Schedule-at-a-Glance

53 PRIMA 2013 AbstractsPancyclicity of 4-connected {K 1,3, Z 8}-freegraphsHong-Jian Lai, Mingquan Zhan, Taoye Zhang, and JuZhouKutztown University of Pennsylvania, USAzhou@kutztown.eduA graph G is said to be pancyclic if G contains cycles oflengths from 3 to |V (G)|. In this paper, we show thatevery 4-connected claw-free Z 8 -free graph is either pancyclicor is the line graph of the Petersen graph. Thisimplies that every 4-connected claw-free Z 6 -free graph ispancyclic, and every 5-connected claw-free Z 8 -free graphis pancyclic.The number of subtrees of a treeXiao-Dong ZhangShanghai Jiao Tong University, P.R. Chinaxiaodong@sjtu.edu.cnIn this talk, we consider how to determine the maximumand minimum number of subtrees a tree with a givendegree tree sequence. It is proven that the greedy treeamong all trees with the same degree sequence has themaximum number subtrees, while it is tough to determinewhich tree has minimum number of subtrees. This work isjoined with Daniel Gray, Hua Wang, and Xiu-Mei Zhang.Contributed Talks Group 4Computational Mathematics & OptimizationA semidefinite approximation for symmetrictravelling salesman polytopesJulián Ariel Romero BarbosaUniversity of los Andes, Colombiaja.romero913@uniandes.edu.coIn this talk we will present a positive semidefinite approximationof compact convex sets introduced by A. Barvinokand E. Veomett [1]. In particular we will discussthe behaviour of this relaxation when the convex sets tobe approximated are the Traveling Salesman PolytopesT n and T n,n associated to the complete graphs K n andK n,n respectively. E. Veomett has shown that the scalingof the k−th approximation by n/k + O(1/n) containsthe polytope T n for k ≤ ⌊n/2⌉ . Here, we will showthat√these metric bounds can be improved by a factor of1 k−13 n2−1 + 2 for the case when n is even. Finally, we3will show new metric bounds for the approximation ofthe polytope T n,n.This results are joint work with M. Velasco and are partof my master’s dissertation at the University of los Andes.[1] Veomett, Ellen. A positive semidefinite approximationof the symmetric traveling salesman polytope. DiscreteComput. Geom. 38 (2007), no. 1, 15-28.An analysis of HDG methods for theHelmholtz equationJintao CuiUniversity of Arkansas at Little Rock, USAjxcui1@ualr.eduIn this talk we discuss the hybridizable discontinuousGalerkin (HDG) methods for the Helmholtz equationwith first order absorbing boundary condition in two andthree dimensions. We prove that the proposed HDGmethods are stable (hence well-posed) without any meshconstraint. The stability constant is independent of thepolynomial degree. By using a projection-based erroranalysis, we also derive the error estimates in L 2 norm forpiecewise polynomial spaces with arbitrary degree. Thisis joint work with Wujun Zhang from University of Maryland.An Uzawa method for solving steady Navier-Stokes equations discretized by mixed elementmethodsJianguo HuangShanghai Jiao Tong University, Chinajghuang@sjtu.edu.cnNumerical solutions of Navier-Stokes equations play fundamentalroles in scientific computing and fluid dynamics.The need to do this frequently occurs in many appliedsciences. Mixed element methods are widely usedfor discretizing steady Navier-Stokes equations in applications.However, it is challenging to devise fast solvers forthe resulting nonlinear system. A typical solver involvesnumerical solution of the discretized Oseen equations ateach iteration step; or equivalently, a non-symmetric saddlepoint system must be solved at each iteration step.However, it is by no means trivial to solve such a subproblemefficiently.In this talk, we are going to design an Uzawa-type iterativemethod for the previous nonlinear system, for whichwe require to solve no saddle point system at each iterationstep. Under some reasonable conditions, we prove itsconvergence rate is independent of the finite element meshsize h, even for the shape regular triangulation. Finally,we provide a series of numerical experiments to show theaccuracy and performance of the method proposed. Thisis a joint work with Puyin Chen and Huashan Sheng.Semi-classical limit for the Schrödinger equationwith lattice potential, and band-crossingQin LiUniversity of Wisconsin-Madison, USAqinli@math.wisc.eduIn this talk, I am going to present the derivation of thesemi-classical limit of the Schrödinger equation with latticepotential, where the lattice constant and the Planckconstant are at the same order. Bloch theory is used todecompose the solution into eigenfunctions. Here we encountertwo problems: 1. eigenvalues degenerate, whenthis happens one cannot distinguish the associated eigenfunctions,and the so called transition rate between energybands should be introduced; 2. the evolution of theprojection coefficients follow a coupled integro-differentialequation, which can be hard to compute. By carryingout the Wigner transformation of all the Bloch bands,we find a complete basis on the phase space. The coefficientsfor them are controlled by a simple hyperbolicequation, and the transition rates at the point of thedegeneracy are characterized explicitly. A domain decompositionmethod based on the distances between energybands is designed associated to this newly developedmodel. This is a joint work with Lihui Chai and Shi Jin.Legendre pseudospectral method for solvingthree-dimensional non-linear hyperbolic partialdifferential equationsAbdur RashidGomal University, Pakistanprof.rashid@yahoo.com