Comparison of non-linear solvers for the solution of radiation transport equations

Electronic Transactions on Numerical Analysis

Volumn 15, Issue , 2003, Pages 78-93

  Stals, Linda ^a,b  

^a Old Dominion University   (United States)

^b NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

FAS; Multigrid; Newton Method; Radiation Transport

Indexed keywords

EID: 2942597843     PISSN: 10689613     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (21)

1. A. BRANDT, Multi-level adaptive solutions to boundary-value problems. Math Comput., 31(138):333-390, April 1977.
2. W. L. BRIGGS, V. E. HENSON, AND S. F. MCCORMICK, A Multigrid Tutorial. SIAM, 2000.
3. P N. BROWN, B. CHANG, F. GRAZIANI AND C. S. WOODWARD, Implicit solution of large-scale radiationmaterial energy transfer problems, Technical Report UCRL-JC-132831, Lawrence Livermore National Laboratory, Jan. 1999. To appear in Proceedings of the Fourth IMACS International Symposium on Iterative Methods in Scientific Computations.
4. P N. BROWN AND C. S. WOODWARD, Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer, Technical Report UCRL-JC-139087, Lawrence Livermore National Laboratory, May. 2000. To appear in SIAM J. Sci. Comput.
5. D. A. KNOLL, W. J. RIDER AND G. L. OLSON, An efficient nonlinear solution method for non-equilibrium radiation diffusion, Technical Report LA- UR-98-2154, Los Alamos National Laboratory, 1998. Submitted to J. Quant. Spec. and Rad. Trans.
6. M. KŘÍŽEK AND L. LIU, Finite element approximation of a nonlinear heat conduction problem in anisotropic media, Technical Report 4/1997, Laboratory of Scientific Computing, University of Jyväskylä, Finland, 1997.
7. D. J. MAVRIPLIS,Multigrid approaches to non-linear diffusion problems on unstructured meshes, Technical Report ICASE Report No. 2001-3, (NASA/CR-2001-210660), February 12, 2001, 16 pages. Submitted to the Journal of Numerical Linear Algebra with Applications.
8. S. F. MCCORMICK, Multigrid Methods. SIAM Frontiers In Applied Mathematics, 1987.
9. W. F. MITCHELL, Unified Multilevel Adaptive Finite Element Methods For Elliptic Problems. PhD thesis, Department Of Computer Science, University Of Illinois at Urbana-Champaign, Urbana, IL, 1988. Technical Report UIUCDCS-R-88-1436.
10. W. F. MITCHELL, A comparison of adaptive refinement techniques for elliptic problems. ACM Trans. Math. Software, 15(4):326-347, December 1989.
11. W. F. MITCHELL, Optimal multilevel iterative methods for adaptive grids. SIAM J. Sci. Stat. Comput, 13(1):146-167, January 1992.
12. V. A. MOUSSEAU, D. A. KNOLL AND W. J. RIDER, Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion. Journal of Computational Physics, 160:743-765, 2000.
13. J .M. ORTEGA AND W .C. RHEINBOLDT, Iterative solution of nonlinear equations in several variables, Academic Press, New York and London, 1970.
14. G. C. POMRANING, The equations of radiation hydrodynamics, Pergamon, New York, 1973.
15. U. RÜDE, Mathematical and computational techniques for multilevel adaptive methods, SIAM, Philadelphia, 1993.
16. W. J. RIDER, D. A. KNOLL AND G. L. OLSON, A multigrid Newton- Krylov method for multimaterial equilibrium radiation diffusion, Technical Report LA-UR-98-2153, Los Alamos National Laboratory, 1998, 34 pages.
17. L. STALS, Adaptive multigrid in parallel, in Proceedings of Seventh SIAM Conference on Parallel Processing for Scientific Computing, D. Bailey, P. Bjørstad, J. Gilbert, M. Mascagni, R. Schreiber, H. Simon, V. Torczon and L.Watson, eds, SIAM, Philadelphia, 1995, pp. 367-372.
18. L. STALS, Parallel multigrid on unstructured grids using adaptive finite element methods, PhD thesis, Department of Mathematics, Australian National University, Canberra, Australia, 1995.
19. L. STALS, Implementation of multigrid on parallel machines using adaptive finite element methods, in Proceedings of 9th International Conference on Domain Decomposition, P. Bjørstad, M. Espedal and D. Keyes, eds, 1998, pp. 488-496.
20. L. STALS, A flexible data structure for the adaptive refinement of unstructured grids in parallel, , in The Proceedings of The 14th Kiel GAMM Seminar on Concepts of Numerical Software, January, 1997. To appear.
21. J. C. A. VILLEGAS, Anisotropic Adaptive Refinement Algorithms for Finite Element Methods. PhD thesis, Graduate School of Arts and Science, Department of Mathematics, New York University, September 2000.