共查询到20条相似文献,搜索用时 15 毫秒
1.
该文讨论了关于 K- S方程的伽辽金方法和非线性伽辽金方法的收敛性和 L2 误差估计 ,并得出误差阶一致的结论 相似文献
2.
加罚Navier—Stokes方程的最佳非线性Galerkin算法 总被引:1,自引:0,他引:1
何银年 《数学物理学报(A辑)》1998,18(3):251-256
该文提出了求解二维加罚Navier-Stokes方程的最佳非线性Galerkin算法.这个算法在于在粗网格有限元空间上求解一非线性子问题,在细网格增量有限元空间Wh上求解一线性子问题.如果线性有限元被使用及,则该算法具有和有限元Galerkin算法同阶的收敛速度.然而该文提出的算法可以节省可观的计算时间. 相似文献
3.
Ismael Herrera Robert Yates 《Numerical Methods for Partial Differential Equations》2005,21(4):672-700
Domain decomposition methods (DDM) have received much attention in recent years. They constitute the most effective means of using parallel computing resources to model continuous systems. However, combining collocation procedures with domain decomposition methods presents complications that must be overcome in order to profit from the advantages of parallel computing. The present paper belongs to a line of research in which a theory that constitutes a general and systematic formulation of discontinuous Galerkin methods (dG) is being investigated. Based on it, a new method of collocation of general applicability, TH‐collocation, was recently introduced. For a broad class of symmetric and positive continuous systems, TH‐collocation yields symmetric and positive matrices. This clears the way for applying effectively DDM and parallel computing, in combination with collocation, to such systems. In this paper the general procedure is explained with some detail and then is applied to develop an effective method for processing elliptic equations of second order. This, by the way, overcomes the difficulties encountered in a previous Herrera and Pinder's article. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005. 相似文献
4.
本文讨论了定常K-S方程关于伽辽金方法和非线性伽辽金方法的收敛性和最大模估计;对相同模数而言,两者的误差阶完全一致,数值结果表明非线性伽辽金方法同样成功地计算出了K-S方程的分歧解,并且在计算时间方面非线性伽辽金方法比伽辽金方法要少得多。 相似文献
5.
In this paper, we consider the Petrov–Galerkin spectral method for fourth‐order elliptic problems on rectangular domains subject to non‐homogeneous Dirichlet boundary conditions. We derive some sharp results on the orthogonal approximations in one and two dimensions, which play important roles in numerical solutions of higher‐order problems. By applying these results to a fourth‐order problem, we establish the H2‐error and L2‐error bounds of the Petrov–Galerkin spectral method. Numerical experiments are provided to illustrate the high accuracy of the proposed method and coincide well with the theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
6.
Masao Fukushima Mounir Haddou Hien Van Nguyen Jean-Jacques Strodiot Takanobu Sugimoto Eiki Yamakawa 《Computational Optimization and Applications》1996,5(1):5-37
In this paper, we propose a parallel decomposition algorithm for solving a class of convex optimization problems, which is broad enough to contain ordinary convex programming problems with a strongly convex objective function. The algorithm is a variant of the trust region method applied to the Fenchel dual of the given problem. We prove global convergence of the algorithm and report some computational experience with the proposed algorithm on the Connection Machine Model CM-5. 相似文献
7.
8.
Selim G. Akl 《BIT Numerical Mathematics》1982,22(2):129-134
The convex hull of a finite set of points in the plane can be computed in constant time using a polynomial number of processors.This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant NSERC - A3336. 相似文献
9.
关于二维Navier-Stokes方程非线性Galerkin校正的注记 总被引:2,自引:0,他引:2
本文在对二维Navier-Stokes方程及其近似惯性流形领域估计的基础上,讨论了非线性Galerkin方法校正量的一种可能的最优选取。 相似文献
10.
