Multigrid methods for S/sub N/ problems

Conference · Thu Jan 01 04:00:00 EST 1987 · Trans. Am. Nucl. Soc.; (United States)

OSTI ID:6996056

Nowak, P F; Larsen, E W; Martin, W R

It has long been known that the standard source iteration (SI) method for obtaining iterative solutions of S/sub N/ problems is very slowly converging in optically thick regions with low absorption. The rebalance and diffusion synthetic acceleration (DSA) methods are generalizations of SI that have been developed to accelerate convergence, but neither of these methods has been completely successful. In particular, the rebalance method tends to become unstable in problems where it is needed most (problems with high scattering ratios c = 1), while the DSA method, to be implemented in a stable fashion, requires the solution of a particular system of acceleration equations, and this has been done efficiently in two-dimensional geometries only for the diamond difference S/sub N/ equations. This paper discusses another extension of the SI method, namely, SI combined with the spatial multigrid algorithm (SIMG). This appears to be a viable way to accelerate many S/sub N/ problems in multidimensional geometries, provided the finest mesh consists of cells that are not optically thick.

• Research Organization: Univ. of Michigan, Ann Arbor (USA)
• OSTI ID: 6996056
• Report Number(s): CONF-8711195-
• Conference Information: Journal Name: Trans. Am. Nucl. Soc.; (United States) Journal Volume: 55
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
ALGORITHMS
CONVERGENCE
EFFICIENCY
MATHEMATICAL LOGIC
MESH GENERATION
NEUTRON TRANSPORT THEORY
SPACE DEPENDENCE
THREE-DIMENSIONAL CALCULATIONS
TRANSPORT THEORY
TWO-DIMENSIONAL CALCULATIONS