Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods....Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.展开更多
A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method ...A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.展开更多
We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
针对内充气吹式排种器组合气嘴低位安装对供气系统气流稳定性要求高、田间作业适应性差的问题,为优化内充气吹式排种器结构、改善工作性能,运用EDEM-CFD耦合分析方法,采用玉米籽粒粘结颗粒模型,以气嘴安装位置、工作压强和前进速度为试...针对内充气吹式排种器组合气嘴低位安装对供气系统气流稳定性要求高、田间作业适应性差的问题,为优化内充气吹式排种器结构、改善工作性能,运用EDEM-CFD耦合分析方法,采用玉米籽粒粘结颗粒模型,以气嘴安装位置、工作压强和前进速度为试验因素进行正交试验优化仿真,提取关键参数充种极限速度和充种时长为评价指标进行分析,结果表明气嘴安装位置、工作压强和前进速度对充种极限速度影响显著而对充种时长影响不显著,充种极限速度和充种时长在0.05水平上呈显著负相关关系,较大充种极限速度和较短充种时长有利于提高排种器充种性能;对不同作业状态下的合格率、重播率、漏播率等作业指标进行分析表明气嘴安装位置在中位时合格率和充种极限速度呈显著正相关,低位和高位时因清种效果不佳导致合格率和充种极限速度呈负相关,中位时排种效果较佳。为验证仿真结果,进行气嘴安装位置和工作压强的全因素试验,结果表明,气嘴安装位置为中位时作业效果最佳,合格率大于90%,明显优于低位、高位状态,与仿真结果一致;在确定组合气嘴中位安装结构参数下,进行工作压强、前进速度的全因素试验,结果表明,前进速度为5~10 km/h、工作压强为4.5~5.5 k Pa时,排种器合格率较高,均为90%以上,该区间各工作参数下对合格率影响不显著。展开更多
The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on...The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.展开更多
Lu Hao首先给出了阶梯矩阵及其一般性的定义和性质.这类矩阵为迭代法提供了新矩阵分裂的基础.基于此新矩阵类的迭代方法的显著特征是它对于并行计算很容易被实现.应用这一新的分解方法,给出了一般的加速松弛方法(GAOR),而关于AOR方法的...Lu Hao首先给出了阶梯矩阵及其一般性的定义和性质.这类矩阵为迭代法提供了新矩阵分裂的基础.基于此新矩阵类的迭代方法的显著特征是它对于并行计算很容易被实现.应用这一新的分解方法,给出了一般的加速松弛方法(GAOR),而关于AOR方法的一些性质可以被延伸到该新方法中,并针对Hermite正定矩阵进行了新方法收敛性的分析.最后,给出了一些例子来表明新方法的优越性.展开更多
基金Project supported by the Natural Science Foundation of Liaoning Province of China (No.20022021)
文摘Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.
基金Project supported by the National Natural Science Foundation of China (Nos. 10232040, 10572002 and 10572003)
文摘A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.
文摘We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
文摘针对内充气吹式排种器组合气嘴低位安装对供气系统气流稳定性要求高、田间作业适应性差的问题,为优化内充气吹式排种器结构、改善工作性能,运用EDEM-CFD耦合分析方法,采用玉米籽粒粘结颗粒模型,以气嘴安装位置、工作压强和前进速度为试验因素进行正交试验优化仿真,提取关键参数充种极限速度和充种时长为评价指标进行分析,结果表明气嘴安装位置、工作压强和前进速度对充种极限速度影响显著而对充种时长影响不显著,充种极限速度和充种时长在0.05水平上呈显著负相关关系,较大充种极限速度和较短充种时长有利于提高排种器充种性能;对不同作业状态下的合格率、重播率、漏播率等作业指标进行分析表明气嘴安装位置在中位时合格率和充种极限速度呈显著正相关,低位和高位时因清种效果不佳导致合格率和充种极限速度呈负相关,中位时排种效果较佳。为验证仿真结果,进行气嘴安装位置和工作压强的全因素试验,结果表明,气嘴安装位置为中位时作业效果最佳,合格率大于90%,明显优于低位、高位状态,与仿真结果一致;在确定组合气嘴中位安装结构参数下,进行工作压强、前进速度的全因素试验,结果表明,前进速度为5~10 km/h、工作压强为4.5~5.5 k Pa时,排种器合格率较高,均为90%以上,该区间各工作参数下对合格率影响不显著。
文摘The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.
