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Title: Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

Abstract

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called ‘‘textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss–Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.

Authors:
 [1];  [2];  [3]
  1. Columbia Univ., New York, NY (United States). Dept. of Applied Physics and Applied Mathematics
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  3. Weizmann Inst. of Science, Rehovot (Israel). Dept. of Computer Science and Applied Mathematics
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Columbia Univ., New York, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1213043
Grant/Contract Number:  
FC02-06ER54863
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 229; Journal Issue: 18; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Adams, Mark F., Samtaney, Ravi, and Brandt, Achi. Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics. United States: N. p., 2010. Web. doi:10.1016/j.jcp.2010.04.024.
Adams, Mark F., Samtaney, Ravi, & Brandt, Achi. Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics. United States. https://doi.org/10.1016/j.jcp.2010.04.024
Adams, Mark F., Samtaney, Ravi, and Brandt, Achi. Wed . "Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics". United States. https://doi.org/10.1016/j.jcp.2010.04.024. https://www.osti.gov/servlets/purl/1213043.
@article{osti_1213043,
title = {Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics},
author = {Adams, Mark F. and Samtaney, Ravi and Brandt, Achi},
abstractNote = {Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called ‘‘textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss–Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.},
doi = {10.1016/j.jcp.2010.04.024},
journal = {Journal of Computational Physics},
number = 18,
volume = 229,
place = {United States},
year = {Wed Sep 01 00:00:00 EDT 2010},
month = {Wed Sep 01 00:00:00 EDT 2010}
}

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Cited by: 14 works
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Works referencing / citing this record:

Multigrid for Matrix-Free High-Order Finite Element Computations on Graphics Processors
journal, May 2019

  • Kronbichler, Martin; Ljungkvist, Karl
  • ACM Transactions on Parallel Computing, Vol. 6, Issue 1
  • DOI: 10.1145/3322813