Fourth‐order compact scheme for the one‐dimensional sine‐Gordon equation

Finite difference scheme to the generalized one‐dimensional sine‐Gordon equation is considered in this paper. After approximating the second order derivative in the space variable by the compact finite difference, we transform the sine‐Gordon equation into an initial‐value problem of a second‐order ordinary differential equation. Then Padé approximant is used to approximate the time derivatives. The resulting fully discrete nonlinear finite‐difference equation is solved by a predictor‐corrector scheme. Both Dirichlet and Neumann boundary conditions are considered in our proposed algorithm. Stability analysis and error estimate are given for homogeneous Dirichlet boundary value problems using energy method. Numerical results are given to verify the condition for stability and convergence and to examine the accuracy and efficiency of the proposed algorithm. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

The group reduction for bounded cosine functions on UMD spaces

It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A)^1/2 generates a bounded C ₀-group. The proof uses a transference principle for cosine functions.      

无光焦度校正板在主镜后的牛顿光学系统的设计

描述了无光焦度校正板放在主反射镜后的无光焦度校正板-牛顿光学系统的设计.光栏放在主镜上,改变相对孔径A,选择校正板光焦度φ21、φ22和遮拦比α,进行光学系统的光线追迹,求解出光学系统的最佳选择,并给出各种设计曲线和设计结果,对光学系统进行合理的评价.     

A stabilized finite element predictor–corrector scheme for the incompressible Navier–Stokes equations using a nodal‐based implementation

A finite element model to solve the incompressible Navier–Stokes equations based on the stabilization with orthogonal subscales, a predictor–corrector scheme to segregate the pressure and a nodal based implementation is presented in this paper. The stabilization consists of adding a least‐squares form of the component orthogonal to the finite element space of the convective and pressure gradient terms, which allows to deal with convection‐dominated flows and to use equal velocity–pressure interpolation. The pressure segregation is inspired in fractional step schemes, although the converged solution corresponds to that of a monolithic time integration. Finally, the nodal‐based implementation is based on an a priori calculation of the integrals appearing in the formulation and then the construction of the matrix and right‐hand side vector of the final algebraic system to be solved. After appropriate approximations, this matrix and this vector can be constructed directly for each nodal point, without the need to loop over the elements and thus making the calculations much faster. Some issues related to this implementation for fractional step and our predictor–corrector scheme, which is the main contribution of this paper, are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

利用衍射光学元件进行共形整流罩像差校正的研究

建立了共形整流罩的模型结构，分析了其成像特性，并提出了采用加入衍射元件的方法来设计共形整流罩后的校正板，软件模拟结果表明带有衍射面的校正板能够进一步地改善共形整流罩成像质量. 关键词： 共形光学 整流罩 像差校正 衍射光学     

Numerical Calculation of Flows and Long-Range Transport of Contaminants in Lowland River Reservoirs

Flows and contaminant transport in the Novosibirsk reservoir are calculated on the basis of a two-dimensional (plane) nonstationary model with Saint Venant's equations. The model allows for the presence of a large number of islands. Coefficients of horizontal exchange (dispersion) are calculated by the formula taking into account dynamic velocity at the bottom. Numerical implementation of the model employs a semi-implicit conservative finite-difference TVD scheme on a distributed grid and procedures allowing for the flow past these islands. Model examples of calculations and computation results for dynamics of long-range transport of contaminants along the Novosibirsk reservoir are given.     

双相介质波动方程孔隙率反演的同伦方法

从材料响应的理论合成应与实际测量数据相拟合这一出发点，将双相介质波劝方程参数的反演问题转化为非线性算子方程的零点求解问题，从而应用一种大范围收敛的同伦方尘土注来解非线性算子方程，并把这种方法用于Simon(1984)给出的具有解析的一维双相介质模型的数值模拟，最后的数值结果表明，给出的算法是十分有效的。     

条纹法实现高分辨率成像

 研究了一种高分辨率成像的方法,该方法利用余弦条纹照射目标以获取目标更宽的频谱。条纹对目标的照射起到了对目标频谱的搬移作用,使光学系统截止频率外的一部分高频分量通过系统。利用多幅条纹照射目标并分别成像,各条纹空间频率相同而相位按照一定规律变化,综合处理照射条纹后获得的图像将叠加在一起的频谱分量分离开并恢复到相应的位置,经过反变换获得高分辨率的图像。通过计算机仿真验证了这种方法的可行性。     

BEPCⅡ LINAC束流光学匹配及轨道校正计算研究

北京正负电子对撞机直线注入器(BEPCⅡ LINAC)的升级改进要求建立束流光学匹配计算和轨道校正系统,为此对束流光学匹配计算和轨道校正计算的方法进行了研究,并采用VC++语言编写了相应的程序,利用最小二乘法原理进行了束流光学匹配计算,模拟了束流轨道校正,取得了较为理想的结果。     

嵌入式波前处理与控制系统设计

建立了一种嵌入式波前处理与控制系统的架构模型,实现对波前畸变的实时测量、重构与校正,并给出了重构与控制算法的理论分析。针对系统设计,引入全数字化设计思想,利用数字电路在底层硬件中完成海量数据计算处理与控制参数生成,讨论了高速波前处理模块与驱动控制模块设计。系统利用嵌入式自适应控制手段,可完全工作于无人值守模式,实现对激光系统光束质量的实时闭环控制。