Operator-based preconditioning of stiff hyperbolic systems

SIAM Journal on Scientific Computing

Volumn 32, Issue 1, 2010, Pages 150-170

  Reynolds, Daniel R ^a   Samtaney, Ravi ^b   Woodward, Carol S ^c  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

^b PRINCETON PLASMA PHYSICS LABORATORY   (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Hyperbolic systems; Implicit methods; Preconditioning

Indexed keywords

GAS DYNAMICS; MAGNETOHYDRODYNAMICS;

ENTIRE SYSTEM; FAST TRANSIENTS; HYPERBOLIC SYSTEM; IMPLICIT METHODS; NUMERICAL RESULTS; PRECONDITIONING; PRECONDITIONING METHOD; REGULAR GRIDS; SPLITTINGS; TRANSIENT WAVES;

STIFFNESS;

EID: 77249097844     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/080713331     Document Type: Conference Paper

References (40)

1. P. ARBENZ AND W. GANDER, A Survey of Direct Parallel Algorithms for Banded Linear Systems, Technical report 221, ETH Zurich, Zurich, Switzerland, 1994.
2. D. S. BALSARA AND D. S. SPICER, A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamics simulations, J. Comput. Phys., 149 (1999), pp. 270-292.
3. M. BERGER AND P. COLELLA, Local adaptive mesh refinement for shock hydrodynamics,J. Comput. Phys., 82 (1989), pp. 64-84.
4. M. BERGER AND J. OLIGER, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), pp. 484-512.
5. H. BIJL, Iterative Methods for Unsteady Flow Computations Using Implicit Runge-Kutta Integration Schemes, AIAA Paper 2006-689, 2006.
6. L. CHACÓN, D. KNOLL, AND J. FINN, An implicit, nonlinear reduced resistive MHD solver,J. Comput. Phys., 178 (2002), pp. 15-36.
7. L. CHACÓN AND D. KNOLL, A fully implicit 3D extended MHD algorithm, Proceedings of the 33rd EPS Conference on Plasma Physics, Rome, Italy, 2006.
8. L. CHACÓN, A non-staggered, conservative, ∇ B = 0, finite-volume scheme for 3Dimplicit extended magnetohydrodynamics in curvilinear geometries, Comput. Phys. Comm., 163 (2004), pp. 143-171.
9. L. CHACÓN, An optimal, parallel, fully implicit Newton-Krylov solver for three-dimensional visco-resistive magnetohydrodynamics, Phys. Plasmas, 15 (2008), 056103.
10. S. CHANDRASEKHAR, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, UK, 1961.
11. B. L. CREURER AND S. GAUTHIER, A return toward equilibrium in a 2D Rayleigh-Taylor instability for compressible fluid with a multidomain adaptive Chebyshev method,Theor. Comput. Fluid Dyn., 22 (2008), pp. 125-144.
12. S. A. E. G. FALLE, S. S. KOMISSAROV, AND P. JOARDER, A multidimensional upwind scheme for magnetohydrodynamics, Month. Notices R. Astron. Soc., 297 (1998), pp. 265-277.
13. T. GARDINER AND J. STONE, An unsplit Godunov method for ideal MHD via constrained transport, J. Comput. Phys., 205 (2005), pp. 509-539.
14. S. K. GODUNOV, The symmetric form of magnetohydrodynamics equation., Numer. Meth. Mech. Contin. Media, 1 (1972), pp. 26-34.
15. G. GOLUB AND C. V. LOAN, Matrix Computations, Johns Hopkins University Press, Baltimore, 1996.
16. T. GOMBOSI, D. D. ZEEUW, K. POWELL, A. RIDLEY, I. SOKOLOV, Q. STOUT, AND G. TOTH, Adaptive mesh refinement for global MHD space weather simulations, in Space Plasma Simulation, Lecture Notes in Phys. 615, Springer-Verlag, Berlin, Heidelberg, New York, 2003, pp. 247-274.
17. A. GREENBAUM, V. PTÁK, AND Z. STRAKOŠ, Any nonincreasing convergence curve is possible for GMRES, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 465-469.
