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, we propose an improved preconditioned algorithm for the conjugate gradient squared method (improved PCGS) for the solution of linear equations. Further, the logical structures underlying the formation o...In this paper, we propose an improved preconditioned algorithm for the conjugate gradient squared method (improved PCGS) for the solution of linear equations. Further, the logical structures underlying the formation of this preconditioned algorithm are demonstrated via a number of theorems. This improved PCGS algorithm retains some mathematical properties that are associated with the CGS derivation from the bi-conjugate gradient method under a non-preconditioned system. A series of numerical comparisons with the conventional PCGS illustrate the enhanced effectiveness of our improved scheme with a variety of preconditioners. This logical structure underlying the formation of the improved PCGS brings a spillover effect from various bi-Lanczos-type algorithms with minimal residual operations, because these algorithms were constructed by adopting the idea behind the derivation of CGS. These bi-Lanczos-type algorithms are very important because they are often adopted to solve the systems of linear equations that arise from large-scale numerical simulations.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, we propose an improved preconditioned algorithm for the conjugate gradient squared method (improved PCGS) for the solution of linear equations. Further, the logical structures underlying the formation of this preconditioned algorithm are demonstrated via a number of theorems. This improved PCGS algorithm retains some mathematical properties that are associated with the CGS derivation from the bi-conjugate gradient method under a non-preconditioned system. A series of numerical comparisons with the conventional PCGS illustrate the enhanced effectiveness of our improved scheme with a variety of preconditioners. This logical structure underlying the formation of the improved PCGS brings a spillover effect from various bi-Lanczos-type algorithms with minimal residual operations, because these algorithms were constructed by adopting the idea behind the derivation of CGS. These bi-Lanczos-type algorithms are very important because they are often adopted to solve the systems of linear equations that arise from large-scale numerical simulations.
基金The work was supported in part by Natural Science Foundation of China(10372087) by Natural Science Foundation of China and Associated Foundation of China Academy of Engineering Physics(10376031)
基金Supported by the National Natural Science Foundation of China under Grant(11371075)the research innovation program of Hunan province of China for postgraduate students under Grant(CX2015B374)
