Anderson acceleration is a kind of effective method for improving the convergence of the general fixed point iteration.In the linear case,Anderson acceleration can be used to improve the convergence rate of matrix spl...Anderson acceleration is a kind of effective method for improving the convergence of the general fixed point iteration.In the linear case,Anderson acceleration can be used to improve the convergence rate of matrix splitting based iterative methods.In this paper,by using Anderson acceleration on general splitting iterative methods for linear systems,three classes of methods are given.The first one is obtained by directly applying Anderson acceleration on splitting iterative methods.For the second class of methods,Anderson acceleration is used periodically in the splitting iteration process.The third one is constructed by combining the Anderson acceleration and split iteration method in each iteration process.The key of this class of method is to determine a combination coefficient for Anderson acceleration and split iteration method.One optimal combination coefficient is given.Some theoretical results about the convergence of the considered three methods are established.Numerical experiments show that the proposed methods are effective.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funded by the National Natural Science Foun China(Grant Nos.12171045,11671051).
文摘Anderson acceleration is a kind of effective method for improving the convergence of the general fixed point iteration.In the linear case,Anderson acceleration can be used to improve the convergence rate of matrix splitting based iterative methods.In this paper,by using Anderson acceleration on general splitting iterative methods for linear systems,three classes of methods are given.The first one is obtained by directly applying Anderson acceleration on splitting iterative methods.For the second class of methods,Anderson acceleration is used periodically in the splitting iteration process.The third one is constructed by combining the Anderson acceleration and split iteration method in each iteration process.The key of this class of method is to determine a combination coefficient for Anderson acceleration and split iteration method.One optimal combination coefficient is given.Some theoretical results about the convergence of the considered three methods are established.Numerical experiments show that the proposed methods are effective.
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.
