Mathematical stencil and its application in finite difference approximation to the poisson equation

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented,and then a new type of the iteration algo- rithm is established for the Poisson equation.The new algorithm has not only the obvious property of parallelism,but also faster convergence rate than that of the classical Jacobi iteration.Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision,and the computational velocity increases obviously when the new iterative method,instead of Jacobi method,is applied to polish operation in multi-grid method,furthermore,the polynomial acceleration method is still applicable to the new iterative method.     

油水驱动半正定问题迎风混合元格式及其数值分析

研究了不可压缩油水两相渗透流驱动问题.在扩散矩阵仅是半正定的假设条件下,提出了迎风混合元方法.混合元方法近似压力方程,饱和度方程的对流项用Godunov迎风格式来处理,扩散项则用推广的混合元来逼进,并推导出格式的误差估计.此种格式的优越性表现在两个方面:首先是饱和度方程的扩散矩阵仅是半正定的;二是摒弃了特征格式所限制的周期性条件,更适用于实际问题.     

Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

The Rank of a Direct Power of a Small-Cancellation Group

We construct an example of a finitely generated group G such that rank((G )ⁿ)=2 for all n1. For each n, we construct a finitely presented group G _n such that rank((G _n )ⁿ)=2. We conjecture that if G is a word-hyperbolic group then rank(G ⁿ ) as $ n. For each m we give an example of a residually finite group K _m such that K _m has exactly two relators, but K _m has no proper subgroups of index $ m. We construct a finitely generated group D such that there is an epimorphism DD×D.     

Local and Parallel Finite Element Algorithms for Eigenvalue Problems

Abstract Some new local and parallel finite element algorithms are proposed and analyzed in this paper foreigenvalue problems.With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced tothe solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraicsystems on fine grid by using some local and parallel procedure.A theoretical tool for analyzing these algorithmsis some local error estimate that is also obtained in this paper for finite element approximations of eigenvectorson general shape-regular grids.     

Review and complements on mixed-hybrid finite element methods for fluid flows

Mixed and hybrid finite element methods for the resolution of a wide range of linear and nonlinear boundary value problems (linear elasticity, Stokes problem, Navier–Stokes equations, Boussinesq equations, etc.) have known a great development in the last few years. These methods allow simultaneous computation of the original variable and its gradient, both of them being equally accurate. Moreover, they have local conservation properties (conservation of the mass and the momentum) as in the finite volume methods.The purpose of this paper is to give a review on some mixed finite elements developed recently for the resolution of Stokes and Navier–Stokes equations, and the linear elasticity problem. Further developments for a quasi-Newtonian flow obeying the power law are presented.     

Some degenerate and quasilinear parabolic systems not in divergence form

This paper deals with positive solutions of degenerate and quasilinear parabolic systems not in divergence form: u_t=u^p(Δu+av), v_t=v^q(Δv+bu), with null Dirichlet boundary conditions and positive initial conditions, where p, q, a and b are all positive constants. The local existence and uniqueness of classical solution are proved. Moreover, it will be proved that all solutions exist globally if and only if ab?λ₁², where λ₁ is the first eigenvalue of −Δ in Ω with homogeneous Dirichlet boundary condition.     

关于Sylow子群皆交换的p~2q~3阶群的构造

设p,q为奇素数,且p>q.本文对Sylow子群皆交换的p2q 3阶群进行了完全分类并获得了其全部构造:1)当q(p2-1)且p(q2+q+1)时,G恰有6个不同构的类型;2)当q(p-1)但p|(q2+q+1)时,G恰有8个不同构的类型;3)当q|(p-1)但q2(p-1)且p(q2+q+1)时,G恰有q2+19个不同构的类型;4)当q|(p-1)且p|(q2+q+1)但q2(p-1)时,G恰有q2+21个不同构的类型;5)当q2|(p-1)但q3(p-1)时,G恰有2q2+q+24个不同构的类型;6)当q3|(p-1)时,G恰有(q3+5q2+2q+52)/2个不同构的类型;7)当q|(p+1)但q2(p+1)时,G恰有10个不同构的类型;8)当q2|(p+1)但q3(p+1)时,G恰有12个不同构的类型;9)当q3|(p+1)时,G恰有13个不同构的类型.     

On a Graph Related to Subgroups Generated by a Conjugacy Class in Finite Groups

Let G be a group,and let (→Γ)C(G) be a digraph whose vertices are the non-trivial conjugacy classes of G and there is an arc from a vertex C to a vertex C'if an...     

在役老旧拱桥的极限承载力分析

在役老旧拱桥的承载力是人们关心的热点问题之一,某些桥梁随着使用年限的不断增加,拱肋以及其他结构部件变形甚至破坏,其承载能力削弱问题会变得尤为突出．以宁波市灵桥为例详细分析了其极限承载力,分析过程中考虑了材料和几何双重非线性,以及涉及到灵桥由于战争、船体碰撞、行车事故和其他意外事故引起的拱肋变形和扭曲情况．计算结果表明：拱肋面外的初始变形极大地削弱了灵桥的极限承载能力;要准确评估该桥的极限承载能力,必须考虑材料非线性和几何非线性的影响．