Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

doi:10.1016/j.jcp.2010.04.024

Title: Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

Journal Article · Wed Sep 01 00:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.04.024· OSTI ID:1213043

Adams, Mark F. ^[1]; Samtaney, Ravi ^[2]; Brandt, Achi ^[3]

Columbia Univ., New York, NY (United States). Dept. of Applied Physics and Applied Mathematics
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Weizmann Inst. of Science, Rehovot (Israel). Dept. of Computer Science and Applied Mathematics

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.

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Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Columbia Univ., New York, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FC02-06ER54863

OSTI ID:: 1213043

Journal Information:: Journal of Computational Physics, Vol. 229, Issue 18; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 14 works

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References (18)

A high accuracy defect-correction multigrid method for the steady incompressible Navier-Stokes equations Altas, Irfan; Burrage, Kevin Journal of Computational Physics, Vol. 114, Issue 2 https://doi.org/10.1006/jcph.1994.1162	journal	October 1994
Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge Birn, J.; Drake, J. F.; Shay, M. A. Journal of Geophysical Research: Space Physics, Vol. 106, Issue A3 https://doi.org/10.1029/1999JA900449	journal	March 2001
Multi-level adaptive solutions to boundary-value problems Brandt, Achi Mathematics of Computation, Vol. 31, Issue 138 https://doi.org/10.1090/S0025-5718-1977-0431719-X	journal	May 1977
Multilevel Adaptive Computations in Fluid Dynamics Brandt, Achi AIAA Journal, Vol. 18, Issue 10 https://doi.org/10.2514/3.50867	journal	October 1980
An optimal, parallel, fully implicit Newton–Krylov solver for three-dimensional viscoresistive magnetohydrodynamics Chacón, L. Physics of Plasmas, Vol. 15, Issue 5 https://doi.org/10.1063/1.2838244	journal	May 2008
Second-order formulation of a multigrid method for steady Euler equations through defect-correction Dick, Erik Journal of Computational and Applied Mathematics, Vol. 35, Issue 1-3 https://doi.org/10.1016/0377-0427(91)90204-W	journal	June 1991
Multi-staging of Jacobi relaxation to improved smoothing properties of multigrid methods for steady Euler equations Dick, Erick; Riemslagh, Kris Journal of Computational and Applied Mathematics, Vol. 50, Issue 1-3 https://doi.org/10.1016/0377-0427(94)90304-2	journal	May 1994
Schwarz Analysis of Iterative Substructuring Algorithms for Elliptic Problems in Three Dimensions Dryja, Maksymilian; Smith, Barry F.; Widlund, Olof B. SIAM Journal on Numerical Analysis, Vol. 31, Issue 6 https://doi.org/10.1137/0731086	journal	December 1994
An algebraic multilevel parallelizable preconditioner for large-scale CFD problems Dutto, Laura C.; Habashi, Wagdi G.; Fortin, Michel Computer Methods in Applied Mechanics and Engineering, Vol. 149, Issue 1-4 https://doi.org/10.1016/S0045-7825(97)00049-2	journal	October 1997
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states Ferraro, N. M.; Jardin, S. C. Journal of Computational Physics, Vol. 228, Issue 20 https://doi.org/10.1016/j.jcp.2009.07.015	journal	November 2009
The SEL macroscopic modeling code Glasser, A. H.; Tang, X. Z. Computer Physics Communications, Vol. 164, Issue 1-3 https://doi.org/10.1016/j.cpc.2004.06.034	journal	December 2004
Multigrid solution of the Euler equations using implicit schemes Jameson, A.; Yoon, S. 23rd Aerospace Sciences Meeting https://doi.org/10.2514/6.1985-293	conference	August 1985
Textbook-efficiency multigrid solver for three-dimensional unsteady compressible Navier–Stokes equations Liao, Wei; Diskin, Boris; Peng, Yan Journal of Computational Physics, Vol. 227, Issue 15 https://doi.org/10.1016/j.jcp.2008.03.026	journal	July 2008
Operator-Based Preconditioning of Stiff Hyperbolic Systems Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S. SIAM Journal on Scientific Computing, Vol. 32, Issue 1 https://doi.org/10.1137/080713331	journal	January 2010
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S. Journal of Computational Physics, Vol. 219, Issue 1 https://doi.org/10.1016/j.jcp.2006.03.022	journal	November 2006
An adaptive mesh semi-implicit conservative unsplit method for resistive MHD Samtaney, R.; Colella, P.; Ligocki, T. J. Journal of Physics: Conference Series, Vol. 16 https://doi.org/10.1088/1742-6596/16/1/005	journal	January 2005
Nonlinear magnetohydrodynamics simulation using high-order finite elements Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A. Journal of Computational Physics, Vol. 195, Issue 1 https://doi.org/10.1016/j.jcp.2003.10.004	journal	March 2004
MHD simulations with resistive wall and magnetic separatrix Strauss, H. R.; Pletzer, A.; Park, W. Computer Physics Communications, Vol. 164, Issue 1-3 https://doi.org/10.1016/j.cpc.2004.06.007	journal	December 2004

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