Unconditionally stable and robust adjacent-cell diffusive preconditioning of weighted-difference particle transport methods is impossible

Journal of Computational Physics

Volumn 182, Issue 1, 2002, Pages 213-233

  Azmy, Y Y ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Diffusive preconditioners; Iterative acceleration; Neutral particle transport; Robustness; Stability; Unconditional

Indexed keywords

ACCELERATION; CYTOLOGY; ITERATIVE METHODS; PARTICLE SEPARATORS;

DIFFUSIVE PRECONDITIONER; ITERATIVE ACCELERATION; NEUTRAL PARTICLE TRANSPORT; NEUTRAL PARTICLES; PARTICLE TRANSPORT; PRECONDITIONERS; ROBUSTNESS; TRANSPORT METHOD; UNCONDITIONAL; UNCONDITIONALLY STABLE;

CELLS;

EID: 0037058052     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7162     Document Type: Article

References (13)

1. W. H. Reed, The effectiveness of acceleration techniques for iterative methods in transport theory, Nucl. Sci. Eng. 45, 245 (197 1).
2. R. E. Alcouffe, Diffusion synthetic acceleration methods for the diamond-differenced discrete ordinates equations, Nucl. Sci. Eng. 64, 344 (1977).
3. E. W. Larsen, Unconditionally stable diffusion synthetic acceleration methods for the slab geometry discrete ordinates equations. Part I: Theory, Nucl. Sci. Eng. 82, 47 (1982).
4. M. L. Adams and E. W. Larsen, Fast iterative methods for discrete-ordinates particle transport calculations, Prog. Nucl. Energy 40, 3 (2002).
5. Y. Y. Azmy, Iterative convergence acceleration of neutral particle transport methods via adjacent-cell preconditioners, J. Comput. Phys. 152, 359 (1999).
6. Y. Y. Azmy, Adjacent-cell preconditioners for accelerating multidimensional neutron transport methods, in Proceedings, Conference on Advances and Applications in Radiation Protection and Shielding, N. Falmouth, MA, April 21-25, 1996 (Am. Nucl. Soc., La Grange Park, IL, 1996), Vol. 1, p. 390.
7. Y. Y. Azmy, Acceleration of multidimensional discrete ordinates methods via adjacent-cell preconditioners, Nucl. Sci. Eng. 136, 202 (2000).
8. Y. Y. Azmy, Analysis and performance of adjacent-cell preconditioners for accelerating multidimensional transport calculations, in Proceedings, OECD/NEA Meeting on 3D Deterministic Radiation Transport Computer Programs, Features, Applications, and Perspectives, Paris, France, December 2-3, 1996 (Organization for Economic Cooperation and Development, Paris, 1997), p. 197.
9. Y. Y. Azmy, The weighted diamond difference form of nodal transport methods, Nucl. Sci. Eng. 98, 29 (1988).
10. Y. Y Azmy, Impossibility of unconditional stability and robustness of diffusive acceleration schemes, in Proceedings, 1998 ANS Topical Meeting on Radiation Protection and Shielding, Nashville, TN, April 19-23, 1998 (Am. Nucl. Soc., La Grange Park, IL, 1998), Vol. 1, p. 480.
11. n methods, in Proceedings, 1999 ANS Topical Meeting on Mathematics and Computation, Madrid, Spain, September 27-30, 1999 (Senda Editorial, Madrid, 1999), Vol. 1, p. 55.
12. T. A. Wareing, New diffusion-synthetic acceleration methods for the SN equations with corner balance differencing, in Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing in Nuclear Applications, Karlsruhe, Germany, April 19-23, 1993 (Kernforschungszentrum, Karlsruhe, Germany, 1993), Vol. 2, p. 500.
13. n equations with linear-bilinear nodal differencing, Nucl. Sci. Eng. 118,