三温辐射扩散问题的一种并行自适应PCTL预条件子
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摘要
三温辐射扩散方程(RDEs)广泛出现于惯性约束聚变等实际问题中,其大规模离散系统的求解效率是影响模拟性能的主要瓶颈.本文首先针对三维三温RDEs的有限体积格式,给出了一种自适应PCTL预条件子;接着,在JASMIN下基于进程分组策略,设计并实现了相应的并行PGMRES解法器;最后,通过对源于实际应用背景的数据进行测试,表明新并行解法器比传统的BoomerAMG-GMRES解法器具有更好的算法可扩展性及运算效率.
3-T radiation diffusion equations(RDEs)arise widely in practical problems such as inertial confinement fusion,whose large-scale discrete system's solution efficiency is the staple bottleneck to influence the simulation performance.In this paper,firstly,we provide an adaptive physical-variable based coarsening two-level preconditioner for 3-D 3-T RDEs.Next,we design and implement the corresponding parallel PGMRES solver for 3-T RDEs by the process-packet strategy under JASMIN.Finally,numerical results on typical problems of practical application demonstrate that our parallel solver possesses better algorithmic scalability and computational efficiency than traditional Boomer AMG-GMRES solver.
3-T radiation diffusion equations(RDEs)arise widely in practical problems such as inertial confinement fusion,whose large-scale discrete system's solution efficiency is the staple bottleneck to influence the simulation performance.In this paper,firstly,we provide an adaptive physical-variable based coarsening two-level preconditioner for 3-D 3-T RDEs.Next,we design and implement the corresponding parallel PGMRES solver for 3-T RDEs by the process-packet strategy under JASMIN.Finally,numerical results on typical problems of practical application demonstrate that our parallel solver possesses better algorithmic scalability and computational efficiency than traditional Boomer AMG-GMRES solver.
引文
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[9]郭美珍,江军,舒适.一种二维三温辐射热传导方程组SFVEM格式的并行预条件子[J].湘潭大学自然科学学报,2007,29(3):42-45.
[9]徐小文,莫则尧,安恒斌.求解二维三温辐射扩散方程组的一种代数两层迭代方法[J].计算物理,2009,26(1):1-8.
[10]周志阳,徐小文,舒适,等.二维三温辐射扩散方程组两层预条件子的自适应求解[J].计算物理,2012,29(4):62-70.
[11]MO Z,ZHANG A,CAO X,et al.JASMIN:aparallel software infrastructure for scientific computing[J].Front Comput Sci,2010,4(4):480-488.
[12]JESSEE J,FIVELAND W,HOWELL L,et al.An adaptive mesh refinement algorithm for the radiative transport equation[J].J Comput Phys,1998,139:380-398.
[13]HENSON V,YANG U.BoomerAMG:aparallel algebraic multigrid solver and preconditioner[J].Applied Numerical Mathematics,2002,41(1):155-177.
[2]莫则尧,张爱清,曹小林,等.多介质辐射流体力学数值模拟中的并行计算研究[J].自然科学进展,2006,16(3):287-292.
[3]聂存云,舒适.一类二维三温辐射热传导方程组的对称有限体格式[J].湘潭大学自然科学学报,2004,26(1):17-22.
[4]YUE X,SHU S,XU X,et al.An adaptive combined preconditioner with applications in radiation diffusion equations[J].Commun Comput Phys,2015,18(5):1313-1335.
[5]YUE X,XU X,SHU S.JASMIN-based two-dimensional adaptive combined preconditioner for radiation diffusion equations in inertial fusion research[J].E Asian J Appl Math,2017,7(3):495-507.
[6]BALDWIN C,BROWN P N,FALGOUT R,et al.Iterative linear solvers in 2Dradiation-hydrodynamics code:Methods and performance[J].J Comput Phys,1999,154:1-40.
[7]MO Z.Parallel adaptive solution for two dimensional 3-T energy equation on UG[J].Comput Visual Sci,2006,9:165-174.
[8]JIANG J,HUANG Y,SHU S,et al.Some new discretiztion and adaptation and multigrid methods for 2-D 3-T diffusion equations[J].J Comput Phys,2007,224(1):168-181.
[9]郭美珍,江军,舒适.一种二维三温辐射热传导方程组SFVEM格式的并行预条件子[J].湘潭大学自然科学学报,2007,29(3):42-45.
[9]徐小文,莫则尧,安恒斌.求解二维三温辐射扩散方程组的一种代数两层迭代方法[J].计算物理,2009,26(1):1-8.
[10]周志阳,徐小文,舒适,等.二维三温辐射扩散方程组两层预条件子的自适应求解[J].计算物理,2012,29(4):62-70.
[11]MO Z,ZHANG A,CAO X,et al.JASMIN:aparallel software infrastructure for scientific computing[J].Front Comput Sci,2010,4(4):480-488.
[12]JESSEE J,FIVELAND W,HOWELL L,et al.An adaptive mesh refinement algorithm for the radiative transport equation[J].J Comput Phys,1998,139:380-398.
[13]HENSON V,YANG U.BoomerAMG:aparallel algebraic multigrid solver and preconditioner[J].Applied Numerical Mathematics,2002,41(1):155-177.