Broyden算法在薛定谔方程和泊松方程自洽求解中的应用

利用Broyden算法,通过自洽求解一维半导体量子线的电子浓度分布和电势分布,和常用的牛顿法以及逐次超松弛(SOR)法相比较,确认了Broyden算法的收敛结果正确,并减少了达到收敛的迭代步数,是对于薛定谔方程和泊松方程组成的非线性方程组系统自洽求解的有力工具.     

由牛顿算法求解Pao-Sah电压方程的一个初始值

目前集约建模的趋势是由基于阈值电压的模型转向基于表面势的模型,而后者需要一个对非线性Pao-Sah电压方程的精确解,作为隐含数方程,Pao-Sah电压方程必须数值求解以求得表面势。牛顿算法是一个收敛较快而常用的算法,但却易收敛到错误的根,提出一个能保证牛顿算法收敛到正确的表面势解、且具有可控的高精度及运算速度的初始值,由该初始值计算并分析了数值计算结果。高精度的数值解可作为其它近似解的检验。     

绝对值方程的一种光滑牛顿算法

绝对值方程Ax-|x|=b,A∈R^n×n,b∈Rⁿ是一类特殊的非线性方程,且是NP-Hard问题。文中根据其半光滑的特性,通过构造光滑逼近函数,提出了求解绝对值方程的光滑牛顿算法。理论分析表明方程有解,A的奇异值＞1时,算法具有全局收敛性,收敛速度为二次,实验结果表明了该算法的可行性。最终在总结中提出了光滑牛顿法可供改进的地方。     

泊松方程数值解法的加速收敛法

用数值方法对泊松方程求解时，往往要对迭代的中间结果作适当的压缩处理，以加快收敛速度和避免溢出。本文提出一种单一指数因子的非线性压缩法。一维数值模拟结果表明，平衡态时不必进行压缩处理。而在非平衡态时，最佳指数压缩因子的大小与杂质浓度有关。参考本文给出的数值计算结果，根据给定器件的杂质浓度分布，选定一最佳指数压缩因子，可以使泊松方程的数值求解过程具有最快的收敛速度。     

GaN HFET的大信号射频工作模型(续)

<正>3短栅长HFET在高漏压下的能带畸变在一般的异质结能带计算中,都只考虑异质结材料生长方向的势垒变化。现在表面电势在x方向产生很大的电场梯度,该表面电场会扩展到整个异质结内,形成复杂的二维电场分布。于是在自洽求解泊松方程和薛定谔方程时就必须求解二维泊松方程     

AlGaN/GaN一维模型自洽求解和二维电子气特性研究

实现了一维Poisson-Schrodinger方程的自洽求解,在此基础上求出了AlGaN/GaN异质结导带结构和二维电子气分布。计算结果表明极化效应是形成高浓度电子面密度的主要因素。研究了AlGaN/GaN系统中隔离层厚度对二维电子气浓度的影响,并对计算结果进行了分析。     

量子点接触器件电势准3D数值模型和模拟方法

采用三维泊松方程和二维薛定谔方程自洽求解方法,建立量子点接触器件（QPC）内的电势分布和二维电子气层的电子密度分布的准三维模型及模拟方法,并将模拟结果与传统的Buttiker鞍型电势分布进行比较。结果表明,器件中的电势分布随结构和偏置对传统鞍型电势有所偏离,并讨论了栅极结构和外加偏压对电势分布影响的规律,对QPC传感器设计具有指导作用。     

AlGaN/GaN势垒层异质结构与二维电子气密度的相互作用

在忽略二维电子气波函数对势垒层渗透的前提下提出了直接求解无电子势垒层泊松方程来计算势垒层能带的新思路,提出了把势垒层以外的极化电荷、杂质电荷及电子电荷作为势垒层边界上的界面电荷来解势垒层泊松方程的新方法。由此计算出的势垒层能带和自洽能带计算结果相吻合。用电子气密度多项式来拟合沟道阱子带能级随电子气密度变化的曲线,推算出新的二维电子气密度的超越方程。对于各种不同异质结构,从超越方程解出的电子气密度和势垒层能带同自洽能带计算结果相吻合,从而创立了一种自洽求解沟道阱泊松方程和薛定谔方程的新方法。研究了二维电子气密度与势垒层异质结构的相互作用,讨论了电子气密度随异质结构的变化,提出了异质结能带剪裁的新思路。     

基于双向抛物方程逆算法的障碍物定位技术研究

在单向抛物方程法的逆算法即逆绕射抛物方程法的基础上,研究了双向抛物方程法的逆算法,对障碍物引起的后向场进行了逆绕射运算,并根据该逆绕射场分布来确定障碍物的位置和高度.基于此逆算法对刃峰形障碍物的定位问题进行了数值仿真求解,分析了天线高度和刃峰位置的变化对定位精度的影响.数值结果表明双向抛物方程逆算法能用于对障碍物进行定位,且对单刃峰的定位精度很高.     

