The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume disc...The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume discretization of the threedimensional multi-group radiation diffusion equations.The key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and approximate the left-hand block matrix selectively spurred by parallel processing considerations.The spectral property of the preconditioned matrix is then analyzed.The practical strategy is considered sequentially and in parallel.Finally,numerical results illustrate the numerical robustness,computational efficiency and parallel strong and weak scalabilities over the real-world structured and unstructured coupled problems,showing its competitiveness with many existing block preconditioners.展开更多
Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy amo...Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy among electrons,ions and photons.In this paper,we suggest a new positivity-preserving finite volume scheme for 2-D 3-T radiation diffusion equations on general polygonal meshes.The vertex unknowns are treated as primary ones for which the finite volume equations are constructed.The edgemidpoint and cell-centered unknowns are used as auxiliary ones and interpolated by the primary unknowns,which makes the final scheme a pure vertex-centered one.By comparison,most existing positivity-preserving finite volume schemes are cell-centered and based on the convex decomposition of the co-normal.Here,the conormal decomposition is not convex in general,leading to a fixed stencil of the flux approximation and avoiding a certain search algo-rithm on complex grids.Moreover,the new scheme effectively alleviates the nu-merical heat-barrier issue suffered by most existing cell-centered or hybrid schemes in solving strongly nonlinear radiation diffusion equations.Numerical experiments demonstrate the second-order accuracy and the positivity of the solution on various distorted grids.For the problem without analytic solution,the contours of the nu-merical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.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 by the National Natural Science Foundation of China(Grant 11971414)Hunan National Applied Mathematics Center(Grant 2020ZYT003)the Research Foundation of Education Bureau of Hunan(Grant 21B0162).
文摘The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume discretization of the threedimensional multi-group radiation diffusion equations.The key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and approximate the left-hand block matrix selectively spurred by parallel processing considerations.The spectral property of the preconditioned matrix is then analyzed.The practical strategy is considered sequentially and in parallel.Finally,numerical results illustrate the numerical robustness,computational efficiency and parallel strong and weak scalabilities over the real-world structured and unstructured coupled problems,showing its competitiveness with many existing block preconditioners.
基金This work was partially supported by the National Natural Science Foundation of China(No.11871009)Postdoctoral Research Foundation of China(No.BX20190013).
文摘Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy among electrons,ions and photons.In this paper,we suggest a new positivity-preserving finite volume scheme for 2-D 3-T radiation diffusion equations on general polygonal meshes.The vertex unknowns are treated as primary ones for which the finite volume equations are constructed.The edgemidpoint and cell-centered unknowns are used as auxiliary ones and interpolated by the primary unknowns,which makes the final scheme a pure vertex-centered one.By comparison,most existing positivity-preserving finite volume schemes are cell-centered and based on the convex decomposition of the co-normal.Here,the conormal decomposition is not convex in general,leading to a fixed stencil of the flux approximation and avoiding a certain search algo-rithm on complex grids.Moreover,the new scheme effectively alleviates the nu-merical heat-barrier issue suffered by most existing cell-centered or hybrid schemes in solving strongly nonlinear radiation diffusion equations.Numerical experiments demonstrate the second-order accuracy and the positivity of the solution on various distorted grids.For the problem without analytic solution,the contours of the nu-merical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.
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.