共查询到19条相似文献,搜索用时 93 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Gaus-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了它的应用范围,数值结果表明了它的有效性和强壮性。 相似文献
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针对运动间断拟合中需频繁更新网格点位置的特点,提出一种基于LU-SGS(lower-upper symmetricGauss-Seidel)迭代方法的非结构弹簧网格运动算法.根据弹簧网格原理构建与网格拓扑关系相对应的稀疏系数矩阵,将LU-SGS思想成功引入动网格迭代算法,并辅以合理的网格运动管理策略,实现动网格的快速迭代.研究表明,在非结构网格下,LU-SGS算法可以满足运动间断拟合的需求,在流场隐式时间推进时,仍能保证获得稳定解;与传统的SOR方法相比,计算时耗减少20%以上. 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(AMG)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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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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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—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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An Algebraic Multigrid Method for Nearly Incompressible Elasticity Problems in Two-Dimensions
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Yingxiong Xiao Shi Shu Hongmei Zhang & Yuan Ouyang 《advances in applied mathematics and mechanics.》2009,1(1):69-88
In this paper, we discuss an algebraic multigrid (AMG) method for
nearly incompressible elasticity problems in two-dimensions. First,
a two-level method is proposed by analyzing the relationship between
the linear finite element space and the quartic finite element
space. By choosing different smoothers, we obtain two types of
two-level methods, namely TL-GS and TL-BGS. The theoretical analysis
and numerical results show that the convergence rates of TL-GS and
TL-BGS are independent of the mesh size and the Young's modulus, and
the convergence of the latter is greatly improved on the order $p$.
However, the convergence of both methods still depends on the
Poisson's ratio. To fix this, we obtain a coarse level matrix with
less rigidity based on selective reduced integration (SRI) method
and get some types of two-level methods by combining different
smoothers. With the existing AMG method used as a solver on the
first coarse level, an AMG method can be finally obtained. Numerical
results show that the resulting AMG method has better efficiency for
nearly incompressible elasticity problems. 相似文献
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推导出代数多重网格法的一个新的插值公式。理论分析和数值计算表明这个公式很有效,且适用性强。推广了原代数多重网格法的应用范围,能够求解一些很病态的代数方程组。 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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Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage
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In studying biomechanical deformation in articular cartilage, the presence of
cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity
problems in which cells are idealized as soft inclusions within a stiff extracellular matrix.
An analytical solution of a soft inclusion problem is derived and used to
evaluate iterative numerical solutions of the associated linear algebraic
system based on discretization via the finite element method, and use of an
iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG).
Accuracy and efficiency of the AMG-PCG algorithm is compared to two other
conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a
modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution.
While all three algorithms are shown to be accurate, the AMG-PCG algorithm
is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased.
In contrast to the other two algorithms, the AMG-PCG algorithm also
exhibits little sensitivity of CPU time and number of iterations to
variations in material properties that are known to significantly affect model variables.
Results demonstrate the benefits of algebraic multigrid preconditioners
for the iterative solution of assembled linear systems based on finite
element modeling of soft elastic inclusion problems and may be particularly
advantageous for large scale problems with many nodal unknowns. 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
n
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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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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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