A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.     

Domain decomposition methods in a geometrical multiscale domain using finite volume schemes

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.     

An analysis of overlapping Schwarz method for a weakly coupled system of singularly perturbed convection-diffusion equations

In this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second-order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.     

L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

Novel local smoothness indicators for improving the third‐order WENO scheme

The local smoothness indicators play an important role in the performance of a weighted essentially nonoscillatory (WENO) scheme. Due to having only 2 points available on each substencil, the local smoothness indicators calculated by conventional methods make the third‐order WENO scheme too dissipative. In this paper, we propose a different method to calculate the indicators by using all the 3 points on the global stencil of the third‐order WENO scheme. The numerical results demonstrate that the WENO scheme with the new indicators has less dissipation and better resolution than the conventional third‐order WENO scheme of Jiang and Shu for both smooth and discontinuous solutions.     

近红外光谱小波分析在土壤参数预测中的应用

从田间采集了150个田间土壤样本,在分析了所有样本的土壤参数统计特征之后,对原始近红外光谱数据进行了聚类分析,分别得到了50个土壤全氮和50个土壤有机质的等价样本及其对应光谱。对样本光谱曲线进行8层Biorthogonal小波包分解,分解得到的最低低频[80]结点对应着土壤水分以及土壤质地的光谱变化趋势,最高高频[8 255]结点对应着土壤粒度、光谱仪精度等引起的高频震荡。对以上两个结点进行重构并从样本光谱曲线中剔除以上影响成分,得到了对应的土壤参数特征光谱。基于特征光谱建立了土壤参数偏最小二乘回归模型：全氮偏最小二乘预测模型的预测系数r_c达到了0.960,验证系数r_v达到了0.920;有机质偏最小二乘预测模型的预测系数r_c达到0.922,验证系数r_v达到0.883。模型精度明显提高,满足实际生产的需要。     

光谱反射率重建中代表颜色分步选取方法

光谱反射率重建一般指采用标准色卡上的颜色样本,对成像系统进行光谱表征(Spectral character-ization),进而从系统响应中精确地求出物体表面的光谱反射率.由于标准色卡的颜色样本数量较大,在实际成像系统中使用时有诸多不便.考虑到颜色样本之间存在较大冗余,可从中选出具代表性的少数样本用于光谱表征.针对已有方法未考虑实际成像系统特性的不足,文章提出了一种代表颜色的分步选取算法,即首先通过假设一个虚拟成像系统,根据全局误差最小的原则,挑选出部分最具代表性的颜色,估计出实际成像系统的光谱响应函数,然后在此基础上继续选择其余的代表颜色.实验表明,对于窄带多光谱成像系统及宽带彩色扫描仪而言,文章提出的方法在光谱精度及色度方面均明显优于先前方法.     

Spectral Changes Due to Performance Environment in Singers, Nonsingers, and Actors

From postrecording interviews of professional singers, it was hypothesized that recording environments, i.e., sound-treated environment versus an auditorium, may induce different vocal behaviors. To test this hypothesis, three groups consisting of nonsingers, singers, and actors were recorded in two different recording environments: a sound-treated booth (IAC) and an auditorium (AUD). Three recordings were obtained from each participant: recording one (IAC) and two (AUD1) required the participants to read in a normal voice; recording three (AUD2) required participants to pretend that they were "performing" before a full house. Results indicated that only the singers and the actors exhibited significant spectral and/or frequency/duration differences from one recording environment to another, with the most dramatic differences exhibited by the singers. It was concluded that the environment in which we record experimental samples from professional voice users, especially singers, should be considered as a variable that can affect results.     

Kp,q-factorization of complete bipartite graphs

Let K_(m,n) be a complete bipartite graph with two partite sets having m and nvertices, respectively. A K_(p,q)-factorization of K_(m,n) is a set of edge-disjoint K_(p,q)-factorsof K_(m,n) which partition the set of edges of K_(m,n). When p=i and q is a prime number,Wang, in his paper "On K_(1,k)-factorizations of a complete bipartite graph" (Discrete Math,1994, 126; 359-364), investigated the K_(1,q)-factorization of K_(m,n) and gave a sufficientcondition for such a factorization to exist. In the paper "K_(1,k)-factorizations of completebipartite graphs" (Discrete Math, 2002, 259: 301-306), Du and Wang extended Wang'sresult to the case that q is any positive integer In this paper, we give a sufficient conditionfor K_(m,n) to have a K_(p,q)-factorization. As a special case, it is shown that the Martin's BACconjecture is true when p: q=k: (k+1) for any positive integer k.     

Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations

A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair which satisfies some approximate assumption. An optimal error estimate of the numerical velocity and pressure is provided for the fully discrete penalty finite element method when the parameters and are sufficiently small.