三维高阶深度偏移方程及其数值求解方法

从三维非均匀介质中的波动方程出发，利用拟微分算子理论，Ｐａｄｅ逼近方法及因式分解技巧，获得了非均匀介质的三维高阶深度偏移方程，相应地提出了逐次低阶方程方法、低阶方程组方法及分裂方法等３种求解方法．与二维情形不同，以上每一种方法在数值求解时均存在由测线坐标ｙ的出现而带来的困难．为了克服这一困难，我们提出了差分算子分解方法，避免了近年来人们竞相研究的ｘ－ｙ方向微分算子分裂带来的分裂误差，保持了应有的相容性，解决了这一令人烦恼的问题．

飞机稳态尾旋平衡点的综合求解方法研究

为求解飞机稳态尾旋平衡点,推导了飞机稳态尾旋的动力学方程,并针对该方程给出了三种求解方法:作图法、数值求解法以及在前两种方法的基础上所提出的一种综合求解方法。综合求解方法首先使用作图法得出方程的所有近似解,并用稳态尾旋判据判断解是否为稳定解,然后将稳定近似解作为数值求解法的初值进行精确求解。运用综合求解方法对算例飞机进行了稳态尾旋平衡点的计算,算法收敛迅速,结果精确,表明该方法具有很好的工程应用价值。

拉索-阻尼器体系振动索力测量法研究

拉索索力的精确测量是索类结构健康监测的一个重要内容。由于阻尼器的存在,已有的不考虑阻尼器的索力识别方法在测量拉索-阻尼器体系索力时精度将受到影响。利用Steffensen不动点迭代法对的拉索阻尼器系统的频率超越方程进行求解,进而给出了一种新的考虑阻尼器因素的索力识别方法,并给出了该方法和其他三种方法在识别拉索阻尼器系统索力时的相对误差表达式。通过数值仿真,研究拉索参数和阻尼器参数对各方法的影响,比较了各方法的相对误差范围。研究表明,基于频率超越方程数值解法的索力识别方法是进行拉索-阻尼器系统索力识别时的最佳选择。

桥梁船撞力实用计算方法

分析介绍了 5种船撞力实用计算方法 ,以哈尔滨松花江斜拉公路桥为例进行了应用计算 ,并对各种方法的应用提出了建议。

基于Simulink电路模拟仿真求解Bagley-Torvik方程

针对定常系数的分数阶Bagley-Torvik方程,提出一种新颖的求解方法——电路模拟仿真法.该方法的核心思想是利用分抗逼近电路构造微积算子s~μ(-1<μ<0)去代替分数导数算子_0D■(-1<μ<0).将分抗逼近电路阻抗函数转换为Simulink中的传输函数模块,然后运用传输函数模块搭建仿真框图求解分数阶微分方程.将电路模拟仿真法与传统的数值逼近求解法进行对比,对比结果表明,电路模拟仿真法求解结果稳定可靠;并且可根据仿真框图搭建实际电路对分数阶微分方程进行实时求解.

高分辨脑电图的技术途径

阐述了近年来发展的高分辨脑电图所实现的技术途径 .着重介绍了目前几种有代表性的从头皮电位测量值重建皮层电位分布的方法 :解析求解法、数值求解法 (包括有限元法和边界元法 )和皮层成像技术等 .系统地分析了这些方法的技术特点 。

Analysis of characteristic functions for equivalent circuit model in monolithic transformer

A model of monolithic transformers is presented, which is analyzed with characteristic functions. A closed- form analytical approach to extract all the model parameters for the equivalent circuit of Si-based on-chip transformers is proposed. A novel de-coupling technique is first developed to reduce the complexity in the Y parameters for the transformer, and the model parameters can then be extracted analytically by a set of characteristic functions. Simulation based on the extracted parameters has been carried out for transformers with different structures, and good accuracy is obtained compared to a 3-demensional full-wave numerical electro- magnetic field solver. The presented approach will be very useful to provide a scalable and wide-band compact circuit model for Si-based RF transformers.

Numerical Solution of Scalar Field for Nariai Case in 5D Ricci-Flat SdS Black String Space with Polynomial Approximation

As one exact candidate of the higher dimensional black hole, the 5D Ricci-flat Schwarzsehild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar field around the Nariai black hole by the polynomial approximation. Unlike the previous tangent approximation, this fitting function makes a perfect match in the leading intermediate region and gives a good description near both the event and the cosmological horizons. We can read from our results that the wave is close to a harmonic one with the tortoise coordinate. Furthermore, with the actual radial coordinate the waves pile up almost equally near the both horizons.

Thermal Design of Power Transformers via CFD

At Siemens, an in-house CFD （computational fluid dynamics） code UniFlow is used to investigate fluid flow and heat transfer in oil-immersed and dry-type transformers, as well as transformer components like windings, cores, tank walls, and radiators. This paper outlines its physical models and numerical solution methods. Furthermore, for oil-immersed transformers, it presents an application to a HV （high voltage） winding in a traction transformer of locomotives, cooled by synthetic ester.

