THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

Solution of scattering from rough surface with a 2D target above it by a hybrid method based on the reciprocity theorem and the forward-backward method

This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.

Iterative methods for a forward-backward heat equation in two-dimension

A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.

Forward-backward热方程差分逼近的直接算法

通过利用区域分解技术和并行算法的思想 ,把原问题分解为几个完全独立的子区域上的问题 ,并直接并行求解 ,然后把这些解作适当的线性组合 ,得到原问题的解 .给出了 Forward-

Solutions to general forward-backward doubly stochastic differential equations

A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.

求解双层凸优化问题的Forward-Backward分裂算法

Forward-Backward分裂算法是求解极大单调算子和问题以及极小化具有可分结构的凸函数和问题的有效算法。本文利用该算法在Hilbert空间中构造出了求解双层优化问题的分裂算法。与已有文献相比,所提算法不仅在参数的选取上更加灵活,而且本文还证明了该算法生成的点列能收敛到双层优化问题的解。

Non Ideal Schottky Barrier Diode’s Parameters Extraction and Materials Identification from Dark I-V-T Characteristics

Several parameters of a commercial Si-based Schottky barrier diode (SBD) with unknown metal material and semiconductor-type have been investigated in this work from dark forward and reverse I-V characteristics in the temperature (T) range of [274.5 K - 366.5 K]. Those parameters include the reverse saturation current (Is), the ideality factor (n), the series and the shunt resistances (Rs and Rsh), the effective and the zero bias barrier heights (ΦB and ΦB0), the product of the electrical active area (A) and the effective Richardson constant (A**), the built-in potential (Vbi), together with the semiconductor doping concentration (NA or ND). Some of them have been extracted by using two or three different methods. The main features of each approach have been clearly stated. From one parameter to another, results have been discussed in terms of structure performance, comparison on one another when extracted from different methods, accordance or discordance with data from other works, and parameter’s temperature or voltage dependence. A comparison of results on ΦB, ΦB0, n and NA or ND parameters with some available data in literature for the same parameters, has especially led to clear propositions on the identity of the analyzed SBD’s metal and semiconductor-type.

一种求解包含问题的算法研究

一种实希尔伯特空间中求解包含问题的算法被提出,所提出的算法基于向前向后方法、压缩方法、惯性方法和无需搜索的自适应步长。算法的特点为迭代中多次使用惯性加速方法,且自适应步长随着迭代次数增加可能增大。在包含问题解集非空、一个映射极大单调、另一个映射单调且利普希茨连续的假设下,算法的强收敛性被证明。

界面特性对InAs/GaSb Ⅱ型超晶格光学性质影响理论研究

InAs/GaSb Ⅱ型超晶格是中红外谱段光电子器件的核心结构,其Ⅱ型能带排列特点使电子、空穴在实空间分离而跨过界面,其非公共原子构型使得界面态丰富。我们在Burt-Foreman包络函数理论的基础上,讨论了不同界面态对超晶格电子能态和波函数的调控作用。理论计算表明,超晶格缓变界面和界面势两种不对称界面态分布,都会导致重空穴带的自旋劈裂,而只有施加界面势时才会使得轻空穴带发生自旋劈裂。此外,研究了改变阱宽和改变势垒时超晶格体系带隙的变化趋势。结果表明,随着势垒厚度增大,陡峭界面和缓变界面两种界面态下的带隙计算结果逐渐降低,并且随着厚度增加带隙趋于收敛,而界面势下的带隙计算结果随着势垒厚度的增大而增大,与前两者呈现相反的趋势,这为中红外超晶格器件的精确设计提供了可参考的理论基础。

地—井瞬变电磁三维各向异性响应特征研究

地—井瞬变电磁法由于抗干扰能力强、响应信号明显等优势而应用广泛。在深部矿产资源调查和地质构造勘查等任务中,多个油气储存在层理发育的沉积岩地区大多数情况下表现为电各向异性,但是目前地—井瞬变电磁反演算法均基于各向同性模型,传统反演成像技术不再适用。为了分析地层电导率各向异性对地—井瞬变电磁勘探结果的影响,对各向异性介质模型研究其电磁响应特性。基于各向异性介质的电导率张量,提出了一种基于有限元方法的三维分析模型,采用PARDISO求解器进行求解。针对多个各向异性角度的情况模拟了各向异性介质的瞬变电磁响应,分析介质各向异性对电磁波传播规律的影响,探讨了各向异性瞬变电磁响应特征。研究结果表明:在垂直各向异性介质中,电磁波传播方向垂直于电导率最大的方向时,电磁响应变化最明显;电磁波传播方向平行于电导率最大的方向时,电磁响应变化最弱。在水平各向异性介质中,电磁波垂直于电导率最小的方向时,电磁响应变化最明显;电磁波平行于电导率最小的方向时,响应变化较弱。最后,针对地—井瞬变电磁方位测井,分析了发射源沿不同方向条件下各向异性地层和异常体模型的电磁响应,结果表明其瞬变电磁响应特征与发射源的方向有关,且对于主轴各向异性异常体,发射源方向的选择直接影响对异常体各向异性方向的判断。该研究结论对油气开发地球物理勘探方法的研究具有一定的参考价值。

求解拟单调变分不等式问题的交替惯性向前向后算法

该文结合线搜索方法,提出了改进的交替惯性向前向后算法求解拟单调变分不等式问题.该算法在每次迭代时只需计算一次到可行集上的投影,在一定的假设下证明了解集的弱收敛性定理.最后通过数值实验验证了算法的有效性.

