[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.1016/j.net.2017.08.009

Multilevel acceleration of scattering-source iterations with application to electron transport

Drumm, Clif (Radiation Effects Theory Department, Sandia National Laboratories)
Fan, Wesley (Radiation Effects Theory Department, Sandia National Laboratories)

Publication Information

Nuclear Engineering and Technology / v.49, no.6, 2017 , pp. 1114-1124 More about this Journal

Abstract

Acceleration/preconditioning strategies available in the SCEPTRE radiation transport code are described. A flexible transport synthetic acceleration (TSA) algorithm that uses a low-order discrete-ordinates ( $S_N$ ) or spherical-harmonics ( $P_N$ ) solve to accelerate convergence of a high-order $S_N$ source-iteration (SI) solve is described. Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. TSA has been applied as a preconditioner to accelerate the convergence of the GMRES iterations. The methods are applied to several problems involving electron transport and problems with artificial cross sections with large scattering ratios. These methods were compared and evaluated by considering material discontinuities and scattering anisotropy. Observed accelerations obtained are highly problem dependent, but speedup factors around 10 have been observed in typical applications.

Keywords

Krylov subspace; Low-order discrete-ordinates solve; Spherical-harmonics solve; Transport synthetic acceleration;

Citations & Related Records

Reference

1	S. Pautz, C. Drumm, W. Bohnhoff, W. Fan, Software engineering in the SCEPTRE code, in: Proc. M&C 2009, American Nuclear Society, La Grange Park, IL, 2009.
2	M. Heroux, R. Bartlett, V.H.R. Hoekstra, J. Hu, T. Kolda, R. Lehoucq, K. Long, R. Pawlowski, E. Phipps, A. Salinger, H. Thornquist, R. Tuminaro, J. Willenbring, A. Williams, An Overview of Trilinos (SAND Rep. No. SAND2003-2927), Sandia National Laboratories, Albuquerque, NM, 2003.
3	A. Prokopenko, C. Siefert, J. Hu, M. Hoemmen, A. Klinvex, Ifpack2 User's Guide 1.0 (Trilinos Version 12.6; SAND Rep. No. SAND2016-5338), Sandia National Laboratories, Albuquerque, NM, 2016.
4	A. Prokopenko, J. Hu, T. Wiesner, C. Siefert, R. Tuminaro, MueLu User's Guide 1.0 (SAND Rep. No. SAND2014-18874), Sandia National Laboratories, Albuquerque, NM, 2014.
5	G.L. Ramone, M. Adams, P. Nowak, A transport synthetic acceleration method for transport iterations, Nucl. Sci. Eng. 125 (1997) 257. DOI
6	B. Patton, J. Holloway, Application of Krylov subspace iterative methods to the slab geometry transport equation, in: Proc. Radiat. Prot. Shielding 1996, American Nuclear Society, La Grange Park, IL, 1996, pp. 384-389.
7	B. Patton, J. Holloway, Some remarks on GMRES for transport theory, in: Proc. M&C 2003, American Nuclear Society, La Grange Park, IL, 2003.
8	J. Warsa, T. Wareing, J. Morel, Krylov iterative methods and the degraded effectiveness of diffusion synthetic acceleration for multidimensional $ $S_N$ $ calculations in problems with material discontinuities, Nucl. Sci. Eng. 147 (2004) 218. DOI
9	J. Morel, Basic Krylov methods with application to transport, in: Proc. M&C 2005, American Nuclear Society, La Grange Park, IL, 2005.
10	J. Warsa, T. Wareing, J. Morel, Fully consistent diffusion synthetic acceleration of linear discontinuous $ $S_N$ $ transport discretizations on three-dimensional unstructured tetrahedral meshes, Nucl. Sci. Eng. 141 (2002) 236-251. DOI
11	M. Adams, E. Larsen, Fast iterative methods for discrete-ordinates particle transport calculations, Prog. Nucl. Energy 40 (2002) 3. DOI
12	B. Turcksin, J. Ragusa, Discontinuous diffusion synthetic acceleration for $ $S_N$ $ transport on 2D arbitrary polygonal meshes, J. Comp. Phys. 274 (2014) 356-369. DOI
13	B. Turcksin, J. Ragusa, J. Morel, Angular multigrid preconditioner for Krylovbased solution techniques applied to the SN equations with highly forwardpeaked scattering, Trans. Theor. Stat. Phys. 41 (2012) 1-22. DOI
14	C. Drumm, Spherical harmonics ($ $P_N$ $) methods in the SCEPTRE radiation transport code, in: Proc. M&C 2015, American Nuclear Society, La Grange Park, IL, 2015 [CD-ROM].
15	C. Drumm, W. Fan, S. Pautz, Phase-space finite elements in a least-squares solution of the transport equation, in: Proc. M&C 2013, American Nuclear Society, La Grange Park, IL, 2013.
16	J. Amelang, C. Trott, H. Edwards, Kokkos Tutorial (SAND Rep. No. SAND2015-9620C), Sandia National Laboratories, Albuquerque, NM, 2015.
17	Y. Saad, M. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Sci. Stat. Comput. 7 (1986) 856. DOI
18	C. Drumm, W.C. Fan, L. Lorence, J.L. Powell, An analysis of the extendedtransport correction with application to electron beam transport, Nucl. Sci. Eng. 155 (2007) 355. DOI
19	L. Lorence, J. Morel, G. Valdez, Physics Guide to CEPXS: a Multigroup Coupled Electron-photon Cross-section Generating Code Version 1.0 (SAND Rep. No. SAND89-1685), Sandia National Laboratories, Albuquerque, NM, 1989.