Klein-Gordon-Schr(o)dinger方程的辛Fourier拟谱格式

主要讨论Klein-Gordon-Sehrodinger方程的Fourier拟谱辛格式,包括中点公式和Stormer/Vedet格式.首先构造一个哈密尔顿方程,针对此哈密尔顿方程,在空间方向用Fourier拟谱离散得到一个有限维的哈密尔顿系统,对此有限维系统在时间方向用St(o)rmer/Verlet方法离散得到KGS...     

SRLW方程的多辛Fourier谱格式及其守恒律

通过引进正则动量，将对称正则长波方程（简称SRLW方程）转化成多辛形式的方程组，它具有多辛守恒律；介绍了空间方向满足周期边界条件的函数的Fourier谱方法；对SRLW方程的多辛方程组在空间方向利用Fourer谱方法，时间方向上应用Euler中点格式离散，得到其多辛Fourier拟谱格式；证明此格式的一些离散守恒律．用此格式模拟了SRLW方程的单个孤立波，还模拟了多个孤立波的追赶、碰撞和分离过程．     

Klein-Gordon-Schrdinger方程的辛Fourier拟谱格式(英文)

主要讨论Klein-Gordon-Schrdinger方程的Fourier拟谱辛格式,包括中点公式和Strmer/Verlet格式.首先构造一个哈密尔顿方程,针对此哈密尔顿方程,在空间方向用Fourier拟谱离散得到一个有限维的哈密尔顿系统,对此有限维系统在时间方向用Strmer/Verlet方法离散得到KGS方程的完全显式的辛格式.中点格式虽然是隐式的但效率也很高,且具有质量守恒律.数值实验表明,辛格式能够在长时间内很好地模拟各类孤立波.     

用谱拟合法计算强激光场中氢原子的高次谐波谱

介绍了一种新的求解含时薛定谔方程的谱拟合法 .该方法把含时波函数在少量且分布稀疏的网格点上拟合 ,结合泰勒级数展开 ,用相对简单的计算得到包括Δt高次项贡献的含时波函数 .并将这一方法用于强激光场中氢原子高次谐波谱的计算 ,得到了与其它方法一致的结果. A new spectral fitting method for solving the time-dependent Schrdinger equation has been developed and applied to the atom in intense laser fields. By using this method, the time-dependent wave functions are determined with few and far between discrete mesh points. And the high accuracy wave functions with contribution of high-order-term of Δt are obtained by using Taylor series expand method. Our method is proved by computing high order harmonic generation spectra of hydrogen in laser fields...     

MKdV方程的拟小波解

用拟小波方法求MKdV方程的数值解-先用拟小波离散格式离散空间导数，然后用四阶Runge-Kutta方法离散时间导数,对一个有精确解的实例ut+6u2ux+uxxx=0进行了数值计算-拟小波解与解析解完全重合，t=10000s时，二者也没有偏差- 关键词： MKdV方程 拟小波方法 孤子解     

SRNS方程求解叶栅流动的研究

为建立ＳＲＮＳ方程适用的数值计算方法，并使下游信息充分反馈到上游，本文对不可压ＳＲＮＳ方程提出了拟压缩性空间推进法，对压气机叶栅和透平叶栅的典型计算表明，该方法可准确而快速地模拟叶轮机械内部流场。     

某型运输机纵向等效拟配的问题及分析

某型运输机试飞纵向短周期等效拟配中在两个问题,一是纵向杆输入时长较长,频域辨识时高频段结果较差,二是在高阶电传飞机等效拟配时选择单拟配还是双拟配的问题,为了解决这两个问题,提出了时域辨识方法和对比分析传统机械式飞机和电传飞机试验数据方法;飞行试验数据处理结果表明,对于输入时间较长的试验动作,时域辨识效果较频域辨识好,使用时域和频域辨识结合的方法,大大提高了试飞数据的适用性;通过比较传统机械式飞机和现代电传飞机的试飞数据及拟配结果,发现高阶电传飞机必须使用双拟配方法才能更全面评价飞机特性;文中提出的辨识方法和分析方法很好地解决了某型运输机等效拟配中遇到的问题,可供其他电传飞机飞行试验参考。     

随机扰动对拟小波方法求解对流扩散方程的影响

引进拟小波方法数值求解对流扩散方程，研究结果表明，计算带宽W有一个极值，当计算带宽W取该极值时，该方程的拟小波解的精度最高，且好于迎风格式。当边界发生随机不等幅扰动时，对于积分时间较长的情况，拟小波格式的效果要稍逊于迎风格式；当边界发生随机等幅扰动时，若计算带宽W取大于等于20的整数时，方程拟小波解的精度与迎风格式相同；当参数受到随机扰动时，W取10时的拟小波解的均方根误差要小于迎风格式；在初值发生随机扰动且计算带宽W取10时，方程的拟小波解的精度最高，好于迎风格式。     

计算物理第23卷（2006）总目录

第1期计算中子增殖率的时间强迫碰撞方法……………………………王瑞宏邓力许海燕裴鹿成(1)Navier-Stokes方程的线性化微分求积法(英)……………………………………………李晨吴雄华(18)统一坐标系下多介质流体力学计算的一种方法…………………………………………………贾鹏彦(19)SRLW方程的多辛Fourier拟谱格式及其守恒律…………………孔令华曾文平刘儒勋孔令健(25)一类正交增强的阶谱六面体矢量单元构造……………………………………………李江海孙秦(32)SALE速度重映算法的改进……………………………………………………熊俊周海…     

用同步调制方法降低偏振模色散影响的理论研究

本文利用分布Fourier变换求解在双折射光纤中的耦合非线性薛定谔方程,数值计算了在20Gb/s的光孤子通信系统中偏振模色散(PMD)的影响.通过数值计算发现用同步调制的方法可以有效的降低偏振模色散对系统的影响.     

