The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this p...The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.展开更多
Based on the block Arnoldi process and minimizing the Frobenius norm of the error,the block generalized minimal error(GMERR)method and its simpler version are proposed for solving large-scale linear systems of equatio...Based on the block Arnoldi process and minimizing the Frobenius norm of the error,the block generalized minimal error(GMERR)method and its simpler version are proposed for solving large-scale linear systems of equations with multiple right-hand sides.However,little is known about the behavior of these methods when they are applied to the solution of linear discrete ill-posed problems with multiple right-hand sides contaminated by errors.In this paper,the regularizing properties of the block GMERR method and the simpler block GMERR method are examined.Both a regularized block GMERR method and a regularized simpler block GMERR method are developed for solving large-scale linear discrete ill-posed problems with multiple right-hand sides.Numerical experiments on typical test matrices show the efficiency of the proposed methods.展开更多
At the Fourth International Conference on Graph Theory and Applications (1980), G. Chartrand posed the following problem: If a graph G contains spanning trees with m and n end-vertices, respecfively, where m<n, doe...At the Fourth International Conference on Graph Theory and Applications (1980), G. Chartrand posed the following problem: If a graph G contains spanning trees with m and n end-vertices, respecfively, where m<n, does G contain a spanning tree with k end-vertices for every integer k where m< k<n? Recently, the problem has been settled by S. Schuster and Cai Maocheng, independently. Here we shall introduce a simpler proof.展开更多
After Nanda et al. had treated the molecular size distribution of the polymers formed in anionic polymerization initiated by an electron transfer, Peebles reported a simpler case of the same reaction system, i.e. inst...After Nanda et al. had treated the molecular size distribution of the polymers formed in anionic polymerization initiated by an electron transfer, Peebles reported a simpler case of the same reaction system, i.e. instantaneous initiation, transfer to monomer, and no termination.The auther of this paper had resolved the set of kinetic differential equations given by Nanda et al., and obtained the exact expres-展开更多
This article studies numerically a familiar important phenomenon in spray combustion which is deformation and breakup of liquid drops in gas flow. The SIMPLER method is used to solve the two-dimensional （2D） unstead...This article studies numerically a familiar important phenomenon in spray combustion which is deformation and breakup of liquid drops in gas flow. The SIMPLER method is used to solve the two-dimensional （2D） unsteady axisymmetric Navier-Stokes equations for both the drop and the ambient gas flow. The level set method is applied to capturing the liquid/gas interface. Through calculation are obtained four typical breakup modes--oscillation, bag breakup, sheet stripping breakup and shear breakup governed by four non-dimensional numbers which are gas Weber number （Weg）, liquid Reynolds number （Rel）, gas Reynolds number （Reg） and density ratio （γ）. Their effects upon each mode are analyzed. The results indicate that among the four numbers, Weg is of the highest importance with Rel, Reg and γfollowing up. By widening the range of the density ratio up to 1 000, the breakup mode is discovered to be so complicated that a new one called multimode breakup mode turns up. This mode contains the shearing breakup and piercing breakup, which successively happen. The calculation results agree well with what is observed from the experiments.展开更多
基金This work was supported by the National Natural Science Foundation of China(11701320)the Shandong Provincial Natural Science Foundation of China(ZR2016AM04).
文摘The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.
基金National Natural Science Foundation of China under Grant No.11571171the anonymous referees for their useful comments and suggestions which greatly improved the representation of this paper.
文摘Based on the block Arnoldi process and minimizing the Frobenius norm of the error,the block generalized minimal error(GMERR)method and its simpler version are proposed for solving large-scale linear systems of equations with multiple right-hand sides.However,little is known about the behavior of these methods when they are applied to the solution of linear discrete ill-posed problems with multiple right-hand sides contaminated by errors.In this paper,the regularizing properties of the block GMERR method and the simpler block GMERR method are examined.Both a regularized block GMERR method and a regularized simpler block GMERR method are developed for solving large-scale linear discrete ill-posed problems with multiple right-hand sides.Numerical experiments on typical test matrices show the efficiency of the proposed methods.
文摘At the Fourth International Conference on Graph Theory and Applications (1980), G. Chartrand posed the following problem: If a graph G contains spanning trees with m and n end-vertices, respecfively, where m<n, does G contain a spanning tree with k end-vertices for every integer k where m< k<n? Recently, the problem has been settled by S. Schuster and Cai Maocheng, independently. Here we shall introduce a simpler proof.
文摘After Nanda et al. had treated the molecular size distribution of the polymers formed in anionic polymerization initiated by an electron transfer, Peebles reported a simpler case of the same reaction system, i.e. instantaneous initiation, transfer to monomer, and no termination.The auther of this paper had resolved the set of kinetic differential equations given by Nanda et al., and obtained the exact expres-
文摘This article studies numerically a familiar important phenomenon in spray combustion which is deformation and breakup of liquid drops in gas flow. The SIMPLER method is used to solve the two-dimensional （2D） unsteady axisymmetric Navier-Stokes equations for both the drop and the ambient gas flow. The level set method is applied to capturing the liquid/gas interface. Through calculation are obtained four typical breakup modes--oscillation, bag breakup, sheet stripping breakup and shear breakup governed by four non-dimensional numbers which are gas Weber number （Weg）, liquid Reynolds number （Rel）, gas Reynolds number （Reg） and density ratio （γ）. Their effects upon each mode are analyzed. The results indicate that among the four numbers, Weg is of the highest importance with Rel, Reg and γfollowing up. By widening the range of the density ratio up to 1 000, the breakup mode is discovered to be so complicated that a new one called multimode breakup mode turns up. This mode contains the shearing breakup and piercing breakup, which successively happen. The calculation results agree well with what is observed from the experiments.
