Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing ...Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.展开更多
In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is als...In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is also used to improve the stability of the algorithm. The computation amount is greatly decreased.展开更多
基于EBE-PCG(element by element-preconditioned conjugate gradient)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高了并行计算的速度和效率,是实现协同优化设计的性能函数快速分析技术的有效途径。文...基于EBE-PCG(element by element-preconditioned conjugate gradient)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高了并行计算的速度和效率,是实现协同优化设计的性能函数快速分析技术的有效途径。文中详细介绍有限元EBE(element by element)的运算方法,给出EBE-PCG并行算法的实现步骤,最后在网络集群环境下,综合运用多种编程语言和分析工具,实现基于EBE-PCG策略的三维有限元并行计算。计算结果表明,该并行算法的计算误差小,并行效率高,适合于性能函数的快速求解。展开更多
A new matrix algebra W, including the set of real symmetric skewcirculant matrices, is introduced. It is proved that all the matrices of W can be simultaneously diagonalized by the discrete W transform matrix. As an a...A new matrix algebra W, including the set of real symmetric skewcirculant matrices, is introduced. It is proved that all the matrices of W can be simultaneously diagonalized by the discrete W transform matrix. As an application, the use of preconditioned iterative method (preconditioner W1Tn belongs to matrix class W) to solve a system of equations with a Toeplitz coefficients matrix is developed. If generating function f（x） is nonnegative piecewise continuous and has enumerable zero points, we conclude that the spectrum of iterative matrix have a cluster at one. The results of numerical tests with this preconditioner are presented.Our preconditioner is comparable, and if f（x） is not smooth that superior, to Strang’s circulant preconditioner and Huckle’s skewcirculant preconditioner.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.5130926141030747+3 种基金41102181and 51121005)the National Basic Research Program of China(973 Program)(No.2011CB013503)the Young Teachers’ Initial Funding Scheme of Sun Yat-sen University(No.39000-1188140)
文摘Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.
基金With the support of the key project of Knowledge Innovation, CAS(KZCX1-y01, KZCX-SW-18), Fund of the China National Natural Sciences and the Daqing Oilfield with Grant No. 49894190
文摘In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is also used to improve the stability of the algorithm. The computation amount is greatly decreased.
文摘基于EBE-PCG(element by element-preconditioned conjugate gradient)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高了并行计算的速度和效率,是实现协同优化设计的性能函数快速分析技术的有效途径。文中详细介绍有限元EBE(element by element)的运算方法,给出EBE-PCG并行算法的实现步骤,最后在网络集群环境下,综合运用多种编程语言和分析工具,实现基于EBE-PCG策略的三维有限元并行计算。计算结果表明,该并行算法的计算误差小,并行效率高,适合于性能函数的快速求解。
文摘A new matrix algebra W, including the set of real symmetric skewcirculant matrices, is introduced. It is proved that all the matrices of W can be simultaneously diagonalized by the discrete W transform matrix. As an application, the use of preconditioned iterative method (preconditioner W1Tn belongs to matrix class W) to solve a system of equations with a Toeplitz coefficients matrix is developed. If generating function f（x） is nonnegative piecewise continuous and has enumerable zero points, we conclude that the spectrum of iterative matrix have a cluster at one. The results of numerical tests with this preconditioner are presented.Our preconditioner is comparable, and if f（x） is not smooth that superior, to Strang’s circulant preconditioner and Huckle’s skewcirculant preconditioner.