A spectral collocation algorithm for two-point boundary value problem in fiber Raman amplifier equations

A novel algorithm implementing Chebyshev spectral collocation (pseudospectral) method in combination with Newton’s method is proposed for the nonlinear two-point boundary value problem (BVP) arising in solving propagation equations in fiber Raman amplifier. Moreover, an algorithm to train the known linear solution for use as a starting solution for the Newton iteration is proposed and successfully implemented. The exponential accuracy obtained by the proposed Chebyshev pseudospectral method is demonstrated on a case of the Raman propagation equations with strong nonlinearities. This is in contrast to algebraic accuracy obtained by typical solvers used in the literature. The resolving power and the efficiency of the underlying Chebyshev grid are demonstrated in comparison to a known BVP solver.     

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach     

A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries

The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE.     

非均匀网格时域伪谱算法在超宽带技术中的应用

 与传统时域有限差分算法相比，采用以伪谱方法离散Maxwell微分方程为基础的时域伪谱(PSTD)算法计算大的电尺度电磁场时域问题，将大大提高计算效率，降低内存需求。为了拓宽PSTD算法的应用，近年来，基于网格插值方法的非均匀时域伪谱算法得到了发展。研究的重点是算法中非均匀网格技术的实现及其在时域瞬态脉冲电磁场模拟和高功率超宽带脉冲技术方面的应用。以高斯脉冲为激励源，用该算法计算了多层介质的反射和透射，并通过超宽带脉冲穿墙实验对这一方法的应用进行了验证。模拟和实验结果具有较好的一致性。     

A TWO-DIMENSIONAL TCHEBYCHEFF COLLOCATION METHOD FOR THE STUDY OF THE VIBRATION OF A BAFFLED FLUID-LOADED RECTANGULAR PLATE

The vibration and the acoustic radiation of a baffled rectangular plate in contact with a dense fluid is considered. By using Green's representation theorem, the original system of differential equations governing both the displacement and the acoustic sound pressure is transformed into a system of coupled boundary integral equations. The unknown functions (the displacement of the plate, the pressure jump at the surface of the plate and the boundary sources) are expanded as series of Tchebycheff polynomials. The new unknowns (the coefficients of the series) are calculated by using a collocation method. Some results, both theoretical and numerical, are given concerning the resolution properties of the Tchebycheff approximation. The numerical difficulties are presented, and solutions of these are proposed. Numerical examples are given.     

Modified Structure-Preserving Schemes for the Degasperis-Procesi Equation

We investigate the structure-preserving numerical algorithm of the Degasperis-Procesi equation which can be transformed into a bi-Hamiltonian form using the discrete variational derivative method.Based on two different space discretization methods,the Fourier pseudospectral method and the wavelet collocation method,we develop two modified structure-preserving schemes under the periodic boundary condition.These proposed schemes are proved to preserve the Hamiltonian invariants theoretically and numerically.Meanwhile,the numerical results confirm that they can simulate the propagation of solitons effectively for a long time.     

Multi-symplectic method for the coupled Schrodinger-KdV equations

In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrtidinger-KdV equations （CS＇KE） with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral （MSFP） scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson （CN） method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.     

Pseudospectral method with symplectic algorithm for the solution of time-dependent SchrSdinger equations

A pseudospectral method with symplectic algorithm for the solution of time-dependent Schrodinger equations （TDSE） is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral method and the time evolution is given in symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSE. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atom in strong laser field as compared with previously published work. The influence of the additional static electric field is also investigated.     

Rational Chebyshev pseudospectral approach for solving Thomas-Fermi equation

In this Letter we propose a pseudospectral method for solving Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on rational Chebyshev pseudospectral method. This method reduces the solution of this problem to the solution of a system of algebraic equations. Comparison with some numerical solutions shows that the present solution is highly accurate.     

Free vibration analysis of non-cylindrical helical springs by the pseudospectral method

The pseudospectral method is applied to the free vibration analysis of non-cylindrical helical springs. The entire domain is considered as a single element and the displacements and the rotations are approximated by the sums of Chebyshev polynomials. The internal forces and moments are substituted to give six equations of motion, which are collocated to yield the system of algebraic equations. The boundary condition is considered as the constraints, and the set of equations is condensed so that the number of degrees of freedom of the problem matches the number of the expansion coefficients. Numerical examples are provided for clamped-clamped, free-free, clamped-free and hinged-hinged boundary conditions.