# Multi-Level iterative methods in computational plasma physics

## Abstract

Plasma physics phenomena occur on a wide range of spatial scales and on a wide range of time scales. When attempting to model plasma physics problems numerically the authors are inevitably faced with the need for both fine spatial resolution (fine grids) and implicit time integration methods. Fine grids can tax the efficiency of iterative methods and large time steps can challenge the robustness of iterative methods. To meet these challenges they are developing a hybrid approach where multigrid methods are used as preconditioners to Krylov subspace based iterative methods such as conjugate gradients or GMRES. For nonlinear problems they apply multigrid preconditioning to a matrix-few Newton-GMRES method. Results are presented for application of these multilevel iterative methods to the field solves in implicit moment method PIC, multidimensional nonlinear Fokker-Planck problems, and their initial efforts in particle MHD.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 757012

- Report Number(s):
- LA-UR-99-1128

TRN: US0003755

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: APS, Atlanta, GA (US), No date supplied; Other Information: Conference held during 03/1999; PBD: 1 Mar 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PLASMA SIMULATION; ITERATIVE METHODS; MESH GENERATION; NONLINEAR PROBLEMS

### Citation Formats

```
Knoll, D A, Barnes, D C, Brackbill, J U, Chacon, L, and Lapenta, G.
```*Multi-Level iterative methods in computational plasma physics*. United States: N. p., 1999.
Web.

```
Knoll, D A, Barnes, D C, Brackbill, J U, Chacon, L, & Lapenta, G.
```*Multi-Level iterative methods in computational plasma physics*. United States.

```
Knoll, D A, Barnes, D C, Brackbill, J U, Chacon, L, and Lapenta, G. Mon .
"Multi-Level iterative methods in computational plasma physics". United States. https://www.osti.gov/servlets/purl/757012.
```

```
@article{osti_757012,
```

title = {Multi-Level iterative methods in computational plasma physics},

author = {Knoll, D A and Barnes, D C and Brackbill, J U and Chacon, L and Lapenta, G},

abstractNote = {Plasma physics phenomena occur on a wide range of spatial scales and on a wide range of time scales. When attempting to model plasma physics problems numerically the authors are inevitably faced with the need for both fine spatial resolution (fine grids) and implicit time integration methods. Fine grids can tax the efficiency of iterative methods and large time steps can challenge the robustness of iterative methods. To meet these challenges they are developing a hybrid approach where multigrid methods are used as preconditioners to Krylov subspace based iterative methods such as conjugate gradients or GMRES. For nonlinear problems they apply multigrid preconditioning to a matrix-few Newton-GMRES method. Results are presented for application of these multilevel iterative methods to the field solves in implicit moment method PIC, multidimensional nonlinear Fokker-Planck problems, and their initial efforts in particle MHD.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {3}

}