共查询到19条相似文献,搜索用时 70 毫秒
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空间-时间守恒(STC)格式是近年来发展出的一种计算格式,在现有的STC格式构造过程中,流动变量在解元中的分布都用其一阶Taylor展开式来表示.STC格式的精度与所采用的Taylor展开式的阶数有关.该文采用流动变量的二阶Taylor展开式来表示其在解元上的分布、构造出了求解一维Euler方程的STC格式.用该格式对几个问题进行了计算,将计算结果与精确解进行了比较,比较表明该格式有较高的精度. 相似文献
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该文叙述的是把多重网格法应用于反应堆扩散方程的一个准备性工作。我们应用V循环和W循环的多重网格法求解一个模型问题,并与SOR方法进行了比较。数值结果表明,W循环的多重网格法要比SOR方法快四倍。 相似文献
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提出一种校正AMG方法来求解排队模型。该方法对一般AMG方法的限制算子进行了改进,从而在求解过程中保留了问题的奇异性。计算结果表明改进后的方法加快了收敛速度,提高了解的精度。 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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采用多重网格法(MG)和对称性理论以及密度泛函理论中著名的Kohn-Sham 方程,开发了一种计算具有一定对称性的原子簇的电子结构的方法,并对H2 分子的基态能进行了实际的计算,并与用其他理论计算得到的结果进行了比较。 相似文献
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Zhi Wang Quan Hu Xiao-Fang Zhu Bin Li Yu-Lu Hu Tao Huang Zhong-Hai Yang Liang Li 《Entropy (Basel, Switzerland)》2022,24(8)
At present, electron optical simulator (EOS) takes a long time to solve linear FEM systems. The algebraic multigrid preconditioned conjugate gradient (AMGPCG) method can improve the efficiency of solving systems. This paper is focused on the implementation of the AMGPCG method in EOS. The aggregation-based scheme, which uses two passes of a pairwise matching algorithm and the K-cyle scheme, is adopted in the aggregation-based algebraic multigrid method. Numerical experiments show the advantages and disadvantages of the AMG algorithm in peak memory and solving efficiency. The AMGPCG is more efficient than the iterative methods used in the past and only needs one coarsening when EOS computes the particle motion trajectory. 相似文献
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针对二维非定常半线性扩散反应方程,空间导数项采用四阶紧致差分公式离散,时间导数项采用四阶向后Euler公式进行离散,提出一种无条件稳定的高精度五层全隐格式.格式截断误差为O(τ4+τ2h2+h4),即时间和空间均具有四阶精度.对于第一、二、三时间层采用Crank-Nicolson方法进行离散,并采用Richardson外推公式将启动层时间精度外推到四阶.建立适用于该格式的多重网格方法,加快在每个时间层上迭代求解代数方程组的收敛速度,提高计算效率.最后通过数值实验验证格式的精确性和稳定性以及多重网格方法的高效性. 相似文献
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An Algebraic Multigrid Method for Nearly Incompressible Elasticity Problems in Two-Dimensions 下载免费PDF全文
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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求解Euler方程的隐式无网格算法 总被引:1,自引:1,他引:0
研究了求解Eluer方程的稳式无网格算法,用点云离散计算区域,代替通常的网格划分;在当地点云上,引入二次平方极小曲面逼近计算空间导数,用Roe的近似Riemann解确定通量;并用LU-SGS算法求解离散得到的Euler方程稳式时间后差联立方程组,数值模拟了二维翼型跨音速绕流,由于无网格算法区域离散只涉及点云,具有灵活性,适合处理复杂的气动外形。 相似文献
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ZHAO Xue-Qin ZHI Hong-Yan 《理论物理通讯》2007,48(5):781-786
A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations (NLEEs). For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinear partial differential equations. The key idea of this method is to introduce an auxiliary ordinary differential equation which is regarded as an extended elliptic equation and whose degree r is expanded to the case of r > 4. The efficiency of the method is demonstrated by the KdV equation and the variant Boussinesq equations. The results indicate that the method not only offers all solutions obtained by using Fu's and Fan's methods, but also some new solutions. 相似文献
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An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinear partial differential equations. The key idea of this method is to introduce an auxiliary ordinary differential equation which is regarded as an extended elliptic equation and
whose degree r is expanded to the case of r>4. The efficiency of the
method is demonstrated by the KdV equation and the variant Boussinesq
equations. The results indicate that the method not only offers all
solutions obtained by using Fu's and Fan's methods, but also some new solutions. 相似文献