Weak order stochastic Runge–Kutta methods for commutative stochastic differential equations

A new explicit stochastic Runge–Kutta scheme of weak order 2 is proposed under a commutativity condition, which is derivative-free and which attains order 4 for ordinary differential equations. The weak order conditions are derived by utilizing multi-colored rooted tree analysis and a solution is found in a transparent way. The scheme is compared with other derivative-free and weak second order schemes in numerical experiments.     

Treatment of numerical diffusion in strong convective flows

A three-dimensional extension of the QUICK scheme adapted for the finite volume method and non-uniform grids is presented to handle convection-diffusion problems for high Peclet numbers and steep gradients. The algorithm is based on three-dimensional quadratic interpolation functions in which the transverse curvature terms are maintained and the diagonal dominance of the coefficient matrix is preserved. All formulae are explicitly given in an appendix. Results obtained with the classical upwind (UDS), the simplified QUICK (transverse terms neglected) and the present full QUICK schemes are given for two benchmark problems, one two-dimensional, steady state and the other three-dimensional, unsteady state. Both QUICK schemes are shown to give superior solutions compared with the UDS in terms of accuracy and efficiency. The full QUICK scheme performs better than the simplified QUICK, giving even for coarse grids acceptable results closer to the analytical solutions, while the computational time is not affected much.     

A wavelet filter enhancement scheme with a fast integral B-wavelet transform and pyramidal multi-B-wavelet algorithm

A construction paradigm is proposed to refine a class of wavelet bases such that the filter characteristics are enhanced. In particular, it is shown that the entire Mth order B-wavelet family belong to this class. Exploiting some recent work, a fast integral wavelet transform is found for the refined B-wavelet family. Moreover, this refined basis can be placed into the setting of a multiresolution analysis that has a multiplicity greater than one. Accordingly, a fast, discrete, pyramidal algorithm is realised.     

抛物型方程非齐次边值问题的推广型LOD有限差分及有限元格式

1引言本文考虑区域Ω=[0,1]~d(d=2,3)上的非齐次抛物型方程第一边值问题(?)-C_1△u C_2u=f(x,t),x∈Ω,t∈(0,T],(1．1) u(x,0)=u_0(x),x∈Ω,(1．2) u(x,t)=(?)(x,t),x∈(?)Ω,t∈(0,T],(1．3)其中C_1,C_2为常数且C_1＞0,C_2≥0．对于以上问题,可以使用有限差分方法及有限元方法进行离散,并采用交替方向方法求解．交替方向方法能够将高维问题转化为一系列的一维问题进行计算,具有计算量少,计算稳定且易于并行实现等优点,在大规模科学计算中起着非常重要的作用,一直是计算数     

求带释放时间的半导体煅烧排序的最短交付时间的一个高效PTAS

本文研究一个目标是最小化最大交付时间的能分批处理的非中断单机排序问题．这个问题来源于半导体制造过程中对芯片煅烧工序的排序．煅烧炉可以看成一个能同时最多加工B（〈n）个工件的处理机．此外，每个工件有一个可以允许其加工的释放时间和一个完成加工后的额外交付时间．该问题就是将工件分批后再依批次的排序加工，使得所有工件都交付后所需的时间最短．我们设计了一个用时O（f（l／ε）n^5/2）的多项式时间近似方案，其中关于1／ε的指数函数厂（1／ε）对固定的ε是个常数.     

Finite analytic boundary condition for a higher‐order finite analytic scheme

A higher‐order finite analytic scheme based on one‐dimensional finite analytic solutions is used to discretize three‐dimensional equations governing turbulent incompressible free surface flow. In order to preserve the accuracy of the numerical scheme, a new, finite analytic boundary condition is proposed for an accurate numerical solution of the partial differential equation. This condition has higher‐order accuracy. Thus, the same order of accuracy is used for the boundary. Boundary conditions were formulated and derived for fluid inflow, outflow, impermeable surfaces and symmetry planes. The derived boundary conditions are treated implicitly and updated with the solution of the problem. The basic idea for the derivation of boundary conditions was to use the discretized form of the governing equations for the fluid flow simplified on the boundaries and flow information. To illustrate the influence of the higher‐order effects at the boundaries, another, lower‐order finite analytic boundary condition, is suggested. The simulations are performed to demonstrate the validity of the present scheme and boundary conditions for a Wigley hull advancing in calm water. Copyright © 2005 John Wiley & Sons, Ltd.     

A FINITE ELEMENT COLLOCATION METHOD FOR TWO-PHASE INCOMPRESSIBLE IMMISCIBLE PROBLEMS

Two-phase,incompressible,immiscible flow in porous media is governed by a coupled system of nonlinear partial differential equations.The pressure equation is elliptic, whereas the concentration equation is parabolic,and both are treated by the collocation scheme.Existence and uniqueness of solutions of the algorithm are proved.A optimal convergence analysis is given for the method.     

工件带安装时间的单机排序问题的列生成算法

在求解大规模NP-困难的最优化问题方法中,列生成技术越来越受到重视.本文研究工件带有与加工次序有关的安装时间的单机排序问题,首先构造它的时间标号模型,结合D-W分解技术和分支定界方法,给出它的列生成算法.其中时间标号模型的线性松弛为原问题提供了很好的下界,然后提出一个近似算法.通过实验数据表明,我们的算法对中等规模的排序问题1|t_(ij),r_j|∑w_jC_j是有效的.     

Duality Maps of Finite Abelian Groups and Their Applications to Spin Models

Duality maps of finite abelian groups are classified. As a corollary, spin models on finite abelian groups which arise from the solutions of the modular invariance equations are determined as tensor products of indecomposable spin models. We also classify finite abelian groups whose Bose-Mesner algebra can be generated by a spin model.