YanXu Chi-wangShu 《计算数学(英文版)》2004,22(2):250-274
In this paper, we further develop the local discontinuous Galerkin method to solve three classes of nonlinear wave equations formulated by the general KdV-Burgers type equations, the general fifth-order KdV type equations and the fully nonlinear K(n, n, n) equations, and prove their stability for these general classes of nonlinear equations. The schemes we present extend the previous work of Yan and Shu [30, 31] and of Levy, Shu and Yan [24] on local discontinuous Galerkin method solving partial differential equations with higher spatial derivatives. Numerical examples for nonlinear problems are shown to illustrate the accuracy and capability of the methods. The numerical experiments include stationary solitons, soliton interactions and oscillatory solitary wave solutions.The numerical experiments also include the compacton solutions of a generalized fifthorder KdV equation in which the highest order derivative term is nonlinear and the fully nonlinear K (n, n, n) equations. 相似文献
11.
Farhad Fakhar‐Izadi Mehdi Dehghan 《Mathematical Methods in the Applied Sciences》2013,36(12):1485-1511
The pseudo‐spectral Legendre–Galerkin method (PS‐LGM) is applied to solve a nonlinear partial integro‐differential equation arising in population dynamics. This equation is a competition model in which similar individuals are competing for the same resources. It is a kind of reaction–diffusion equation with integral term corresponding to nonlocal consumption of resources. The proposed method is based on the Legendre–Galerkin formulation for the linear terms and interpolation operator at the Chebyshev–Gauss–Lobatto (CGL) points for the nonlinear terms. Also, the integral term, which is a kind of convolution, is directly computed by a fast and accurate method based on CGL interpolation operator, and thus, the use of any quadrature formula in its computation is avoided. The main difference of the PS‐LGM presented in the current paper with the classic LGM is in treating the nonlinear terms and imposing boundary conditions. Indeed, in the PS‐LGM, the nonlinear terms are efficiently handled using the CGL points, and also the boundary conditions are imposed strongly as collocation methods. Combination of the PS‐LGM with a semi‐implicit time integration method such as second‐order backward differentiation formula and Adams‐Bashforth method leads to reducing the complexity of computations and obtaining a linear algebraic system of equations with banded coefficient matrix. The desired equation is considered on one and two‐dimensional spatial domains. Efficiency, accuracy, and convergence of the proposed method are demonstrated numerically in both cases. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
We consider a scalar advection-diffusion problem and a recently proposed discontinuous Galerkin approximation, which employs discontinuous finite element spaces and suitable bilinear forms containing interface terms that ensure consistency. For the corresponding sparse, nonsymmetric linear system, we propose and study an additive, two-level overlapping Schwarz preconditioner, consisting of a coarse problem on a coarse triangulation and local solvers associated to a family of subdomains. This is a generalization of the corresponding overlapping method for approximations on continuous finite element spaces. Related to the lack of continuity of our approximation spaces, some interesting new features arise in our generalization, which have no analog in the conforming case. We prove an upper bound for the number of iterations obtained by using this preconditioner with GMRES, which is independent of the number of degrees of freedom of the original problem and the number of subdomains. The performance of the method is illustrated by several numerical experiments for different test problems using linear finite elements in two dimensions.
13.
Automatic parallel generation of tetrahedral grids by using a domain decomposition approach 总被引:1,自引:0,他引:1
H. Andrä O. N. Gluchshenko E. G. Ivanov A. N. Kudryavtsev 《Computational Mathematics and Mathematical Physics》2008,48(8):1367-1375
An algorithm for the automatic parallel generation of three-dimensional unstructured grids based on geometric domain decomposition is proposed. A software package based on this algorithm is described. Examples of generating meshes for some application problems on a multiprocessor computer are presented. It is shown that the parallel algorithm can significantly (by a factor of several tens) reduce the mesh generation time. Moreover, it can easily generate meshes with as many as 5 × 107 elements, which can hardly be generated sequentially. Issues concerning the speedup and the improvement of the efficiency of the computations and of the quality of the resulting meshes are discussed. 相似文献
14.