基于前后向矩阵束方法的线性排布无人机集群目标规模估算

利用前后向矩阵束方法,提出了一种有效的“蜂群”无人机群目标个数估计方法用于目标检测。与传统的参数估算方法相比,所提方法对于稀疏信号也能准确地进行估算。首先,在一定的角度或频率下,获取线阵排列群目标的雷达散射截面;然后,根据已知的雷达回波构造Hankel-Toeplitz矩阵,并对该矩阵进行奇异值分解;最后,通过设置合适的阈值选取比例较大的奇异值,以此准确地估算线阵排列群目标的个数。此外,文中还讨论了不同信噪比对估算结果的影响。为了提高精度,文中采用多组不同方位角度的回波信号来联合估算群目标的个数。仿真结果表明,该方法能够有效、准确地估算线阵排列群目标的个数,而且估计结果不受噪声的影响,具有较好的鲁棒性。

基于前推回代法的高低压反窃电技术研究

窃电行为不仅造成了国家电力的损失,在配电网中形成潜在的安全隐患,还为工作人员增加了工作难度。为探索高效可行的反窃电技术,采用前推回代法计算配电网电路潮流,得到线路损失值,确定疑似窃电位置。进一步计算电压偏移率和关联度,准确判定窃电点,并计算补足功率与实际功率差值得出窃电量。验证表明,该方法的潮流计算效率提高了30%左右。对高低压用户用电量实例分析时,共发现3个窃电点,电压关联度平均值在0.35左右,比正常关联度值低,证实了前推回代法在反窃电技术中的有效性,为电力系统反窃电工作的实施提供了合理参考。

基于改进电量法及前推回代法的高渗透率新能源配电网线损计算研究

分布式电源(DG)的高比例接入使得配电网潮流双向流动,传统的线损计算方法不再适用。首先,针对传统电量法电压与功率因数需全网一致假设条件的限制,提出电压电量法和电压功率因数电量法;然后,对多种分布式电源进行节点类型建模,提出改进前推回代法,实现对高渗透率配电网线损的精细求解;最后,对某地区实际配电线路进行计算,探究各种线损计算方法的误差及适用条件,并通过3种场景对比分析分布式电源接入容量、位置及其他参数对配电网电压以及线损的影响,验证了改进电量法以及改进前推回代法的可行性,对配电网线损计算具有参考意义。

A NEW PSEUDOSPECTRAL APPROXIMATION FOR THE FOWARD-BACKWARD HEAT EQUATION

In this paper,we propose a new numerical method which is a least squares approximaton based on pseudospectral method for the Forward-Backward heat equation. The existence and uniqueness of the solution of the least squares approximation are proved. Error estimates for this approximation are given,which show that tile order of convergence depends only on the regularity of tile solution and the right hand of the Forward-Backward heat equation.

牵引供电系统网压计算方法研究

研究目的:牵引供电系统电压计算方法在现行规范《牵引供电系统电压损失的计算条件和方法》(TB/T 1652—1996)中有详细规定,然而在实际运营中发现,当牵引供电系统负荷较重、牵引网电压降较大时,上述规范的计算结果已不能满足实际需求。已有文献对上述情况进行分析,但提出的改进方法与实测结果仍有一定差异。本文针对上述情况,借鉴电力系统前推回代电压计算方法对单线牵引供电系统电压进行计算,分别从理论推导证明、时域仿真、现场实测三个方面对上述三类方法进行分析比较。研究结论:(1)电力系统前推回代方法在单线牵引供电系统电压计算时较现行规范与前人改进算法更为准确;(2)本研究结论可作为现行规范《牵引供电系统电压损失的计算条件和方法》(TB/T 1652—1996)的有效补充。

ITERATIVE METHODS FOR THE FORWARD-BACKWARD HEAT EQUATION

In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. Then we discuss the iterative method based on the domain decomposition for our scheme and derive the bounds for the rates of convergence. Finally we present some numerical experiments to support our analysis.

Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations

By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.

Domain Decomposition Method for the Forward-Backward Heat Equation

The forward-backward heat equation arises in a remarkable variety of physical applications. A non-overlaping domain decomposition method was constructed to obtain numerical solutions of the forward-backward heat equation. The primary advantage is that the method reduces the computation time tremendously. The convergence of the given method is established. The numerical performance shows that the domain decomposition method is effective.

分布式电源并网的潮流计算

分布式电源DG(distributed generation)并网对配电系统的电压和网损有着重要影响。分析了常见的几种DG,提出了它们各自在潮流计算中的模型以及处理方法,并采用前推回代法来计算有DG并网的配电系统的潮流。考虑到前推回代法处理PV节点的能力较差,引入了注入无功补偿法,该方法适合DG并入配电系统的潮流计算。然后,通过在33节点配电系统中进行大量测试,表明该方法是可行的。最后分析DG并网对系统电压和网损的影响。