A finite element modified method of characteristics for convective heat transport

We propose a finite element modified method of characteristics for numerical solution of convective heat transport. The flow equations are the incompressible Navier‐Stokes equations including density variation through the Boussinesq approximation. The solution procedure consists of combining an essentially non‐oscillatory modified method of characteristics for time discretization with finite element method for space discretization. These numerical techniques associate the geometrical flexibility of the finite elements with the ability offered by modified method of characteristics to solve convection‐dominated flows using time steps larger than its Eulerian counterparts. Numerical results are shown for natural convection in a squared cavity and heat transport in the strait of Gibraltar. Performance and accuracy of the method are compared to other published data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

由半导体激光器端面输出谱确定自发辐射谱

利用射线法和平均载流子分布近似，从理论上预言了用阈值以下半导体激光器的端面输出谱来确定自发辐射谱的可能性。在此基础上，通过实验测得的阈值以下半导体激光器的端面输出谱确定了自发辐射谱，并且对自发辐射谱和增益谱进行了比较和分析。     

Streamline upwind/full Galerkin method for solution of convection dominated solute transport problems

A new streamline method for the solution of convection-dominated transport problems is introduced. First, an analysis is made of the nature of classic streamline upwinding from the perspective of space and spacetime solution domains, as they pertain to the nature of the problems. From this analysis emerges a rigorous logic for upwinding, which can easily be implemented in the full (spacetime) Galerkin formulation of the transport equation. Comparative performance testing of this technique, in solving a number of examples, proves it to be robust and versatile. The advantage of this method resides in its applicability to a wider range of Courant numbers.     

Polyhedral study of the capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP) considered in this paper occurs when goods must be delivered from a central depot to clients with known demands, usingk vehicles of fixed capacity. Each client must be assigned to exactly one of the vehicles. The set of clients assigned to each vehicle must satisfy the capacity constraint. The goal is to minimize the total distance traveled. When the capacity of the vehicles is large enough, this problem reduces to the famous traveling salesman problem (TSP). A variant of the problem in which each client is visited by at least one vehicle, called the graphical vehicle routing problem (GVRP), is also considered in this paper and used as a relaxation of CVRP. Our approach for CVRP and GVRP is to extend the polyhedral results known for TSP. For example, the subtour elimination constraints can be generalized to facets of both CVRP and GVRP. Interesting classes of facets arise as a generalization of the comb inequalities, depending on whether the depot is in a handle, a tooth, both or neither. We report on the optimal solution of two problem instances by a cutting plane algorithm that only uses inequalities from the above classes.This work was supported in part by NSF grant DDM-8901495.     

Facets for the cut cone II: Clique-web inequalities

We study new classes of facets for the cut coneC _n generated by the cuts of the complete graph onn vertices. This cone can also be interpreted as the cone of all semi-metrics onn points that are isometricallyl ₁-embeddable and, in fact, the study of the facets of the cut polytope is in some sense equivalent to the study of the facets ofC _n . These new facets belong to the class of clique-web inequalities which generalize the hypermetric and cycle inequalities as well as the bicycle odd wheel inequalities.     

The symmetric Choquet integral with respect to Riesz-space-valued capacities

A definition of “Šipoš integral” is given, similarly to [3], [5], [10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved. This paper was supported by the cooperation project between Slovak Academy of Sciences (S.A.V.) and Italian National Council of Researches (C.N.R.)     

VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL GOVERNED BY CONVECTION DOMINATED DIFFUSION EQUATIONS

In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the L^2-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.     

A dominated ergodic theorem for some bilinear averages

Let T be a positive invertible linear operator with positive inverse on some Lp(μ), 1?p<∞, where μ is a σ-finite measure. We study the convergence in the Lp(μ)-norm and the almost everywhere convergence of the bilinear operators

     

A modified Crank-Nicolson scheme with incremental unknowns for convection dominated diffusion equations

A modified Crank-Nicolson scheme based on one-sided difference approximations is proposed for solving time-dependent convection dominated diffusion equations in two-dimensional space. The modified scheme is consistent and unconditionally stable. A priori L² error estimate for the fully discrete modified scheme is derived. With the use of the incremental unknowns preconditioner at each time step, a comparison among several classical numerical schemes has been made and numerical results confirm stability and efficiency of the modified Crank-Nicolson scheme.     

Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles

The C ¹ density conjecture of Palis asserts that diffeomorphisms exhibiting either a homoclinic tangency or a heterodimensional cycle are C ¹ dense in the complement of the C ¹ closure of hyperbolic systems. In this paper we prove some results towards the conjecture.* Work supported by the National Natural Science Foundation and the Doctoral Education Foundation of China, and the Qiu Shi Science and Technology Foundation of Hong Kong.