Fast algorithms for transport models. Final report
This project has developed a multigrid in space algorithm for the solution of the S{sub N} equations with isotropic scattering in slab geometry. The algorithm was developed for the Modified Linear Discontinuous (MLD) discretization in space which is accurate in the thick diffusion limit. It uses a red/black two-cell {mu}-line relaxation. This relaxation solves for all angles on two adjacent spatial cells simultaneously. It takes advantage of the rank-one property of the coupling between angles and can perform this inversion in O(N) operations. A version of the multigrid in space algorithm was programmed on the Thinking Machines Inc. CM-200 located at LANL. It was discovered that on the CM-200 a block Jacobi type iteration was more efficient than the block red/black iteration. Given sufficient processors all two-cell block inversions can be carried out simultaneously with a small number of parallel steps. The bottleneck is the need for sums of N values, where N is the number of discrete angles, each from a different processor. These are carried out by machine intrinsic functions and are well optimized. The overall algorithm has computational complexity O(log(M)), where M is the number of spatial cells. The algorithm is very efficient and represents the state-of-the-art for isotropic problems in slab geometry. For anisotropic scattering in slab geometry, a multilevel in angle algorithm was developed. A parallel version of the multilevel in angle algorithm has also been developed. Upon first glance, the shifted transport sweep has limited parallelism. Once the right-hand-side has been computed, the sweep is completely parallel in angle, becoming N uncoupled initial value ODE`s. The author has developed a cyclic reduction algorithm that renders it parallel with complexity O(log(M)). The multilevel in angle algorithm visits log(N) levels, where shifted transport sweeps are performed. The overall complexity is O(log(N)log(M)).
- Research Organization:
- Colorado Univ., Boulder, CO (United States). Applied Mathematics Program
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG02-90ER25086
- OSTI ID:
- 10190744
- Report Number(s):
- DOE/ER/25086-T2; ON: DE95001702; BR: KC0701010/KC0701030; TRN: 94:022675
- Resource Relation:
- Other Information: PBD: [1994]
- Country of Publication:
- United States
- Language:
- English
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