求解IETD问题的CFIE方程之比较

针对基于矩量法的积分方程时域求解存在的晚时震荡问题,分析两种稳定求解时域积分方程的混合场积分方程方法:隐式时间步进算法的混合场积分方程和基于拉盖尔多项式阶数步进算法的混合场积分方程。计算了目标的时域散射场和单站雷达散射截面,两种方法求得的结果吻合较好,表明两种方法解决时域积分方程晚时震荡问题的有效性。     

Comparison of simulation algorithms for accelerated determination of periodic steady state of switched networks

This paper presents a comparison of the following algorithms for accelerated determination of periodic steady state of switched networks: Newton's method with analytically determined Jacobian; Newton's method with numerically determined Jacobian; Newton's method with Broyden updates of an initial numerically determined Jacobian; Newton's method with a globally convergent strategy (and numerical Jacobian); Bukowski's method; and Skelboe's method. Each algorithm is incorporated into a very accurate power electronics' simulator (PECS) at source-code level and compared on a common basis. The results on several switching converters suggest the analytical Newton's method to be the most accurate and fastest. When analytical derivatives are not available, both Broyden's and Skelboe's methods are competitive.     

A fast reliable iteration method for dc analysis of nonlinear networks

A new iteration method for nonlinear dc analysis, based on Broyden's modification of the Newton-Raphson method, is described. Broyden introduces a variable correction factor which is chosen so as to minimize, or at least reduce, the size of the error vector at each iteration. This completely precludes divergence of the algorithm. Broyden also develops a means for updating the inverse Jacobian matrix without ever having to compute or invert it explicitly. Two algorithms are described, one for solving a single nonlinear problem and the other for solving a large number of neighboring problems such as are encountered in statistical (Monte Carlo) analysis. Timing measurements on these two algorithms are reported. Application of these algorithms to statistical ac analysis and to frequency response calculations is proposed and a possible method of improving the basic algorithm by means of a sparse matrix technique is described.     

Method of solving ambiguity for sparse array via power estimation based on MUSIC algorithm

Sparse linear arrays provide better performance than the filled linear arrays in terms of direction estimation and resolution with reduced size and low cost. However, they are subject to manifold ambiguity. A method based on the Multiple Signal Classification (MUSIC) algorithm to solve the manifold ambiguity of uncorrelated sources for sparse array is proposed in this paper. The method consists of two steps. The first step is to obtain all the directions of arrivals (DOAs), including true and spurious DOAs, using traditional MUSIC. The second step is to estimate the power values of the all DOAs by substituting all the DOAs to a cost function. The well-known Davidson Fletcher Powell (DFP) and Broyden Fletcher Goldfarb Shanno (BFGS) algorithms are used to estimate the power values. The power values of spurious DOAs are very small or tend to zero compared with the values of the true DOAs. The true DOAs are then discriminated easily from the spurious DOAs with the power values. Simulation results demonstrate the effectiveness and the feasibility of the method.     

基于正交校正共轭梯度法的快速神经网络学习算法研究

前馈神经网络由于具有理论上逼近任意非线性连续映射的能力,因而非常适合于非线性系统建模及构成自适应控制。为了提高前馈神经网络的权的学习效率及稳定性,该文提出一种基于正交校正共轭梯度优化方法的快速神经网络学习算法,通过与其它学习算法(如:BP算法、变尺度法、用差商近似代替导数的Powell法等)的比较,经仿真试验表明,本算法是一种高效、快速的学习算法。     