Yinnian He 《Numerical Methods for Partial Differential Equations》2008,24(1):79-103
In this article we consider the spectral Galerkin method with the implicit/explicit Euler scheme for the two‐dimensional Navier–Stokes equations with the L2 initial data. Due to the poor smoothness of the solution on [0,1), we use the the spectral Galerkin method based on high‐dimensional spectral space HM and small time step Δt2 on this interval. While on [1,∞), we use the spectral Galerkin method based on low‐dimensional spectral space Hm(m = O(M1/2)) and large time step Δt. For the spectral Galerkin method, we provide the standard H2‐stability and the L2‐error analysis. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 相似文献
15.
对称三对角线特征值问题的一个并行修正拟Laguerre算法 总被引:1,自引:0,他引:1
李桂华 《纯粹数学与应用数学》2001,17(3):233-237
在拟Laguerre算法的基础上,提出了用修正拟Lagureer算法来求求解对称三角线特征值问题,并给出了算法的并行实现。 相似文献
16.
In this article we consider the application of Schwarz-type domain decomposition preconditioners
to the discontinuous Galerkin finite element approximation of the compressible
Navier-Stokes equations. To discretize this system of conservation laws,
we exploit the (adjoint consistent) symmetric version of the
interior penalty discontinuous Galerkin finite element method.
To define the necessary coarse-level solver required for the definition
of the proposed preconditioner, we exploit ideas from composite finite
element methods, which allow for the definition of finite element schemes
on general meshes consisting of polygonal (agglomerated) elements.
The practical performance of the proposed preconditioner is demonstrated for a
series of viscous test cases in both two- and three-dimensions. 相似文献
17.
基于一个含有控制参数的修正Lagrangian函数,该文建立了一个求解非线性约束优化问题的修正Lagrangian算法.在一些适当的条件下,证明了控制参数存在一个阀值,当控制参数小于这一阀值时,由这一算法产生的序列解局部收敛于问题的Kuhn-Tucker点,并且建立了解的误差上界.最后给出一些约束优化问题的数值结果. 相似文献
18.
Kang Li & Zhijun Tan 《高等学校计算数学学报(英文版)》2020,13(4):1050-1067
A two-grid finite element approximation is studied in the fully discrete
scheme obtained by discretizing in both space and time for a nonlinear hyperbolic
equation. The main idea of two-grid methods is to use a coarse-grid space ($S_H$) to
produce a rough approximation for the solution of nonlinear hyperbolic problems
and then use it as the initial guess on the fine-grid space ($S_h$). Error estimates are
presented in $H^1$-norm, which show that two-grid methods can achieve the optimal
convergence order as long as the two different girds satisfy $h$ = $\mathcal{O}$($H^2$). With the
proposed techniques, we can obtain the same accuracy as standard finite element
methods, and also save lots of time in calculation. Theoretical analyses and numerical examples are presented to confirm the methods. 相似文献
19.
In this paper we develop a fast Petrov–Galerkin method for solving the generalized airfoil equation using the Chebyshev polynomials. The conventional method for solving this equation leads to a linear system with a dense coefficient matrix. When the order of the linear system is large, the computational complexity for solving the corresponding linear system is huge. For this we propose the matrix truncation strategy, which compresses the dense coefficient matrix into a sparse matrix. We prove that the truncated method preserves the optimal order of the approximate solution for the conventional method. Moreover, we solve the truncated equation using the multilevel augmentation method. The computational complexity for solving this truncated linear system is estimated to be linear up to a logarithmic factor. 相似文献
20.
A smoothing self-adaptive Levenberg-Marquardt algorithm for solving system of nonlinear inequalities
In this paper, we consider the smoothing self-adaptive Levenberg-Marquardt algorithm for the system of nonlinear inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations H(x) = 0. A smoothing self-adaptive Levenberg-Marquardt algorithm is proposed for solving the system of nonlinear inequalities based on the new smoothing function. The Levenberg-Marquardt parameter μk is chosen as the product of μk = ∥Hk∥δ with δ ∈ (0, 2] being a positive constant. We will show that if ∥Hk∥δ provides a local error bound, which is weaker than the non-singularity, the proposed method converges superlinearly to the solution for δ ∈ (0, 1), while quadratically for δ ∈ [1, 2]. Numerical results show that the new method performs very well for system of inequalities. 相似文献