双曲型守恒律的一种五阶半离散中心迎风格式

给出一种求解双曲型守恒律的五阶半离散中心迎风格式.对一维问题,该格式以五阶中心WENO重构为基础;对二维问题,用逐维计算的方法将五阶中心WENO重构进行推广.时间方向的离散采用Runge-Kutta方法.格式保持了中心差分格式简单的优点,即不用求解Riemann问题,避免进行特征分解.用该格式对一维和二维Euler方程进行数值试验,结果表明该格式是高精度、高分辨率的.     

用有限元方法求解双曲守恒律

分片线性插值有限元给出了求解双曲守恒律的计算方法。有别于不连续有限元方法求解双曲守恒律在相邻单元边界上求Ｒｉｅｍａｎｎ解,利用双曲守恒律的Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ方程形式,直接应用有限元求解,在ＣＦＬ下,证明了计算格式满足极大值原理,并且是ＴＶＤ格式。数值例子在文后给出。此外,方法推广到流体力学方程组和高维问题,将在另文中邓以讨论。     

数值求解Navier-Stokes方程的一个新的系数矩阵分裂法

在一个单步格式的基础上构造了一个新的隐式系数矩阵分裂法来数值求解可压Navier-St-okes方程。对方程中的无粘项部分利用守恒型方程中流通量向量为一齐次函数这一特性,根据Jacobian矩阵特征值的符号而将流通向量分裂成两部分。在此基础上据风向而构造逼近于无粘项的差分格式。对方程中的粘性项部分利用算子附加修正的方法来改进计算的收敛过程。所建立的差分格式被用来数值求解Couette流以考查这一方法。     

二阶STC格式及其对跨音速湍流流动的数值模拟

ＳＴＣ格式是一种求解积分形式物理守恒律的计算方法,具有守恒性好,精度高的特点。目前求解Ｅｕｌｅｒ方程的ＳＴＣ格式已经建立起来,但求解Ｎ－Ｓ方程的ＳＴＣ格式尚在发展之中。为了使ＳＴＣ格式能够有效地求解粘性流动的问题,本文构造出了求解曲线坐标系下的二维Ｎ－Ｓ方程的二阶ＳＴＣ格式。用该格式对跨音速湍流流动问题进行了计算。     

Vlasov-Poisson方程半拉格朗日守恒算法

利用三阶迎风插值多项式结合限制子方法，构造Vlasov-Poisson方程的半拉格朗日守恒型格式，可保持Vlasov-Poisson方程解的正性.计算朗道阻尼，双束不稳定性等典型问题，并与样条插值方法、UGKS方法进行比较，模拟结果表明半拉格朗日守恒性格式在Vlasov-Poisson方程求解中具有较高分辨率.     

龙格库塔间断有限元方法在计算爆轰问题中的应用

构造求解带源项守恒律方程组的龙格库塔间断有限元(RKDG)方法,并分别结合源项的Strang分裂法和无分裂法数值求解模型守恒律方程和反应欧拉方程.为了和有限体积型WENO方法进行比较,设计计算源项的WENO重构格式.对一维带源项守恒律的计算表明,对于非刚性问题,RKDG方法比有限体积型WENO方法的误差更小;对于刚性问题,RKDG方法对于间断面位置的捕捉更为精确.对于一二维爆轰波问题的计算结果表明,RKDG方法对爆轰波结构的分辨和爆轰波位置的捕捉能力更强.     

二维交错网格的GAUSS型格式

利用Gauss型求积公式在交错网格的情况下构造了一类不需解Riemann问题的求解二维双曲守恒律的二阶显式Gauss型差分格式,该格式在CFL条件限制下为MmB格式.并将格式推广到二维方程组,进行了数值试验.     

球坐标下二维激光驱动内爆的数值模拟

概述了球坐标下二维内爆动力学研究的物理问题和使用的计算方法.讨论了用隐式完全守恒差分格式求解流体力学方程组,用变分原理求解热传导方程等特点.给出了数值模拟的算例,以考查激光不对称性对直接驱动内爆过程的影响.     

非线性Schrdinger方程的直接间断Galerkin方法

讨论一维和二维非线性Schrdinger(NLS)方程的数值求解.基于扩散广义黎曼问题的数值流量,构造一种直接间断Galerkin方法(DDG)求解非线性Schrdinger方程.证明该方法L2稳定性,并说明DDG格式是一种守恒的数值格式.对一维NLS方程的计算表明,DDG格式能够模拟各种孤立子形态,而且可以保持长时间的高精度.二维NLS方程的数值结果显示该方法的高精度和捕捉大梯度的能力.     

A Direct Discontinuous Galerkin Method for Nonlinear Schr(o)dinger Equation

讨论一维和二维非线性Schr(o)dinger (NLS)方程的数值求解.基于扩散广义黎曼问题的数值流量,构造一种直接间断Galerkin方法(DDG)求解非线性Schr(o)dinger方程.证明该方法L2稳定性,并说明DDG格式是一种守恒的数值格式.对一维NLS方程的计算表明,DDG格式能够模拟各种孤立子形态,而且可以保持长时间的高精度.二维NLS方程的数值结果显示该方法的高精度和捕捉大梯度的能力.     