Range-free localization algorithm based on connectivity and motion

Information about the position of entities is very valuable in many fields. People, animals, robots and sensors are some examples of entities that have been targeted as nodes of interest for localization purposes. Technical advances in ubiquitous computing and wireless communications properties are very valuable means to obtain localization information. This paper presents a novel range-free localization algorithm based on connectivity and motion (LACM). The core of the algorithm is an error function that measures the error of the obtained trajectories with respect to the localization solution space, a multi-dimensional space that encompasses all solutions that satisfy completely the constraints of a range-free localization problem. LACM is a centralized method that can be used standalone or as a refinement phase for other localization methods. Limited-memory Broyden–Fletcher–Goldfarb–Shanno, an unconstrained optimization algorithm, is the numerical method used to minimize the error function. The performance of LACM is validated both through extensive simulations with excellent results in scenarios with irregular communications and by transforming real Bluetooth connectivity traces into localization information.     

Multiuser Margin Optimization in Digital Subscriber Line (DSL) Channels

This paper presents efficient multiuser margin optimization algorithms suitable for multicarrier digital subscriber line (DSL) systems using Dynamic Spectrum Management (DSM). The favorable monotonicity and fairness properties of multiuser margin are employed to formulate a box-constrained nonlinear least squares (NLSQ) problem for multiuser margin maximization, which is efficiently solved by using a scaled-gradient trust-region approach with Broyden Jacobian update. Based on this NLSQ formulation, a multiuser harmonized margin (MHM) optimization algorithm for resource allocation is developed. A Newton–Raphson method is also developed for fast margin estimation and used within the MHM. The MHM algorithm converges efficiently to a solution for the best common equal margin to all users, while explicitly guaranteeing their target rate requirements. (This is the reason for the term harmonized.) Furthermore, its predominantly distributed structure can be implemented in DSL/DSM scenarios with only Level 1 coordination. Simulation results of various cases verify the convergence to the unique optimal solution within 5–10 iterations.     

分布式CFAR检测系统的最优门限求取新方法

针对并行分布式检测网络结构局部采用CFAR检测器的情形,提出了一种在融合规则给定时,局部CFAR检测器最优门限的求取方法。给出了在任意融合规则下融合中心的检测概率和虚警概率关于局部门限的一阶导数的数值计算公式,并利用Broyden方法求取最优的局部门限。该方法避免了传统方法需要计算二阶导数的复杂性,并且更容易推广到局部采用多类CFAR检测器的情形。实验分析表明了算法的有效性。     

有限衍射X波非线性声场特性研究

X波用于超声成像可以获得很高的帧率，但在线性成像模式下图像空间分辨率相对于传统的聚焦成像有所下降。本文通过时域数值方法求解KZK(Khokhlov-Zabolotskaya-Kuznetsov)方程，研究有限衍射X波的非线性声场特性。结果表明：无论宽带或限带X波，其非线性声场同样是有限衍射波，并且二次谐波具有比基波更窄的主瓣和更小的副瓣。采用X波的二次谐波进行成像能够在整个成像区域获得更高的分辨率。理论分析验证了数值计算结果。     

FAST gradient based yield optimization of nonlinear circuits

Yield optimization of nonlinear microwave circuits operating in the steady state under large-signal periodic excitations is studied. Two novel high-speed methods of gradient calculation, the integrated gradient approximation technique (IGAT) and the feasible adjoint sensitivity technique (FAST) are introduced. IGAT utilizes the Broyden formula with special iterations of Powell to update the approximate gradients. FAST combines the efficiency and accuracy of the adjoint sensitivity technique with the simplicity of the perturbation technique. IGAT and FAST are compared with the simple perturbation approximate sensitivity technique (PAST) on the one extreme and the theoretical exact adjoint sensitivity technique (EAST) on the other. A FET frequency doubler example treats statistics of both linear elements and nonlinear device parameters. This design has six optimizable variables, including input power and bias conditions, and 34 statistical parameters. Using either IGAT or FAST, yield is driven from 40% to 70%. FAST exhibits superior efficiency     

应用积分法的发动机内壁瞬态温度测试研究

在传热学基本原理和能量守恒定律的基础上,本文提出了利用积分法求解航空发动机壁面导热的偏微分方程,进而实现对航空发动机内壁瞬态温度的测量。借助螺塞热电偶温度传感器和多路数据采集卡,建立了瞬态温度测量系统,利用氢氧焰模拟航空发动机内部瞬态高温源,分别得出了传感器和红外测温仪测得的发动机内壁表面温度变化曲线。实验结果表明该方...