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 this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the ite...In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, ft is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.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
Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image...Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.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
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
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.
文摘In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, ft is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.
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.
基金supported by the National Basic Research Program (No.2005CB321702)the National Outstanding Young Scientist Foundation(No. 10525102)the Specialized Research Grant for High Educational Doctoral Program(Nos. 20090211120011 and LZULL200909),Hong Kong RGC grants and HKBU FRGs
文摘Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.
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。
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。
