共查询到20条相似文献,搜索用时 15 毫秒
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对一般的热机械问题提出了一种有效的数值方法,并对二维的热弹性问题进行了测试.该方法的基本思路是将描述热机械耦合问题的偏微分方程进行降阶,使之成为一组微分代数方程,应力应变关系被写成代数方程.所得到的微分代数系统采用全隐式的向后差分公式进行求解.对该方法进行了详细的说明.为了验证该方法的有效性,将其应用于一个动态非耦合的热弹性问题的求解和一个耦合的二维热弹性问题的求解. 相似文献
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We consider the problem of estimating the magnitude of the error of an iterative linear solver after k iterations. Assuming that the initial error can be described using a probability distribution we derive L2-estimates for the magnitude of the error in the average case. In Part 1 the ideas are presented and applied to a simple splitting method, while Part 2 extends the same ideas to the conjugate gradient method.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
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Nicola Secomandi 《Journal of Heuristics》2003,9(4):321-352
The paper considers sequencing problems, the traveling salesman problem being their natural representative. It studies a rollout approach that employs a cyclic heuristic as its main base algorithm. The theoretical analysis establishes that it is guaranteed to improve (at least in a weak sense) the quality of any feasible solution to a given sequencing problem. Besides other applications, the paper shows that it is well suited for applications that are embedded in dynamic and stochastic environments. The computational performance of the approach is investigated with applications to two stochastic routing problems. The dynamic version of the heuristic appears to be the first algorithm available in the literature to approximately solve a variant of one of these problems. 相似文献
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We illustrate the use of white noise analysis in the solution of stochastic partial differential equations by explicitly solving the stochastic Neumann boundary-value problem LU(x)–c(x)U(x)=0, xDR
d
,(x)U(x)=–W(x), xD, where L is a uniformly elliptic linear partial differential operator and W(x), xR
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, is d-parameter white noise. 相似文献
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We propose a novel solution approach for the class of two-stage nonlinear integer stochastic programming models. These problems
are characterized by large scale dimensions, as the number of constraints and variables depend on the number of realizations
(scenarios) used to capture the underlying distributions of the random data. In addition, the integrality constraints on the decision
variables make the solution process even much more difficult preventing the application of general purpose solvers. The proposed
solution approach integrates the branch-and-bound framework with the interior point method. The main advantage of this choice
is the effective exploitation of the specific structure exhibited by the different subproblems at each node of the search
tree. A specifically designed warm start procedure and an early branching technique improve the overall efficiency. Our contribution
is well founded from a theoretical point of view and is characterized by good computational efficiency, without any loss in
terms of effectiveness. Some preliminary numerical results, obtained by solving a challenging real-life problem, prove the
robustness and the efficiency of the proposed approach. 相似文献
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In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the text.The homogenized limit is then computed by using a perturbation approach.This computation requires repeatedly solving a corrector-like equation for various configurations of the material.For this purpose,the reduced basis approach is employed and adapted to the specific context.The authors perform numerical tests that demonstrate the efficiency of the approach. 相似文献
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To solve the multipoint boundary-value problem (MPBVP) associated with a constrained optimal control problem, one needs a good guess not only for the state but also for the costate variables. A direct multiple shooting method is described, which yields approximations of the optimal state and control histories. The Kuhn–Tucker conditions for the optimal parametric control are rewritten using adjoint variables. From this representation, estimates for the adjoint variables at the multiple shooting nodes are derived. The estimates are proved to be consistent, in the sense that they converge toward the MPBVP solution if the parametrization is refined. An optimal aircraft maneuver demonstrates the transition from the direct to the indirect method. 相似文献
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利用严格对角占优M-矩阵的逆矩阵的无穷大范数的范围,给出了B-矩阵线性互补问题误差界新的估计式.相应数值算例表明了结果的有效性. 相似文献
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We analyze the discretization errors of discontinuous Galerkin solutions of steady two-dimensional hyperbolic conservation laws on unstructured meshes. We show that the leading term of the error on each element is a linear combination of orthogonal polynomials of degrees p and p+1. We further show that there is a strong superconvergence property at the outflow edge(s) of each element where the average discretization error converges as O(h
2p+1) compared to a global rate of O(h
p+1). Our analyses apply to both linear and nonlinear conservation laws with smooth solutions. We show how to use our theory to construct efficient and asymptotically exact a posteriori discretization error estimates and we apply these to some examples. 相似文献
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Frederic Bonnans Stefania Maroso Housnaa Zidani 《Applied Mathematics and Optimization》2007,55(3):327-357
We obtain error bounds for monotone approximation schemes of a stochastic impulse control problem. This is an extension of
the theory for error estimates for the Hamilton-Jacobi-Bellman equation. We obtain almost the same estimate on the rate of
convergence as in the equation without impulsions [2], [3]. 相似文献
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Computational Mathematics and Mathematical Physics - A new algorithm for a posteriori estimation of the error in solutions to linear operator equations of the first kind in a Hilbert space is... 相似文献
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For the nonlinear complementarity problem, we derive norm bounds for the error of an approximate solution, generalizing the known results for the linear case. Furthermore, we present a linear system with interval data, whose solution set contains the error of an approximate solution. We perform extensive numerical tests and compare the different approaches. 相似文献