016.09.007. https://www.osti.gov/servlets/purl/1331283.
```

```
@article{osti_1331283,
```

title = {A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model},

author = {Chacon, Luis and Stanier, Adam John},

abstractNote = {Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.},

doi = {10.1016/j.jcp.2016.09.007},

journal = {Journal of Computational Physics},

number = C,

volume = 326,

place = {United States},

year = {2016},

month = {12}

}