Convergence properties of iterative algorithms for solving the nodal diffusion equations
Conference
·
OSTI ID:7222675
We drive the five point form of the nodal diffusion equations in two-dimensional Cartesian geometry and develop three iterative schemes to solve the discrete-variable equations: the unaccelerated, partial Successive Over Relaxation (SOR), and the full SOR methods. By decomposing the iteration error into its Fourier modes, we determine the spectral radius of each method for infinite medium, uniform model problems, and for the unaccelerated and partial SOR methods for finite medium, uniform model problems. Also for the two variants of the SOR method we determine the optimal relaxation factor that results in the smallest number of iterations required for convergence. Our results indicate that the number of iterations for the unaccelerated and partial SOR methods is second order in the number of nodes per dimension, while, for the full SOR this behavior is first order, resulting in much faster convergence for very large problems. We successfully verify the results of the spectral analysis against those of numerical experiments, and we show that for the full SOR method the linear dependence of the number of iterations on the number of nodes per dimension is relatively insensitive to the value of the relaxation parameter, and that it remains linear even for heterogenous problems. 14 refs., 1 fig.
- Research Organization:
- Oak Ridge National Lab., TN (USA)
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 7222675
- Report Number(s):
- CONF-900418-1; ON: DE89016859
- Country of Publication:
- United States
- Language:
- English
Similar Records
Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme
Iterative solution of a nonlinear system arising in phase change problems
A nodal diffusion technique for synthetic acceleration of nodal S /sup n/ calculations
Journal Article
·
Wed May 27 20:00:00 EDT 2015
· Journal of Computational Physics
·
OSTI ID:1437429
Iterative solution of a nonlinear system arising in phase change problems
Technical Report
·
Wed Dec 31 23:00:00 EST 1986
·
OSTI ID:6905578
A nodal diffusion technique for synthetic acceleration of nodal S /sup n/ calculations
Journal Article
·
Mon Jul 01 00:00:00 EDT 1985
· Nucl. Sci. Eng.; (United States)
·
OSTI ID:6073359
Related Subjects
654003 -- Radiation & Shielding Physics-- Neutron Interactions with Matter
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700209* -- Fusion Power Plant Technology-- Component Development & Materials Testing
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ALGORITHMS
ARRAY PROCESSORS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
NEUTRON DIFFUSION EQUATION
NUMERICAL SOLUTION
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700209* -- Fusion Power Plant Technology-- Component Development & Materials Testing
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ALGORITHMS
ARRAY PROCESSORS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
NEUTRON DIFFUSION EQUATION
NUMERICAL SOLUTION