Numerical Computation of Hard Excitation in an Autocatalytic Biochemical System

An autocatalytic biochemical system in the presence of recycling enzyme is solved numerically using two numerical methods based on finite difference schemes. The first method is the well known Euler method which is an explicit method, whereas the second method is implicit. Although the implicit method, method 2, is first-order accurate in time it converges to the fixed point（s） for large time step, L Numerical results show the existence of hard excitation and birhythmicity.

Robust nonlinear control of spacecraft formation flying using constraint forces

A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE).The nonlinear control laws are developed by solving the DAE.Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting con-trol laws are not robust in engineering application,the robust control law designed method is further developed by designing the correct coefficients to correct the errors of the formation array constraints.A numeral study simulated the robustness of this method for the various errors in the formation flying mission,including the initial errors of spacecraft formation,the reference satellite orbit determination errors,the relative perturbation forces model errors,and so on.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.

A Laplace Decomposition Method for Nonlinear Partial Diferential Equations with Nonlinear Term of Any Order

A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial differential equations with nonlinear term of any order, utt ＋ auxx ＋ bu ＋ cup ＋ du^2p-1 = 0, which contains some important equations of mathematical physics. Three distinct initial conditions are constructed and generalized numerical solutions are thereby obtained, including numerical hyperbolic function solutions and doubly periodic ones. Illustrative figures and comparisons between the numerical and exact solutions with different values of p are used to test the efficiency of the proposed method, which shows good results are azhieved.

On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schr¨odinger Equation for Interdiffused Quantum Wells and Quantum Wires

We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schr¨odinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domain.The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires.Also,the model of a linear harmonic oscillator is considered for comparison reasons.It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range,which is thus considered to be optimal.This range is found to depend on the number of mesh nodes N approximately as α_0 log_e^(α1)(α_2N),where the values of the constants α_0,α_1,and α_2are determined by fitting the numerical data.And the optimal range is found to be a weak function of the diffusion length.Moreover,it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schr¨odinger equation.

Parallel computing study for the large-scale generalized eigenvalue problems in modal analysis

In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis.Three predominant subspace algorithms,i.e.,Krylov-Schur method,implicitly restarted Arnoldi method and Jacobi-Davidson method,are modified with some complementary techniques to make them suitable for modal analysis.Detailed descriptions of the three algorithms are given.Based on these algorithms,a parallel solution procedure is established via the PANDA framework and its associated eigensolvers.Using the solution procedure on a machine equipped with up to 4800processors,the parallel performance of the three predominant methods is evaluated via numerical experiments with typical engineering structures,where the maximum testing scale attains twenty million degrees of freedom.The speedup curves for different cases are obtained and compared.The results show that the three methods are good for modal analysis in the scale of ten million degrees of freedom with a favorable parallel scalability.

Numerical study on the gas-kinetic high-order schemes for solving Boltzmann model equation

The high-order compact finite difference technique is introduced to solve the Boltzmann model equation, and the gas-kinetic high-order schemes are developed to simulate the different kinetic model equations such as the BGK model, the Shakhov model and the Ellipsoidal Statistical (ES) model in this paper. The methods are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the inner flows of normal shock wave for different Mach numbers, and the two-dimensional flows past a circular cylinder and a NACA 002 airfoil to verify the reliability of the present high-order algorithm and simulate gas transport phenomena covering various flow regimes. The computed results are found in good agreement both with the theoretical prediction from continuum to rarefied gas dynamics, the related DSMC solutions, and with the experimental results. The numerical effect of the schemes with the different precision and the different types of Boltzmann collision models on the computational efficiency and computed results is investigated and analyzed. The numerical experience indicates that an approach developing and applying the gas-kinetic high-order algorithm is feasible for directly solving the Boltzmann model equation.

On the Numerical Solution of Some Eikonal Equations:An Elliptic Solver Approach

The steady Eikonal equation is a prototypical first-order fully nonlinear equation. A numerical method based on elliptic solvers is presented here to solve two different kinds of steady Eikonal equations and compute solutions, which are maximal and minimal in the variational sense. The approach in this paper relies on a variational argument involving penalty, a biharmonic regularization, and an operator-splitting-based time-discretization scheme for the solution of an associated initial-value problem. This approach allows the decoupling of the nonlinearities and differential operators.Numerical experiments are performed to validate this approach and investigate its convergence properties from a numerical viewpoint.

Stripe theory based numerical method for solving asymmetrical hysteresis of friction force in linear rolling guideways

Linear rolling guideways(LRGs) play an important role in precision engineering. In the pre-rolling region, the hysteretic friction force exerts great impacts on the positioning accuracy. Numerical and experimental studies of the hysteresis of friction force are presented in this paper. A model, which is based on the stripe theory and the simplified theory of rolling contact, is built to describe the transient hysteresis of the friction force. Then, the model is modified by taking the anelasticity effect into consideration. Experimentally, a linear motor direct-drive setup is utilized to measure the transient asymmetrical hysteresis of the friction force in the pre-rolling region of an LRG. The influences of the pre-rolling displacement and the dwelling time on the asymmetrical hysteresis of the friction force are studied. The numerical and experimental results are well correlated, which shows good accuracy of the model. The transient asymmetrical hysteresis of friction force in the pre-rolling region of LRGs can thus be determined using the model.