共查询到20条相似文献,搜索用时 78 毫秒
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提出了代数多重网格法(AMG)的一种新算法。新算法改进了插值公式和粗网格方程,并把它应用到求解一维的分裂格式Euler方程。数值结果表明,对于具有高CFL条件数的Euler方程,代数多重网格法可以求解;对于Gauss-Seidel方法求解不能收敛的代数方程组,代数多重网格法求解可以收敛。新算法改进了代数多重网格法的收敛性和扩展和它的应用范围,数值结果表明了它的有效性和强壮性。 相似文献
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在基于漂移-扩散模型的三维半导体器件数值模拟中,通过有限体积法进行数值离散,采用完全耦合的牛顿迭代求解非线性代数方程组,并使用基于代数多重网格预条件子的GMRES方法求解牛顿迭代中的线性方程组,构造一种稳健且高度可扩展的非结构四面体网格上求解半导体方程的并行算法.基于PHG平台实现该算法的并行计算程序,并对PN结和MOS场效应晶体管等问题进行了最大网格规模达到5亿单元、最大并行规模达到1 024进程的大规模数值模拟实验,结果表明,该算法计算效率高,可扩展性好. 相似文献
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求解二维三温辐射扩散方程组的一种代数两层迭代方法 总被引:2,自引:2,他引:0
在二维三温辐射扩散方程离散代数方程组的求解中,由于光子、电子和离子温度之间存在耦合关系,而且三个温度在同种介质中有不同的扩散性质,使得经典的代数多重网格(AMC)方法难以直接应用.基于特殊粗化策略,在粗网格层解除了这种耦合关系,得到一种代数两层网格方法,而粗网格方程由经典AMG方法求解.将这一算法具体应用于JFNK(Jacobian自由的Newton-Krylov)框架中预处理方程的求解,并基于该框架求解二维三温辐射扩散方程组.数值结果显示了算法的可扩展性和健壮性. 相似文献
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采用光谱分析技术,系列研究了已有代数迭代重建算法,并进一步研制了改进算法一简单自相关代数迭代重建算法(SSART).采用数值模拟的方法模拟重建一个含遮挡物场,研究了SSART模拟效果和重建精度.作为对照,分析了已有的传统代数迭代算法同条件下的重建结果,包括基本代数迭代重建算法(ART)、联合代数迭代重建法(SART)和改进的联合代数迭代重建法(MSART).重建精度用均方误差(MSE),绝对平均误差(AVE)和峰值相对误差(PE)三种误差指数标定.结果发现,SSART重建结果的三种误差指数都明显减小,其中MSE在10-4数量级上比ART的降低了26.6%,PE在10-2数量级降低了77.6%.因此,SSART重建含遮挡物模型场时,重建精度大幅度提高,重建效果明显改善,对传统代数迭代重建算法显著改进. 相似文献
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P. Thum T. Clees G. Weyns G. Nelissen J. Deconinck 《Journal of computational physics》2010,229(19):7260-7276
The article discusses components and performance of an algebraic multigrid (AMG) preconditioner for the fully coupled multi-ion transport and reaction model (MITReM) with nonlinear boundary conditions, important for electrochemical modeling. The governing partial differential equations (PDEs) are discretized in space by a combined finite element and residual distribution method. Solution of the discrete system is obtained by means of a Newton-based nonlinear solver, and an AMG-preconditioned BICGSTAB Krylov linear solver. The presented AMG preconditioner is based on so-called point-based classical AMG. The linear solver is compared to a standard direct and several one-level iterative solvers for a range of geometries and chemical systems with scientific and industrial relevance. The results indicate that point-based AMG methods, carefully designed, are an attractive alternative to more commonly employed numerical methods for the simulation of complex electrochemical processes. 相似文献
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The algebraic method of perturbation theory is used to solve problems in molecular spectroscopy. Formulas for the shifts in the band centers, changes of the form factors of excited vibrational transitions, and changes of the components of the kinematic interaction matrix are derived by this method for the nth order of perturbation theory. 相似文献
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研究了由扩散张量导出的各向异性扩散的图像处理模型,并构造了隐式差分格式,形成了有13条对角线的大型稀疏矩阵.利用代数多重网格法求解了这个线性代数方程组.并进行了数值试验. 相似文献
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Shlomy Shitrit David Sidilkover Alexander Gelfgat 《Journal of computational physics》2011,230(4):1707-1729
This article presents the latest developments of an algebraic multigrid (AMG) based on full potential equation (FPE) solver for transonic flow problems with emphasis on advanced applications. The mathematical difficulties of the problem are associated with the fact that the governing equation changes its type from elliptic (subsonic flow) to hyperbolic (supersonic flow). The flow solver is capable of dealing with flows from subsonic to transonic and supersonic conditions and is based on structured body-fitted grids approach for treating complex geometries. The computational method was demonstrated on a variety of problems to be capable of predicting the shock formation and achieving residual reduction of roughly an order of magnitude per cycle both for elliptic and hyperbolic problems, through the entire range of flow regimes, independent of the problem size (resolution). 相似文献
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Recent results concerning isometric embeddings of charged spherically symmetric space-times as algebraic 4-surfaces of a pseudo-Euclidean
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are given. Several problems arising in algebraic isometric embeddings of space-times with horizons are analyzed by studying the Reissner-Nordström solution. The connection between the images of radial null geodesics and the possibility of extending the algebraic isometric embedding through a horizon is studied in detail. 相似文献
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针对光催化制氢反应器内液固两相流的特点,运用代数滑移模型,对反应器内的催化剂颗粒-水两相流动进行了数值模拟。采用分块的结构化网格,并运用多重网格方法进行求解。通过与前人实验中压力梯度结果的比较,对模型进行了验证,并最终得到了反应器内催化剂颗粒的典型分布及相应的类型图。 相似文献
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The Shape invariant method has the algebraic structure and its algebras are infinite-dimensional. These algebras are converted
into finite-dimensional under conditions. Based on the property of this method we obtain the algebraic structure of some physical
potentials in the s-wave Klein-Gordon equation with scalar and vector potential which satisfy the Shape invariant condition. 相似文献
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M Bednář 《Annals of Physics》1973,75(2):305-331
Nonrelativistic models with modified Coulomb potentials are solved by an algebraic method based on SO(4,2) dynamical group. The nonrelativistic model with Yukawa long-range potential and the Stark effect in the nonrelativistic hydrogen atom in the homogeneous and inhomogeneous external electrostatic fields are studied in details. The algebraic method for the Dirac and Klein-Gordon relativistic hydrogen atom as well as relativistic models with the rotationally symmetric modified Coulomb potentials are also discussed. 相似文献
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Raymon A. d'Inverno 《General Relativity and Gravitation》1975,6(6):567-593
The purpose of this paper is to bring to the attention of potential users the existence of algebraic computing systems, and to illustrate their use by reviewing a number of problems for which such a system has been successfully used in General Relativity. In addition, some remarks are included which may be of help in the future design of these systems. 相似文献
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The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves.From quasi-geostrophic potential vorticity equation,basing on the multiple-scale method,an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers(KdV-B-O-Burgers) equation is obtained.This equation has not been previously derived for Rossby waves.By analysis and calculation,four conservation laws associated with the above equation are first obtained.With the help of pseudo-spectral method,the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied.The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves. 相似文献