18. A. GREENBAUM, Iterative Methods for Solving Linear Systems, Frontiers Appl. Math. 17, SIAM, Philadelphia, 1997.
19. W. GROPP, D. KEYES, L. MclNNES, AND M. TIDRIRI, Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD, Internat. J. High Perf. Comput. Appl., 14 (2000), pp. 102-136.
20. D. HARNED AND W. KERNER, Semi-implicit method for three-dimensional compressible mag- netohydrodynamic simulation, J. Comput. Phys., 60 (1985), pp. 62-75.
21. D. HARNED AND W. KERNER, Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions, J. Comput. Phys., 65 (1986), pp. 57-70.
22. A. Hindmarsh, P. Brown, K. Grant, S. Lee, R. Serban, D. Shumaker, and C. Woodward, SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers,ACM Trans. Math. Software, 31 (2005), pp. 363-396.
23. T. JONES, J. GAALAAS, D. Ryu, AND A. FRANK, The MHD Kelvin Helmholtz instability II. The roles of weak and oblique fields in planar flows, Ap. J., 482 (1997), pp. 230-244.
24. C. KELLEY, Iterative Methods for Linear and Nonlinear Equations, Frontiers Appl. Math. 16, SIAM, Philadelphia, 1995.
25. D. KEYES, D. R. REYNOLDS, AND C. S. WOODWARD, Implicit solvers for large-scale nonlinear problems, J. Phys.: Conf. Ser., 46 (2006), pp. 433-442.
26. D. A. KNOLL AND J. U. BRACKBILL, The Kelvin-Helmholtz instability, differential rotation, and three-dimensional, localized, magnetic reconnection, Phys. Plasmas, 9 (2002), pp. 3775-3782.
27. D. A. KNOLL AND D. E. KEYES, Jacobian-free Newton-Krylov methods: A survey of approaches and applications, J. Comput. Phys., 193 (2004), pp. 357-397.
28. C. B. LANEY, Computational Gasdynamics, Cambridge University Press, Cambridge, UK, 1998.
29. D. MAVRIPLIS, Three-dimensional unstructured multigrid for the Euler equations, AIAA J., 30 (1992), pp. 1753-1761.
30. S. McCormick, Multilevel Adaptive Methods for Partial Differential Equations, Frontiers Appl. Math. 6, SIAM, Philadelphia, 1989.
31. W. Park, E. Belova, G. Fu, and X. Tang, Plasma simulation studies using multilevel physics models, Phys. Plasmas, 6 (1999), pp. 1796-1803.
32. M. PERNICE AND R. HORNUNG, Newton-Krylov-FAC methods for problems discretized on locally refined grids, Comput. Vis. Sci., 8 (2005), pp. 107-118.
33. B. PHILIP, L. CHACÓN, AND M. PERNICE, Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics, J. Comput. Phys., 227 (2008), pp. 8855-8874.
34. K. G. POWELL, P. L. ROE, T. J. LINDE, T. I. GOMBOSI, AND D. L. DEZEEUW, Asolution-adaptive upwind scheme for ideal magnetohydrodynamics, J. Comput. Phys., 154 (1999), pp. 284-309.
35. J. RAEDER, Global geospace modeling: Tutorial and review, in Space Plasma Simulation, Lecture Notes in Phys. 615, Springer-Verlag, Berlin, 2003, pp. 212-246.
36. D. R. REYNOLDS, R. SAMTANEY, AND C. S. WOODWARD, A fully implicit numerical method for single-fluid resistive magnetohydrodynamics, J. Comput. Phys., 219 (2006), pp. 144-162.
37. D. R. REYNOLDS, F. D. SWESTY, AND C. S. WOODWARD, A Newton-Krylov solver for implicit solution of hydrodynamics in core collapse supernovae, J. Phys.: Conf. Ser., 125 (2008), 012085.
38. R. SAMTANEY, P. COLELLA, T. LIGOCKI, D. MARTIN, AND S. JARDIN, An adaptive mesh semi- implicit conservative unsplit method for resistive MHD, J. Phys.: Conf. Ser., 16 (2005), pp. 40-48.
39. L. TREFETHEN AND D. B. III, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
40. L. WANG AND D. J. MAVRIPLIS, Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations, J. Comput. Phys., 225 (2007), pp. 1994-2015.