M stepJacobi预处理共轭梯度法被用于求解源于自共轭椭圆偏微分方程的有限元或有限差分逼近的大型稀疏线性系统。这种方法的应用基础是相应的Jacobi迭代收敛。研究结果表明:偶数步的Jacobi预处理共轭梯度法较相邻奇数步的Jacobi预处理...M stepJacobi预处理共轭梯度法被用于求解源于自共轭椭圆偏微分方程的有限元或有限差分逼近的大型稀疏线性系统。这种方法的应用基础是相应的Jacobi迭代收敛。研究结果表明:偶数步的Jacobi预处理共轭梯度法较相邻奇数步的Jacobi预处理共轭梯度法更有效,步数越多,收敛速度越快。展开更多
针对基于PVM的桌面PC机联网而成的网络并行计算环境中,处理机的运算速度较快而处理机间的通信相对较慢,以及微机的内存有限的实际情况,从实用的角度出发,给出了基于PVM的网上求解有限元方程组的并行m-Step Jacob i PCG方法,该算法的矩...针对基于PVM的桌面PC机联网而成的网络并行计算环境中,处理机的运算速度较快而处理机间的通信相对较慢,以及微机的内存有限的实际情况,从实用的角度出发,给出了基于PVM的网上求解有限元方程组的并行m-Step Jacob i PCG方法,该算法的矩阵和向量采用行元素相邻单元贡献法实现有限元总体刚度矩阵和荷载向量的并行计算与组装,分块储存在各处理机上,其处理机间通信较少。并在1-4台桌面PC机连接成的局域网,PVM3.4 on W indow2000,VC 6.0并行计算平台上编程对该算法进行了数值试验,得到了较理想的结果。展开更多
Linear precoding methods such as zero-forcing(ZF)are near optimal for downlink massive multi-user multiple input multiple output(MIMO)systems due to their asymptotic channel property.However,as the number of users inc...Linear precoding methods such as zero-forcing(ZF)are near optimal for downlink massive multi-user multiple input multiple output(MIMO)systems due to their asymptotic channel property.However,as the number of users increases,the computational complexity of obtaining the inverse matrix of the gram matrix increases.Forsolving the computational complexity problem,this paper proposes an improved Jacobi(JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems.The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel implementation.However,the conventional JC has poor error performance when the number of users increases,which means that the diagonal dominance component of the gram matrix is reduced.In this paper,the preconditioning method is proposed to improve the error performance.Before executing the JC,the condition number of the linear equation and spectrum radius of the iteration matrix are reduced by multiplying the preconditioning matrix of the linear equation.To further reduce the condition number of the linear equation,this paper proposes a polynomial expansion precondition matrix that supplements diagonal components.The results show that the proposed method provides better performance than other iterative methods and has similar performance to the ZF.展开更多
文摘针对基于PVM的桌面PC机联网而成的网络并行计算环境中,处理机的运算速度较快而处理机间的通信相对较慢,以及微机的内存有限的实际情况,从实用的角度出发,给出了基于PVM的网上求解有限元方程组的并行m-Step Jacob i PCG方法,该算法的矩阵和向量采用行元素相邻单元贡献法实现有限元总体刚度矩阵和荷载向量的并行计算与组装,分块储存在各处理机上,其处理机间通信较少。并在1-4台桌面PC机连接成的局域网,PVM3.4 on W indow2000,VC 6.0并行计算平台上编程对该算法进行了数值试验,得到了较理想的结果。
基金supported by the MSIT(Ministry of Science and ICT),Korea,under the ITRC(Information Technology Research Center)support program(IITP-2019-2018-0-01423)supervised by the IITP(Institute for Information&communications Technology Promotion)+1 种基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2020R1A6A1A03038540).
文摘Linear precoding methods such as zero-forcing(ZF)are near optimal for downlink massive multi-user multiple input multiple output(MIMO)systems due to their asymptotic channel property.However,as the number of users increases,the computational complexity of obtaining the inverse matrix of the gram matrix increases.Forsolving the computational complexity problem,this paper proposes an improved Jacobi(JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems.The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel implementation.However,the conventional JC has poor error performance when the number of users increases,which means that the diagonal dominance component of the gram matrix is reduced.In this paper,the preconditioning method is proposed to improve the error performance.Before executing the JC,the condition number of the linear equation and spectrum radius of the iteration matrix are reduced by multiplying the preconditioning matrix of the linear equation.To further reduce the condition number of the linear equation,this paper proposes a polynomial expansion precondition matrix that supplements diagonal components.The results show that the proposed method provides better performance than other iterative methods and has similar performance to the ZF.
