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1.
并行二级多分裂迭代方法   总被引:8,自引:0,他引:8       下载免费PDF全文
谷同祥  刘兴平 《计算数学》1998,20(2):153-166
1.二级多分裂迭代法本义考虑求解线性代数方程组的几种同步与异步二级多分裂迭代法,其中A为nXn非奇异矩阵.多分别选代法考虑A的多种分裂用IF负对角权矩阵EI(ZEI一川进行组合,可得l=1.多分裂迭代法任给刘始向量。0对k—1,2,…,直到收敛如果(1.2)中对所有l,MI=Dilg(Al;…;A。。),EI=(O,…,O,I,O,…,O),则多分裂迭代法退化成块Jacobi迭代法,同样,多分裂迭代法具有自然的并行性,若EI的某个对角元为0,则从的对应分量无需计算.当然,(1.3)可用直接法精确求解,如Gauss消去法,LU分解法等,但有…  相似文献
2.
红黑排序混合算法收敛速度分析   总被引:6,自引:0,他引:6       下载免费PDF全文
The algorithm of applying the block Gauss elimination to the Red-Black or-dering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid Red-Black Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale prob-lem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural order-ing methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods.  相似文献
3.
非线性波动方程的交替显-隐差分方法   总被引:4,自引:0,他引:4       下载免费PDF全文
蔚喜军 《计算数学》1998,20(3):225-238
1.引言众所周知,非线性波动方程在自然科学领域有广泛的物理背景,诸如物理、化学反应方程,机械动力学方程,地球物理与大气海洋方程等.差分方法求解非线性波动方程已有研究,如[1]和IZ]就给出了非线性波动方程组的显式和隐式差分格式以及收敛性分析.虽然古典的显式差分格式易于并行计算,但是它的稳定性条件差(条件稳定);古典的隐式差分格式稳定性条件好(绝对稳定);但对非线性问题,一般需要线性化,然后求解一个线性代数方程组,并行计算能力差.本文正是在这样一种前题下,给出了一维问题的一种交替分段显一隐差分格式,…  相似文献
4.
非线性抛物组非均匀网格差分解的唯一性和稳定性   总被引:2,自引:0,他引:2       下载免费PDF全文
袁光伟 《计算数学》2000,22(2):139-150
1.引言 1.对一维非线性抛物组,在文献山中已构造一般非均匀网格差分格式,其中差分逼近的组合系数对不同的网格点和不同的网格层可以不同,并且运用不动点原理证明了差分解的存在性和收敛性.在非均匀网格差分格式中差分逼近的组合系数为常数的情形,文献[2]证明了具有有界二阶差商的离散向量解的存在性、唯一性和稳定性.本文将对文献[1]中构造的一般非均匀网格差分格式,证明所得到的差分解的唯一性和稳定性. 考虑如下非线性抛物组其中是未知的m-维向量函数是给定的矩阵函数,j(x,t,u,p)。是给定的m-维向量函数…  相似文献
5.
A cell-centered lagrangian scheme in two-dimensional cylindrical geometry   总被引:2,自引:0,他引:2  
A new Lagrangian cell-centered scheme for two-dimensional compressible flows in planar geometry is proposed by Maire et al.The main new feature of the algorithm is that the vertex velocities and the numerical fluxes through the cell interfaces are all evaluated in a coherent manner contrary to standard approaches.In this paper the method introduced by Maire et al.is extended for the equations of Lagrangian gas dynamics in cylindrical symmetry.Two different schemes are proposed,whose difference is that one uses volume weighting and the other area weighting in the discretization of the momentum equation.In the both schemes the conservation of total energy is ensured,and the nodal solver is adopted which has the same formulation as that in Cartesian coordinates.The volume weighting scheme preserves the momentum conservation and the area-weighting scheme preserves spherical symmetry.The numerical examples demonstrate our theoretical considerations and the robustness of the new method.  相似文献
6.
带雪崩项的半导体方程的瞬态解   总被引:1,自引:0,他引:1  
研究带雪崩项的半导体方程的混合初边值问题.采用逼近过程和先验估计,在一定条件下,证明了该问题整体弱解的存在性或局部弱解的存在性.  相似文献
7.
In this paper we investigate the superconvergence phenomenonof the second-order quadrature formula of Newton–Cotestype for the computation of finite-part integrals with a second-ordersingularity on an interval. Superconvergence points are foundand a superconvergence estimate is obtained. The validity ofthe theoretical result is demonstrated by numerical experiments.  相似文献
8.
ATTRACTOR FOR WEAKLY DAMPED DRIVEN LONG WAVE-SHORT WAVE RESONANCE EQUATION   总被引:1,自引:0,他引:1  
The existence of solution and universal attractor for weakly damped driven long wave-short wave resonance equation are obtained.  相似文献
9.
An improved GPBi-CG algorithm suitable for distributed parallel computing   总被引:1,自引:0,他引:1  
An improved generalized product-type bi-conjugate gradient (GPBi-CG) method (IGPBi-CG method, in brief) for solving large sparse linear systems with unsymmetrical coefficient matrices is proposed for distributed parallel environments. The method reduces three global synchronization points to two by reconstructing GPBi-CG method and the communication time required for the inner product can be efficiently overlapped with useful computation. The cost is only slightly increased computation time, which can be ignored compared with the reduction of communication time. Performance and isoefficiency analysis show that the IGPBi-CG method has better parallelism and scalability than the GPBi-CG method. Numerical experiments show that the scalability can be improved by a factor greater than 1.5 and the improvement in parallel communication performance approaches 33.3˙%.  相似文献
10.
We consider the general (composite) Newton-Cotes method for the computation of Cauchy principal value integrals and focus on its pointwise superconvergence phenomenon, which means that the rate of convergence of the Newton-Cotes quadrature rule is higher than what is globally possible when the singular point coincides with some a priori known point. The necessary and sufficient conditions satisfied by the superconvergence point are given. Moreover, the superconvergence estimate is obtained and the properties of the superconvergence points are investigated. Finally, some numerical examples are provided to validate the theoretical results.  相似文献
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