Selection of near infrared spectral information based on section combination moving window partial least squares北大核心CSCD

Selection of near infrared spectral information is research focus on the application of NIR, which enable to simplify the model and improve accuracy of prediction. Aiming at selecting optimal modeling spectral width of near infrared spectroscopy, section combination moving window partial least squares (SCMWPLS) is proposed in this paper. This method selects continuous modeling screened interval.by continuously varying size of moving window and cross validation. Taking Glucose solution near-infrared spectroscopy as test specimen, near infrared prediction models are established respectively by proposed method, and traditional interval partial least squares (IPLS) and moving window partial least squares (MWPLS). Comparing proposed method with two traditional methods, squares prediction RMSE is decreased by 44% and 25% respectively. © 2017, Editorial Board, Journal of Applied Optics. All right reserved.     

两种偏最小二乘分光光度法同时测定三组分混合物

本文研究两种偏最小二乘法（经典编最小二乘法（ＣＰＬＳ）和基于核心矩阵的偏最小二乘法（ＫＰＬＳ）同时测定三组分混合物，根据数学原理编制三个程序（ＳＰＧＲＡＦＡ，ＳＰＧＲＰＬＳ和ＳＰＧＲＫＰＬＳ）执行这些计算，八个误差函数用以推断因子数目，因为核心矩阵维数小于原始数据矩阵，所以ＫＰＬＳ法适于计算具有较多光谱数和较少样品数的数据矩阵，实验结果显示对相互重叠的光谱用这两种方法均能获得令人满意且十分吻合的结     

近红外光谱法分析油页岩含油率中波长选择方法的研究

波长选择是光谱建模分析的重要步骤。研究了近红外光谱法分析油页岩含油率过程中的波长选择方法,用以剔除光谱数据中的冗余信息和干扰信息,提高分析模型的建模效率和预测能力。分别采用相关系数法(CC)、移动窗口偏最小二乘法(MWPLS)和无信息变量消除法（UVE）对油页岩近红外漫反射光谱数据的波长区间进行了选择,研究了不同阈值、窗口宽度和噪声矩阵对上述方法的影响,建立了所选择波长处的反射率数据和样品含油率标准值间的偏最小二乘（PLS）分析模型,比较了上述方法的选择效果。结果表明：与使用全谱数据建模相比,采用上述方法筛选过的光谱数据均能提高模型的建模效率和预测能力,其中经UVE法筛选后的光谱数据仅占全谱数据总数的22.8%,模型的RMSECV却降低了9.3%,RMSEP降低了4.5%。     

Quantum algorithm for total least squares data fitting

The total least squares (TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the variables. In this work, the TLS problem is transformed to finding the ground state of a Hamiltonian matrix. We propose quantum algorithms for solving this problem based on quantum simulation of resonant transitions. Our algorithms can achieve at least polynomial speedup over the known classical algorithms.     

基于黎曼解的移动最小二乘粒子动力学数值方法

叙述移动最小二乘粒子动力学(MLSPH)的基本原理,讨论一维MLSPH计算方法,提出两种不同精度的基于无网格的构造黎曼问题初值的方法.通过黎曼解近似粒子间的相互作用,减小接触间断附近的震荡,并给出多介质一维激波管问题的算例,验证此方法的有效性.     

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

We first give a stabilized improved moving least squares(IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.     

中厚板弯曲问题的Kriging插值无网格法

基于Reissner-Mindlin板弯曲理论,将Kriging插值无网格法应用于中厚板弯曲问题,推导相应的离散方程.该方法可以只依赖于一组离散的节点建立试函数,有效地避免了复杂的网格划分和网格畸变的影响.相对于无网格法中常用的移动最小二乘近似而言,滑动Kriging插值法的形函数满足Kronecker delta函数性质,可以直接施加本质边界条件.算例分析表明,用Kriging插值无网格法分析中厚板弯曲问题,具有效率高,精度高和易于实现等优点.     

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (相似文献   

Research on exponential regularization approach for nonnegative Tucker3 decomposition

Methods of nonnegative tensor factorization (NTF), such as NTF1, NTF2, etc., are extension of nonnegative matrix factorization (NMF) for multi-way data analysis. As an existing NTF method, nonnegative Tucker3 decomposition (NTD) is researched for three-way decomposition in this paper. Firstly, an approach utilizing matrix exponentials built on Tikhonov-type regularization to enforce sparseness is proposed to extract image features instead of exclusively using Tucker tensor decomposition. Meanwhile, updating algorithms, derived from updating rules of NMF, are allowed to efficiently implement updating of mode matrices and core tensors alternatively for accuracy. Then, experimental cases of alternating least squares (ALS) and conjugate nonnegative constraints, called nonnegative alternating least squares (NALS), are studied to remedy data overfitting in computing procedures. Lastly, the proposed method exhibits more advantageous results than other algorithms of Tucker3 for feature extraction, thanks to computer simulations performed in the context of data analysis.     

The accuracy evaluation method of baseline estimation algorithms in energy dispersive X-ray fluorescence spectrum analysis

In energy dispersive X-ray fluorescence analysis (EDXRF), many baseline estimation algorithms have been proposed for the accurate characteristic peak area. However, the true value of the characteristic peak area of measured spectrum is unknown and cannot be used to evaluate the accuracy of the baseline estimation algorithms. In this article, an assessment method was proposed based on Monte Carlo simulation, which can obtain the characteristic peak area, and evaluate the accuracy of the baseline estimation algorithms directly. Meanwhile, the accuracy and practicality of four baseline estimation algorithms were evaluated by the assessment method, which include statistics-sensitive nonlinear iterative peak-clipping (SINP), fast Fourier transform (FFT), adaptive iteratively reweighted penalized least squares (AirPLS), and automated iterative moving averaging (AIMA). Comparing the relative error of the characteristic peak area, AirPLS gave the best performance for baseline estimation in EDXRF.