Transport synthetic acceleration with opposing reflecting boundary conditions
The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.
- Research Organization:
- Lawrence Livermore National Lab., CA (US)
- Sponsoring Organization:
- USDOE; National Science Foundation (NSF)
- DOE Contract Number:
- AC05-76OR00033; W-7405-ENG-48
- OSTI ID:
- 20014326
- Journal Information:
- Nuclear Science and Engineering, Vol. 134, Issue 2; Other Information: PBD: Feb 2000; ISSN 0029-5639
- Country of Publication:
- United States
- Language:
- English
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