JXPAMG is a parallel algebraic multigrid(AMG)solver for solving the extreme-scale,sparse linear systems on modern supercomputers.JXPAMG features the following characteristics:1)It integrates some application-driven pa...JXPAMG is a parallel algebraic multigrid(AMG)solver for solving the extreme-scale,sparse linear systems on modern supercomputers.JXPAMG features the following characteristics:1)It integrates some application-driven parallel AMG algorithms,including α Setup-AMG(adaptive Setup based AMG),AI-AMG(algebraic interface based AMG)and AMGPCTL(physical-variable based coarsening two-level AMG);2)A hierarchical parallel sparse matrix data structure,labeled hierarchical parallel Compressed Sparse Row(hpCSR),that matches the computer architecture is designed,and the highly scalable components based on hpCSR are implemented;3)A flexible software architecture is designed to separate algorithm development from implementation.These characteristics allow JXPAMG to use different AMG strategies for different application features and architecture features,and thereby JXPAMG becomes aware of changes in these features.This paper introduces the algorithms,implementation techniques and applications of JXPAMG.Numerical experiments for typical real applications are given to illustrate the strong and weak parallel scaling properties of JXPAMG.展开更多
The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence mod...The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.展开更多
Consider an AMG for the linear system Au=f. Up to now, only the uniform convergence of two-level AMG is proved for symmetric and positive definite L-matrices with weak diagonal dominance. Using the new form (1), we ex...Consider an AMG for the linear system Au=f. Up to now, only the uniform convergence of two-level AMG is proved for symmetric and positive definite L-matrices with weak diagonal dominance. Using the new form (1), we extend the results in [1] to the case that A is a general symmetric and positive definite matrix with weak diagonal dominance. In the following, we shall use the same notations as in [1].展开更多
The algebraic multigrain(AMG)is one of the most frequently used algorithms for the solution of large-scale sparse linear systems in many realistic simulations of science and engineering applications.However,as the con...The algebraic multigrain(AMG)is one of the most frequently used algorithms for the solution of large-scale sparse linear systems in many realistic simulations of science and engineering applications.However,as the concurrency of supercomputers increasing,the AMG solver increasingly leads to poor parallel scalability due to its coarse-level construction in the setup phase.In this paper,to improve the parallel scalability of the traditional AMG to solve the sequence of sparse linear systems arising from PDE-based simulations,we propose a new AMG procedure calledαSetup-AMG based on an adaptive setup strategy.The main idea behindαSetup-AMG is the introduction of a setup condition in the coarsening process so that the setup is constructed as it needed instead of constructing in advance via an independent phase in the traditional procedure.As a result,αSetup-AMG requires fewer setup cost and level numbers for the sequence of linear systems.The numerical results on thousands of cores for a radiation hydrodynamics simulation in the inertial confinement fusion(ICF)application show the significant improvement in the efficiency of theαSetup-AMG solver.展开更多
基金supported by the Science Challenge Project(TZZT2019)and NSFC(62032023,11971414).
文摘JXPAMG is a parallel algebraic multigrid(AMG)solver for solving the extreme-scale,sparse linear systems on modern supercomputers.JXPAMG features the following characteristics:1)It integrates some application-driven parallel AMG algorithms,including α Setup-AMG(adaptive Setup based AMG),AI-AMG(algebraic interface based AMG)and AMGPCTL(physical-variable based coarsening two-level AMG);2)A hierarchical parallel sparse matrix data structure,labeled hierarchical parallel Compressed Sparse Row(hpCSR),that matches the computer architecture is designed,and the highly scalable components based on hpCSR are implemented;3)A flexible software architecture is designed to separate algorithm development from implementation.These characteristics allow JXPAMG to use different AMG strategies for different application features and architecture features,and thereby JXPAMG becomes aware of changes in these features.This paper introduces the algorithms,implementation techniques and applications of JXPAMG.Numerical experiments for typical real applications are given to illustrate the strong and weak parallel scaling properties of JXPAMG.
基金Projects(59375211,10771178,10676031) supported by the National Natural Science Foundation of ChinaProject(07A068) supported by the Key Project of Hunan Education CommissionProject(2005CB321702) supported by the National Key Basic Research Program of China
文摘The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.
基金Project supported by the National Natural Science Foundation of China.
文摘Consider an AMG for the linear system Au=f. Up to now, only the uniform convergence of two-level AMG is proved for symmetric and positive definite L-matrices with weak diagonal dominance. Using the new form (1), we extend the results in [1] to the case that A is a general symmetric and positive definite matrix with weak diagonal dominance. In the following, we shall use the same notations as in [1].
文摘时间相关偏微分方程隐式离散后,通常需要求解一个稀疏线性代数方程组序列.利用序列中相邻方程组性质的差异性与相似性,自适应地选取预条件子,提升方程组序列的并行求解效率,从而缩短总体求解时间,是一个值得研究的问题.本文针对科学与工程计算中广泛使用的代数多重网格(AMG)预条件子,设计了方程组序列相关的自适应预条件策略.通过惯性约束聚变(ICF)的辐射流体力学数值模拟典型应用,验证了该策略的有效性.测试结果表明,在某高性能计算机的3125个CPU核上,自适应预条件策略可将并行效率从47%提升到61%,将模拟总时间从19.7 h降为14.5 h.
基金supported by National Key R&D Program of China under Grant No.2017YFB0202103Science Challenge Project under Grant no.TZZT2016002National Nature Science Foundation of China under Grant Nos.61370067 and 11971414.
文摘The algebraic multigrain(AMG)is one of the most frequently used algorithms for the solution of large-scale sparse linear systems in many realistic simulations of science and engineering applications.However,as the concurrency of supercomputers increasing,the AMG solver increasingly leads to poor parallel scalability due to its coarse-level construction in the setup phase.In this paper,to improve the parallel scalability of the traditional AMG to solve the sequence of sparse linear systems arising from PDE-based simulations,we propose a new AMG procedure calledαSetup-AMG based on an adaptive setup strategy.The main idea behindαSetup-AMG is the introduction of a setup condition in the coarsening process so that the setup is constructed as it needed instead of constructing in advance via an independent phase in the traditional procedure.As a result,αSetup-AMG requires fewer setup cost and level numbers for the sequence of linear systems.The numerical results on thousands of cores for a radiation hydrodynamics simulation in the inertial confinement fusion(ICF)application show the significant improvement in the efficiency of theαSetup-AMG solver.
