Non-Linear Filtering and Limiting in High Order Methods for Ideal and Non-Ideal MHD

The adaptive nonlinear filtering and limiting in spatially high order schemes (Yee et al. J. Comput. Phys. 150, 199–238, (1999), Sjögreen and Yee, J. Scient. Comput. 20, 211–255, (2004)) for the compressible Euler and Navier–Stokes equations have been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations, (Sjögreen and Yee, (2003), Proceedings of the 16th AIAA/CFD conference, June 23–26, Orlando F1; Yee and Sjögreen (2003), Proceedings of the International Conference on High Performance Scientific Computing, March, 10–14, Honai, Vietnam; Yee and Sjögreen (2003), RIACS Technical Report TR03. 10, July, NASA Ames Research Center; Yee and Sjögreen (2004), Proceedings of the ICCF03, July 12–16, Toronto, Canada). The numerical dissipation control in these adaptive filter schemes consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of discontinuity capturing nonlinear numerical dissipation for both the ideal and non-ideal MHD.     

对流方程的离散化问题

讨论了用矩形网格离散化对流方程的一般方法 若格式含有N个网点 ,则其最高阶格式为N- 2阶 ,同时构造了一些新的高精度差分格式     

基于IC卡的电子支付模型研究

电子支付技术是电子商务中的核心技术,也是目前制约电子商务发展的一个根本性问题。文章就电子商务中的电子支付技术进行了探讨,以SET协议为基础,提出了三种参考模型,并对这三种电子支付模型进行了对比分析,给出了这三种电子支付模型的优缺点和共同点。     

OpenBSD下基于IPSec协议的VPN研究与设计

IPSec提供一种对用户透明的IP层安全服务，包括机密性、完整性、可认证性和数据重放保护。IPSec可用于保护主机间、安全网关间或安全网关－－主机间的一条或多条路径的安全通信。文章对IPSec的结构与组成，IPSec在OPENBSD下的实现进行了较为详细的研究对；并对系统的利弊进行了评价。     

A new ADI technique for two-dimensional parabolic equation with an integral condition

Nonclassical parabolic initial-boundary value problems arise in the study of several important physical phenomena. This paper presents a new approach to treat complicated boundary conditions appearing in the parabolic partial differential equations with nonclassical boundary conditions. A new fourth-order finite difference technique, based upon the Noye and Hayman (N-H) alternating direction implicit (ADI) scheme, is used as the basis to solve the two-dimensional time dependent diffusion equation with an integral condition replacing one boundary condition. This scheme uses less central processor time (CPU) than a second-order fully implicit scheme based on the classical backward time centered space (BTCS) method for two-dimensional diffusion. It also has a larger range of stability than a second-order fully explicit scheme based on the classical forward time centered space (FTCS) method. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from the 1974 work of Warming and Hyeet. This allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference methods. The results of numerical experiments for the new method are presented. The central processor times needed are also reported. Error estimates derived in the maximum norm are tabulated.     

Numerical simulation of the MHD equations by a kinetic-type method

We introduce a flux-splitting formula for the approximation of the ideal MHD equations in conservative form. The Faraday equation is considered as the average of an abstract kinetic equation, giving a flux-splitting formula. For the other part of the equations, we generalize formally the classical half-Maxwellian flux-splitting of the Euler equations. Numerical results on MHD shock tube problems are displayed.     

Performance measures of an ant based decentralised routing scheme for circuit switching communication networks

 Swarm intelligence is a new challenging branch of artificial life which takes advantage of the collective behaviour of animals with limited intellectual faculties (insects, flocking birds, schools of fish) to solve algorithmically complex problems. Recently a new routing method based on the way that ants are communicating with each other has been applied to solve routing problems in telecommunication networks. This paper examines the behavior of an ant based decentralised router using an adequate set of commonly acceptable and some newly introduced metrics.     

Computational investigation of elliptic systems with discontinuous coefficients

The Dirichlet problem is considered for a linear elliptic system of the second order with discontinuous coefficients in a rectangle Ω. For this problem, a difference scheme of the order of accuracy is constructed in a net norm W ₂ ¹ (ω), provided that the solution of the original problem belongs to the space W ₂ ^k (Ω_α), α= 1,2, k=2,3, in each of the subdomains into which the rectangle is divided by the curve of discontinuity of coefficients. This work was supported by the State Foundation for Basic Research. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 157–161, July–August, 2000.     

Distance estimation and object location via rings of neighbors

We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: low-stretch routing schemes [48], distance labeling [25], searchable small worlds [31], and triangulation-based distance estimation [34]. Focusing on metrics of low doubling dimension, we approach these problems with a common technique called rings of neighbors, which refers to a sparse distributed data structure that underlies all our constructions. Apart from improving the previously known bounds for these problems, our contributions include extending Kleinberg’s small world model to doubling metrics, and a short proof of the main result in Chan et al. [15]. Doubling dimension is a notion of dimensionality for general metrics that has recently become a useful algorithmic concept in the theoretical computer science literature. This work was done when A. Slivkins was a graduate student at Cornell University and was supported by the Packard Fellowship of Jon Kleinberg. Preliminary version of this paper has appeared in 24th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC), 2005.     

A set of compact finite-difference approximations to first and second derivatives,related to the extended Numerov method of Chawla on nonuniform grids

Summary The extended Numerov scheme of Chawla, adopted for nonuniform grids, is a useful compact finite-difference discretisation, suitable for the numerical solution of boundary value problems in singularly perturbed second order non-linear ordinary differential equations. A new set of three-point compact approximations to first and second derivatives, related to the Chawla scheme and valid for nonuniform grids, is developed in the present work. The approximations economically re-use intermediate quantities occurring in the Chawla scheme. The theoretical orders of accuracy are equal four for the central and one-sided first derivative approximations obtained, whereas the central second derivative formula is either fourth, third, or second order accurate, depending on the grid ratio. The approximations can be used for accurate a posteriori derivative evaluations. A Hermitian interpolation polynomial, consistent with the derivative approximations, is also derived. The values of the polynomial can be used, among other things, for guiding adaptive grid refinement. Accuracy orders of the new derivative approximations, and of the interpolating polynomial, are verified by computational experiments.