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
The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to th...The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is challenging.To address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve subsystems.Despite its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of subsystems.Furthermore,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear systems.To address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as αSetup-PCTL.The adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear systems.The proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall efficiency.Numerical results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.展开更多
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
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.
基金financially supported by the National Natural Science Foundation of China(62032023 and 11971414)Hunan National Applied Mathematics Center(2020ZYT003)the Research Foundation of Education Bureau of Hunan(21B0162).
文摘The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is challenging.To address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve subsystems.Despite its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of subsystems.Furthermore,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear systems.To address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as αSetup-PCTL.The adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear systems.The proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall efficiency.Numerical results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.
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.
