Designing a good preconditioner for accelerating the iterative solution of the three-dimensional multi-group radiation diffusion equations based on a cell-centered finite volume discretization has been the focus of in...Designing a good preconditioner for accelerating the iterative solution of the three-dimensional multi-group radiation diffusion equations based on a cell-centered finite volume discretization has been the focus of intensive research efforts over the past few decades.In the present paper,we develop a physics-wise splitting preconditioning algorithm with selective relaxation and algebraic multigrid subsolves.The spectral distribution and the degree of the minimal polynomial of its rightpreconditioned matrix together with the conditional convergence property of its iteration method are analyzed.Subsequently,we discuss its sequential implementation as well as the two-level parallelization.Lastly,the new preconditioner is applied to the experimental test cases arising from realistic simulations of the hydrodynamic instability during the deceleration phase of a laser-driven spherical implosion to illustrate the numerical robustness,computational efficiency,parallel strong and weak scalabilities,and its competitiveness with some existing monolithic and block preconditioning approaches.展开更多
We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unstea...We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high dimensions.In this article,motivated by[M.J.Gander,S.Loisel,D.B.Szyld,SIAM J.Matrix Anal.Appl.33(2012)653–680]and[S.Nardean,M.Ferronato,A.S.Abushaikha,J.Comput.Phys.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear systems.Robustness,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.展开更多
基金supported in part by National Natural Science Foundation of China(12371373)Hunan National Applied Mathematics Center(2020ZYT003)+1 种基金Research Foundation of Education Bureau of Hunan(21B0162)Shandong Provincial Natural Science Foundation(ZR2020MA046).
文摘Designing a good preconditioner for accelerating the iterative solution of the three-dimensional multi-group radiation diffusion equations based on a cell-centered finite volume discretization has been the focus of intensive research efforts over the past few decades.In the present paper,we develop a physics-wise splitting preconditioning algorithm with selective relaxation and algebraic multigrid subsolves.The spectral distribution and the degree of the minimal polynomial of its rightpreconditioned matrix together with the conditional convergence property of its iteration method are analyzed.Subsequently,we discuss its sequential implementation as well as the two-level parallelization.Lastly,the new preconditioner is applied to the experimental test cases arising from realistic simulations of the hydrodynamic instability during the deceleration phase of a laser-driven spherical implosion to illustrate the numerical robustness,computational efficiency,parallel strong and weak scalabilities,and its competitiveness with some existing monolithic and block preconditioning approaches.
基金financially supported by Hunan National Applied Mathematics Center(2020ZYT003)National Natural Science Foundation of China(11971414,62102167)+1 种基金Research Foundation of Education Bureau of Hunan(21B0162)Guangdong Basic and Applied Basic Research Foundation(2020A1515110364).
文摘We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high dimensions.In this article,motivated by[M.J.Gander,S.Loisel,D.B.Szyld,SIAM J.Matrix Anal.Appl.33(2012)653–680]and[S.Nardean,M.Ferronato,A.S.Abushaikha,J.Comput.Phys.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear systems.Robustness,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.
