Incomplete domain decomposition preconditioning for coarse mesh neutron diffusion problems
- Purdue Univ., West Lafayette, IN (United States)
Incomplete domain decomposition preconditioning for parallel implementation of the conjugate gradient-like methods is applied to solve the two-group, three-dimensional, coarse mesh finite differenced neutron diffusion equation on the PARAGON XP/S-10 parallel computer. The linear system resulting from implicit time differencing of the time-dependent neutron diffusion equation is solved by the preconditioned biconjugate gradient squared method without employing the fission source iteration. An efficient domain decomposition preconditioning scheme is constructed by taking advantage of strong diagonal dominance of the coarse mesh finite difference formulation. Simplifications are made in the incomplete LU factorization process to construct a preconditioner for a three dimensional subdomain and the coupling between subdomains is approximated by incorporating only the effect of the non-leakage terms of neighboring subdomains. The method is applied to quarter core and full core fixed source problems which are created from the IAEA three-dimensional benchmark problem. Results show that on a single processor the computation time for the preconditioned biconjugate gradient method is comparable to other conventional iteration methods such as Line-SOR and the cyclic Chebyshev semi-iterative method. The effectiveness of the incomplete domain decomposition preconditioning on a multi-processor is evidenced by the small increase in the number of iterations as the number of subdomains increases. Speedups up to 32.1 are achievable with 64 processing elements for a 34{times}34{times}36 full core three-dimensional problem.
- OSTI ID:
- 459278
- Report Number(s):
- CONF-950420--
- Country of Publication:
- United States
- Language:
- English
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