A Parallel Algorithm for 2-D Cylindrical Geometry Transport Equation with Interface Corrections
In order to make conventional implicit algorithm to be applicable in large scale parallel computers , an interface prediction and correction of discontinuous finite element method is presented to solve time-dependent neutron transport equations under 2-D cylindrical geometry. Domain decomposition is adopted in the computational domain.The numerical experiments show that our parallel algorithm with explicit prediction and implicit correction has good precision, parallelism and simplicity. Especially, it can reach perfect speedup even on hundreds of processors for large-scale problems.
[1] W.H. Reed and T.R. Hill, Triangular mesh methods for the neutron
transport equation,
Tech. Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973.
[2] F.Lianxiang and Y.Shulin. Researches on 2-D neutron transport
solver NTXY2D. Technical report, Institute of Applied Physics and
Computational Mathematics in Beijing, 1999.10.
[3] E.E. Lewis, W.F. Miller. Computational Methods of Neutron
Transport (M). New York: John Wiley & Sons Publisher, 1984.
[4] R.S.Baker, K.R.Koch. An Sn algorithm for the massively parallel
CM-200 computer (J). Nuclear Science and Engineering, 1998, Vol.128
: 312-320.
[5] S.Plimpton, B.Hendrickson, S.Burns, W.McLendon. Parallel
algorithms for radiation transprt on unstructured grids (A). Proceeding of
SuperComputing-2000.
[6] Shawn D Pautz. An Algorithm for Parallel Sn Sweeps on
Unstructured Meshes (J). Nuclear Science and Engineering ,2002 ,140 (2)
:111-136.
[7] Mo Z, Fu L. Parallel flux sweeping algorithm for neutron transport on
unstructured grid. Journal of Supercomputing, 2004, 30(1): 5-17.
[8] WEI Jun-xia , YANG Shu-lin, FU Lian-xiang. A Parallel Domain
Decomposition Method for Neutron Transport Equations Under 2-D
Cylindrical Geometry(J). Chinese J Comput Phys, 2010, 27(1):1-7.
[9] Yuan Guangwei, Hang Xudeng. A parallel algorithm for the particle
transport SN method with interface corrections (J). Chinese J Comput
Phys, 2006, 23(6):637-641.
[10] Zhenying Hong,Guangwei Yuan, Aparallel algorithm with interface
prediction and correction for spherical geometric transport equation.
Prog.Nucl.Energy,51,268-273(2009).
[11] Zhang Aiqing , Mo Zeyao. Parallelization of the 2D multi-group
radiation transport code LARED-R-1 (J). Chinese J Comput Phys, 2007,
24(2): 146-152.
[12] Yang Shulin, Mo Zeyao, Shen Longjun. The Domain Decomposition
Parallel Iterative Algorithm foe the 3-D Transport Issue (J). Chinese J
Comput Phys, 2004, 21(1): 1-9.
[13] T.A. Wareing, J.M. McGhee, J.E. Morel and S.D. Pautz,
Discontinuous Finite Methods Sn Methods on 3-D unstructured Grids, in
Proceeding of International Conference on Mathematics and
Computation, Reactor Physics and Environment Analysis in Nuclear
Applications, 1999, Madrid, Spain.
[14] SWEEP3D:3D Discrete Ordinates Neutron Transport Benchmark
Codes,
http://www.llnl.gov/asci_benchmarks/asci/limited/sweep3d/sweep3d_rea
dme.html.
[1] W.H. Reed and T.R. Hill, Triangular mesh methods for the neutron
transport equation,
Tech. Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973.
[2] F.Lianxiang and Y.Shulin. Researches on 2-D neutron transport
solver NTXY2D. Technical report, Institute of Applied Physics and
Computational Mathematics in Beijing, 1999.10.
[3] E.E. Lewis, W.F. Miller. Computational Methods of Neutron
Transport (M). New York: John Wiley & Sons Publisher, 1984.
[4] R.S.Baker, K.R.Koch. An Sn algorithm for the massively parallel
CM-200 computer (J). Nuclear Science and Engineering, 1998, Vol.128
: 312-320.
[5] S.Plimpton, B.Hendrickson, S.Burns, W.McLendon. Parallel
algorithms for radiation transprt on unstructured grids (A). Proceeding of
SuperComputing-2000.
[6] Shawn D Pautz. An Algorithm for Parallel Sn Sweeps on
Unstructured Meshes (J). Nuclear Science and Engineering ,2002 ,140 (2)
:111-136.
[7] Mo Z, Fu L. Parallel flux sweeping algorithm for neutron transport on
unstructured grid. Journal of Supercomputing, 2004, 30(1): 5-17.
[8] WEI Jun-xia , YANG Shu-lin, FU Lian-xiang. A Parallel Domain
Decomposition Method for Neutron Transport Equations Under 2-D
Cylindrical Geometry(J). Chinese J Comput Phys, 2010, 27(1):1-7.
[9] Yuan Guangwei, Hang Xudeng. A parallel algorithm for the particle
transport SN method with interface corrections (J). Chinese J Comput
Phys, 2006, 23(6):637-641.
[10] Zhenying Hong,Guangwei Yuan, Aparallel algorithm with interface
prediction and correction for spherical geometric transport equation.
Prog.Nucl.Energy,51,268-273(2009).
[11] Zhang Aiqing , Mo Zeyao. Parallelization of the 2D multi-group
radiation transport code LARED-R-1 (J). Chinese J Comput Phys, 2007,
24(2): 146-152.
[12] Yang Shulin, Mo Zeyao, Shen Longjun. The Domain Decomposition
Parallel Iterative Algorithm foe the 3-D Transport Issue (J). Chinese J
Comput Phys, 2004, 21(1): 1-9.
[13] T.A. Wareing, J.M. McGhee, J.E. Morel and S.D. Pautz,
Discontinuous Finite Methods Sn Methods on 3-D unstructured Grids, in
Proceeding of International Conference on Mathematics and
Computation, Reactor Physics and Environment Analysis in Nuclear
Applications, 1999, Madrid, Spain.
[14] SWEEP3D:3D Discrete Ordinates Neutron Transport Benchmark
Codes,
http://www.llnl.gov/asci_benchmarks/asci/limited/sweep3d/sweep3d_rea
dme.html.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57406", author = "Wei Jun-xia and Yuan Guang-wei and Yang Shu-lin and Shen Wei-dong", title = "A Parallel Algorithm for 2-D Cylindrical Geometry Transport Equation with Interface Corrections", abstract = "In order to make conventional implicit algorithm to be applicable in large scale parallel computers , an interface prediction and correction of discontinuous finite element method is presented to solve time-dependent neutron transport equations under 2-D cylindrical geometry. Domain decomposition is adopted in the computational domain.The numerical experiments show that our parallel algorithm with explicit prediction and implicit correction has good precision, parallelism and simplicity. Especially, it can reach perfect speedup even on hundreds of processors for large-scale problems.
", keywords = "Transport Equation, Discontinuous Finite Element, Domain Decomposition, Interface Prediction And Correction", volume = "5", number = "5", pages = "753-5", }
