Monolithic Multigrid Methods for Magnetohydrodynamics
Abstract
The magnetohydrodynamics equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting system of equations is generally difficult to solve due to the coupling between variables and the heterogeneous coefficients induced by the linearization process. In this paper, we investigate multigrid preconditioners for this system based on specialized relaxation schemes that properly address the system structure and coupling. Here, three extensions of Vanka relaxation are proposed and applied to problems with up to 170 million degrees of freedom and fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to 20,000 for time-dependent problems.
- Authors:
-
[1];
[4];
[5];
- Tufts Univ., Medford, MA (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Univ. of Oxford (United Kingdom)
- Univ. of Newfoundland (Canada)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1841848
- Report Number(s):
- LLNL-JRNL-811901
Journal ID: ISSN 1064-8275; 1018684
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- SIAM Journal on Scientific Computing
- Additional Journal Information:
- Journal Volume: 43; Journal Issue: 5; Journal ID: ISSN 1064-8275
- Publisher:
- Society for Industrial and Applied Mathematics (SIAM)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; magnetohydrodynamics; monolithic multigrid; Vanka relaxation
Citation Formats
Adler, James H., Benson, Thomas R., Cyr, Eric C., Farrell, Patrick E., MacLachlan, Scott P., and Tuminaro, Ray S. Monolithic Multigrid Methods for Magnetohydrodynamics. United States: N. p., 2021.
Web. doi:10.1137/20m1348364.
Adler, James H., Benson, Thomas R., Cyr, Eric C., Farrell, Patrick E., MacLachlan, Scott P., & Tuminaro, Ray S. Monolithic Multigrid Methods for Magnetohydrodynamics. United States. https://doi.org/10.1137/20m1348364
Adler, James H., Benson, Thomas R., Cyr, Eric C., Farrell, Patrick E., MacLachlan, Scott P., and Tuminaro, Ray S. Tue .
"Monolithic Multigrid Methods for Magnetohydrodynamics". United States. https://doi.org/10.1137/20m1348364. https://www.osti.gov/servlets/purl/1841848.
@article{osti_1841848,
title = {Monolithic Multigrid Methods for Magnetohydrodynamics},
author = {Adler, James H. and Benson, Thomas R. and Cyr, Eric C. and Farrell, Patrick E. and MacLachlan, Scott P. and Tuminaro, Ray S.},
abstractNote = {The magnetohydrodynamics equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting system of equations is generally difficult to solve due to the coupling between variables and the heterogeneous coefficients induced by the linearization process. In this paper, we investigate multigrid preconditioners for this system based on specialized relaxation schemes that properly address the system structure and coupling. Here, three extensions of Vanka relaxation are proposed and applied to problems with up to 170 million degrees of freedom and fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to 20,000 for time-dependent problems.},
doi = {10.1137/20m1348364},
journal = {SIAM Journal on Scientific Computing},
number = 5,
volume = 43,
place = {United States},
year = {Tue Feb 16 00:00:00 EST 2021},
month = {Tue Feb 16 00:00:00 EST 2021}
}
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