Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma

Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation.

Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations

The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L2-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.

Secret Sharing Schemes Based on the Dual Code of the Code of a Symmetric （v, k, λ）-Design and Minimal Access Sets

Secret sharing has been a subject of study for over 30 years. The coding theory has been an important role in the constructing of the secret sharing schemes. It is known that every linear code can be used to construct the secret sharing schemes. Since the code of a symmetric （V, k, λ）-design is a linear code, this study is about the secret sharing schemes based on C of Fp-code C of asymmetric （v, k, λ）-design.

A Note on Crank-Nicolson Scheme for Burgers’ Equation

In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analyzed for a third test problem, nu-merical solutions as well as exact solutions for different values of viscosity are calculated and we find that the numerical solutions are very close to exact solution.

CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

In this paper, the Crank-Nicolson/Newton scheme for solving numerically second- order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nieolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank- Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the efficient performance of the proposed scheme.

Random Crank-Nicolson Scheme for Random Heat Equation in Mean Square Sense

The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.

Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

有限元Crank-Nicolson格式高阶求解非稳态扩散方程

基于空间尺度的有限元法,结合时间尺度的有限差分格式求解一维非稳态扩散方程的初边值问题.建立变分形式和有限维逼近空间,给出有限元结合Crank-Nicolson格式的理论框架和计算步骤,并构造全离散θ-型隐格式,再分别利用线性有限元和二次有限元对非稳态对流扩散反应方程进行数值模拟.结果表明,在空间方向的一致剖分下,时间层离散分别结合线性有限元和二次有限元计算均可得到一致收敛结果,且二次有限元在Crank-Nicolson格式离散下的精度更高,其误差范数的收敛阶可达三阶,应用优势更为显著.

价k_i（i≠0）均为2的交换结合Scheme

价是交换结合Ｓｃｈｅｍｅ的重要数量特征，有较强的组合性质，利用价来讨论某些交换结合Ｓｃｈｅｍｅ的构造与性质，是一个常用的方法．设＝（Ｘ，｛Ｒｉ｝ｉ＝０，１，．．．，ｄ）是一个类ｄ的交换结合Ｓｃｈｅｍｅ．ｋ０，ｋ１，．．．，ｋｄ是的价．本文证明了，若ｋ１＝ｋ２＝．．．＝ｋｄ＝２，则 是对称结合Ｓｃｈｅｍｅ．

NON-SYMMETRIC ASSOCIATION SCHEMES OF SYMMETRIC MATRICES

constant whenever （x, y）∈Rk. This constant is denoted by pijk. Then we call X=(X,{Ri}0≤i≤d) and association scheme of class d on X. The non-negative integers pijk are called the intersection numbers of X.

Symmetric Semi-perfect Obstruction Theory Revisited

In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne-Mumford stack X constructed by Chang-Li,and Behrend’s theorem equating the weighted Euler characteristic of X and the virtual count of X by symmetric semi-perfect obstruction theories.As an application,we prove that Joyce’s d-critical scheme admits a symmetric semi-perfect obstruction theory,which can be applied to the virtual Euler characteristics by Jiang-Thomas.

Association Schemes of Symmetric Matrices Over Finite Fields of Characteristic Two

Association schemes have close connections with coding, design and finite group theory, etc. In 1965, Wan Zhe-xian first discussed the association schemes based on the n×n Hermitian matrices over finite fields, and calculated their parameters when n=2. Later,Wang Yang-xian gave a recurrence calculation formula of

A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems

In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems. Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O（△t2 ＋ h） and present some numerical examples at the end of the paper.

Symplectic schemes and symmetric schemes for nonlinear Schr¨odinger equation in the case of dark solitons motion

In this paper,symplectic schemes and symmetric schemes are presented to simulate Nonlinear Schrodinger Equation(NLSE)in case of dark soliton motion.Firstly,by Ablowitz–Ladik model(A–L model),the NLSE is discretized into a non-canonical Hamiltonian system.Then,different kinds of coordinate transformations can be used to standardize the non-canonical Hamiltonian system.Therefore,the symplectic schemes and symmetric schemes can be employed to simulate the solitons motion and test the preservation of the invariants of the A–L model and the conserved quantities approximations of the original NLSE.The numerical experiments show that symplectic schemes and symmetric schemes have similar simulation effect,and own significant superiority over non-symplectic and non-symmetric schemes in long-term tracking the motion of solitons,preserving the invariants and the approximations of conserved quantities.Moreover,it is obvious that coordinate transformations with more symmetry have a better simulation effect.

Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries

We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s flux-limited diffusion operators.Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation.Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors.The harmonic average approach in spherical geometry is analyzed,and its second order accuracy is demonstrated.By formal analysis,we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties.By designing associated manufactured solutions and reference solutions,we verify the desired performance of the fully discrete schemes with numerical tests,which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate,hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.

Symmetric Energy-Conserved Splitting FDTD Scheme for the Maxwell’s Equations

In this paper,a new symmetric energy-conserved splitting FDTD scheme(symmetric EC-S-FDTD)for Maxwell’s equations is proposed.The new algorithm inherits the same properties of our previous EC-S-FDTDI and EC-S-FDTDII algorithms:energy-conservation,unconditional stability and computational efficiency.It keeps the same computational complexity as the EC-S-FDTDI scheme and is of second-order accuracy in both time and space as the EC-S-FDTDII scheme.The convergence and error estimate of the symmetric EC-S-FDTD scheme are proved rigorously by the energy method and are confirmed by numerical experiments.

NON-SYMMETRIC ASSOCIATION SCHEMES OF SYMMETRIC MATRICES

Let X_n be the set of n×n symmetric matrices over a finite field F_q,where q is a power of an odd prime.For S_1,S_2 ∈ X_n,we define (S_1,S_2)∈ R_0 iff S_1=S_2;(S_1,S_2)∈R_(r,ε)iff S_1-S_2 is congruent to where?=1 or z,z being afixed non-square element of F_q.Then X_n=(X_n,{R_0,R_(r,ε)|1≤r≤n,?=1 or z}) is a non-symmetric association scheme of class 2n on X_n.The parameters of X_n have been computed.And we also prove that X_n is commutative.

VSC-HVDC三相不平衡控制策略

分析了电网三相不平衡时电压源换流器高压直流输电(VSC-HVDC)系统的谐波传递特性,设计了一种基于瞬时对称分量法的序分量检测技术,适用于VSC-HVDC系统的正、负序双回路的双闭环控制策略。该控制策略利用瞬时对称分量变换获取电压和电流的无延迟正、负序分量,不仅在时域范围内对传统对称分量法进行了扩展,而且也解决了正、负序分解时所带来的延迟问题。另外,提出在三相不平衡电力系统的控制中增加一个不平衡指令补偿模块,改善VSC-HVDC系统在电网三相不平衡时的运行特性。最后,在仿真软件PSCAD/EMTDC的环境下建立了一个VSC-HVDC系统及相关控制策略,验证了所设计控制策略的正确性。

一种支持共享的高可用数据库加密机制

加密数据库可以保证数据在数据库存储期间的机密性,但往往难以很好地支持多用户的共享访问,难以保证良好的可用性及易用性。文章在基于字段加密的前提下,提出了一种由数据密钥对敏感数据进行加密保护,由数据库用户公钥对数据密钥进行加密保护,最终由数据库用户口令对用户私钥进行加密保护的完整数据库加密机制。据此理论建立的加密数据库模型既可以保证数据的安全性,也支持对加密信息的共享访问,在可用性、易用性方面也比以往系统有明显增强。

对称不稳定对梅雨锋暴雨影响的数值模拟

在Kuo-Anthes垂直对流参数化方案和Nordeng倾斜对流参数化方案基础上,提出了垂直-倾斜对流一体化参数化方案,在引入MM5模式后,对1999年6月发生在长江流域的一次大尺度带状强降水过程进行了数值模拟及敏感性试验。结果表明:在模式中引入倾斜对流参数化方案,可有效改进模式模拟的降水强度和位置,加快形成锋面附近的垂直环流并使之得到增强,模拟结果更接近实况。同时也表明,在模拟和预报具有对称不稳定的天气系统时,在模式中考虑倾斜对流参数化方案是必要的。