Stieltjes-Newton型有理插值

Stieltjes型分叉连分式在有理插值问题中有着重要的地位，它通过定义反差商和混合反差商构造给定结点上的二元有理函数，我们将Stieltjes型分叉连分式与二元多项式结合起来，构造Stieltje- Newton型有理插值函数，通过定义差商和混合反差商，建立递推算法，构造的Stieltjes-Newton型有理插值函数满足有理插值问题中所给的插值条件，并给出了插值的特征定理及其证明，最后给出的数值例子，验证了所给算法的有效性．     

B-值鞅Hardy空间与BMO空间的实内插

研究了B值鞅Hardy空间与BMO空间的实内插，并利用所得结果，讨论了鞅Hardy空间的内插空间的共轭问题。     

光纤法珀应变传感器串并联混合复用的离散腔长变换解调研究

光纤法珀传感器复用的输出信号复杂,解调相当困难.为实现其串并联混合结构复用,根据光纤法珀应变传感器的双光干涉原理,阐述了传感器串并联混合复用的输出信号特征,分析了信号中各项成分对离散腔长变换方法解调结果的影响,并进行了计算机仿真.最后搭建实验平台,进行了四个传感器串并联混合复用的实验研究,证明该方案可行,解调准确度1 μm.     

闭区间[0,1]上的分形插值函数的分数阶积分

介绍了分形插值函数和迭代函数系统以及v阶黎曼-刘准尔分数阶积分的概念及相关定理.利用这些概念及定理讨论了分形插值函数的分数阶积分在[0,1]上连续性及判定[0,1]上的分形插值函数的分数阶积分也是[0,1]上的分形插值函数,并给予了证明.     

求解二维Poisson方程的重心插值配点法

采用重心Lagrange插值配点法计算了二维Poisson方程.采用重心Lagrange插值法构造近似函数,由配点法离散Poisson方程及其边界条件.数值算例表明方法具有理论简单、计算精度高的特点.     

Constrained moving least‐squares immersed boundary method for fluid‐structure interaction analysis

A numerical method is presented for the analysis of interactions of inviscid and compressible flows with arbitrarily shaped stationary or moving rigid solids. The fluid equations are solved on a fixed rectangular Cartesian grid by using a higher‐order finite difference method based on the fifth‐order WENO scheme. A constrained moving least‐squares sharp interface method is proposed to enforce the Neumann‐type boundary conditions on the fluid‐solid interface by using a penalty term, while the Dirichlet boundary conditions are directly enforced. The solution of the fluid flow and the solid motion equations is advanced in time by staggerly using, respectively, the third‐order Runge‐Kutta and the implicit Newmark integration schemes. The stability and the robustness of the proposed method have been demonstrated by analyzing 5 challenging problems. For these problems, the numerical results have been found to agree well with their analytical and numerical solutions available in the literature. Effects of the support domain size and values assigned to the penalty parameter on the stability and the accuracy of the present method are also discussed.     

GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates (S_n) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.     

Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|^2σu. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ+1<3.68; bistability, in a finite range of values of the soliton’s power, for 3.68<2σ+1<5; and the presence of a threshold (minimum norm of the FS), for 2σ+1≥5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely.     

Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.     

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.