Implicit solvers for large-scale nonlinear problems

Journal of Physics: Conference Series

Volumn 46, Issue 1, 2006, Pages 433-442

  Keyes, David E ^a   Reynolds, Daniel R ^b   Woodward, Carol S ^c  

^a Department of Earth and Environmental Sciences   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749072669     PISSN: 17426588     EISSN: 17426596     Source Type: Conference Proceeding    
DOI: 10.1088/1742-6596/46/1/060     Document Type: Conference Paper

References (26)

1. HYPRE (High Performance Preconditioners). http://www.llnl.gov/casc/linear_solvers
2. PETSC (Portable, Extensible Toolkit for Scientific Computation). http://www-unix.mcs.anl.gov/petsc
3. SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic Solvers). http://www.llnl.gov/casc/sundials
4. SuperLU. http://www.nersc.gov/xiaoye/SuperLU
5. Trilinos. http://software.sandia.gov/trilinos
6. Birn J and et al 2001 Geospace Environmental Modeling (GEM) magnetic reconnection challenge J. Geophys. Res. 106 3715-3719
7. Biskamp D 2000 Magnetic reconnection in plasmas Cambridge monographs on plasma physics third edition
8. Brown P N 1987 A local convergence theory for combined inexact-Newton/finite-difference projection methods SIAM J. Numer. Anal. 24 407-434
9. Brown P N and Y Saad 1990 Hybrid Krylov methods for nonlinear systems of equations SIAM J. Sci. Statist. Comput. 11 450-481
10. Brown P N, H F Walker, R Wasyk and C S Woodward 2006 On using approximate finite-differences in matrix-free Newton-Krylov methods. Submitted. LLNL Technical Report UCRL-JRNL-219284
11. Dembo R S, S C Eisenstat and T Steihaug 1982 Inexact Newton methods SIAM J. Numer. Anal. 19 400-408
12. Dennis J E and R B Schnabel 1996 Numerical Methods for Unconstrained Optimization and Nonlinear Equations (SIAM, Philadelphia, PA)
13. Eisenstat S C and H F Walker 1996 Choosing the forcing terms in an inexact Newton method SIAM J. Sci. Comp. 17 (1) 16-32
14. Freund R W, G H Golub and N M Nachtigal 1992 Iterative solution of linear systems Acta Numerica In A Iserles (Cambridge Univ. Press, New York) p 57-100
15. Gropp W D, D E Keyes, L C McInnes and M D Tidriri 2000 Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD Int. J. High Performance Computing Appl. 14 102-136
16. Hindmarsh A C, P N Brown, K E Grant, S L Lee, R Serban, D E Shumaker and C S Woodward 2005 SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers ACM Trans. Math. Softw. 31 (3) 363-396
17. Hindmarsh A C and R Serban 2004 User documentation for CVODE v. 2.2.1. Technical Report UCRL-SM-208108, LLNL
18. Kelley C T 2003 Solving Nonlinear Equations with Newton's Method, volume 1 of Fundamentals of Algorithms (SIAM, Philadelphia, PA)
19. Knoll D A and D E Keyes 2004 Jacobian-free Newton-Krylov methods: a survey of approaches and applications J. Comp. Phys. 193 357-397
20. Miller C T, G A Williams, C T Kelley and M D Tocci 1998 Robust solution of Richards' equation for nonuniform porous media Water Resour. Res. 34 2599-2610
21. Reynolds D R, R Samtaney and C S Woodward 2006 A fully implicit numerical method for single-fluid resistive magnetohydrodynamics J. Comp. Phys. in press
22. Richtmyer R D and K W Morton 1957 Difference Methods for Initial-value Problems (Wiley Interscience, New York)
23. Saad Y and M H Schultz 1986 GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 7 (3) 856-869
24. van der Vorst H A 1992 Bi-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 13 (2) 631-644
25. Venkatakrishnan V 1995 Convergence to steady state solutions of the Euler equations on unstructured grids with limiters J. Comp. Phys. 118 120-130
26. Weiser M, A Schiela and P Deuflhard 2005 Asymptotic mesh independence of Newton's method revisited SIAM J. Numer. Anal. 42 1830-1845