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61.
The parameterized Uzawa preconditioners for saddle point problems are studied in this paper. The eigenvalues of the preconditioned matrix are located in (0, 2) by choosing the suitable parameters. Furthermore, we give two strategies to optimize the rate of convergence by finding the suitable values of parameters. Numerical computations show that the parameterized Uzawa preconditioners can lead to practical and effective preconditioned GMRES methods for solving the saddle point problems. 相似文献
62.
We prove the superconvergence of Morley element and the incomplete biquadratic nonconforming element for the plate bending
problem. Under uniform rectangular meshes, we obtain a superconvergence property at the symmetric points of the elements and
a global superconvergent result by a proper postprocessing method.
The research is supported by the Special Funds For Major State Basic Research Project (No. 2005CB321701). 相似文献
63.
It has long been recognized that many direct parallel tridiagonal solvers are only efficient for solving a single tridiagonal equation of large sizes, and they become inefficient when naively used in a three-dimensional ADI solver. In order to improve the parallel efficiency of an ADI solver using a direct parallel solver, we implement the single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication costs. The measured performances show that the longest allowable message vector length (MVL) is not necessarily the best choice. To understand this observation and optimize the performance, we propose an improved model that takes the cache effect into consideration. The optimal MVL for achieving the best performance is shown to depend on number of processors and grid sizes. Similar dependence of the optimal MVL is also found for the popular block pipelined method. 相似文献
64.
Zhiru REN 《Frontiers of Mathematics in China》2012,7(6):1151-1168
The linear third-order ordinary differential equation (ODE) can be transformed into a system of two second-order ODEs by introducing a variable replacement, which is different from the common order-reduced approach. We choose the functions p(x) and q(x) in the variable replacement to get different cases of the special order-reduced system for the linear third-order ODE. We analyze the numerical behavior and algebraic properties of the systems of linear equations resulting from the sinc discretizations of these special second-order ODE systems. Then the block-diagonal preconditioner is used to accelerate the convergence of the Krylov subspace iteration methods for solving the discretized system of linear equation. Numerical results show that these order-reduced methods are effective for solving the linear third-order ODEs. 相似文献
65.
In order to solve the time-dependent Stokes equation, we follow the “Method of Lines” to obtain structured linear constant-coefficient differential–algebraic equations (DAEs). By taking advantage of the structure, we propose a class of waveform relaxation methods, called continuous-time accelerated block SOR (CABSOR) methods, for solving the obtained DAEs. The new methods are theoretically analyzed. The theory is applied to a two-dimensional time-dependent Stokes equation and verified by numerical experiments. 相似文献
66.
Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems 总被引:4,自引:0,他引:4
In this paper, some local and parallel discretizations and adaptive finite element algorithms are proposed and analyzed for nonlinear elliptic boundary value problems in both two and three dimensions. The main technique is to use a standard finite element discretization on a coarse grid to approximate low frequencies and then to apply some linearized discretization on a fine grid to correct the resulted residual (which contains mostly high frequencies) by some local/parallel procedures. The theoretical tools for analyzing these methods are some local a priori and a posteriori error estimates for finite element solutions on general shape-regular grids that are also obtained in this paper. 相似文献
67.
A three-parameter family of nonlinear conjugate gradient methods 总被引:3,自引:0,他引:3
In this paper, we propose a three-parameter family of conjugate gradient methods for unconstrained optimization. The three-parameter family of methods not only includes the already existing six practical nonlinear conjugate gradient methods, but subsumes some other families of nonlinear conjugate gradient methods as its subfamilies. With Powell's restart criterion, the three-parameter family of methods with the strong Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the three-parameter family of methods. This paper can also be regarded as a brief review on nonlinear conjugate gradient methods.
68.
On the truncated conjugate gradient method 总被引:7,自引:0,他引:7
Y. Yuan 《Mathematical Programming》2000,87(3):561-573
In this paper, we consider the truncated conjugate gradient method for minimizing a convex quadratic function subject to a
ball trust region constraint. It is shown that the reduction in the objective function by the solution obtained by the truncated
CG method is at least half of the reduction by the global minimizer in the trust region.
Received January 19, 1999 / Revised version received October 1, 1999?Published online November 30, 1999 相似文献
69.
《Applied Mathematics Letters》2000,13(2):131-137
The existence of almost periodic, asymptotically almost periodic, and pseudo almost periodic solutions of differential equations with piecewise constant argument is characterized in terms of almost periodic, asymptotically, and pseudo almost periodic sequences. Thus Meisters's and Opial's theorems are extended. 相似文献
70.
NONNESTED MULTILEVEL PRECONDITIONING METHODS WITH SIMPLE AND IDENTICAL COARSE MESH CORRECTION SPACES
Li Likang 《高等学校计算数学学报(英文版)》2000,9(1):19-36
1 IntroductionMultilevelmethodshavebecomesomeofthemostpopularmethodsforsolvinglargesystemoflinearequationsresultingfromthefiniteelementdiscretizationofpartialdifferentialequations.ThepioneerworkofmultilevelmethodsistheYserentant’sHierarchicalbasismeth… 相似文献