对迭代最小二乘法天文像复原方法的改进

在天文班点成像技术中，Hofmann等提出的迭代最小二乘法－－积木法，能避免在由被观测目标像的重谱复原相位谱时复杂的相位递推过程，因此相误差的传递和积累也被消除了，但在该方法中，存在着新的问题；需要大量投放木块的迭代次数和长时间的处理过程，为提高该方法的工作效率，用“迭代位移叠加法”对目标斑点图进行预处理，经少数几次位移叠加的步骤后，很快就提供了目标像的基本结构和分布，得到了积木块投放点的位置，从而避免了盲目投放，大大减少了迭代投放的次数，显著地提高了该方法的效率。     

天文像复原迭代位移叠加法中的噪声偏差补偿

当工作于实际数据时，由于存在着多种噪声，导致了天文像复原迭代位移叠加法中的噪声偏差项，为消除这些噪声偏差项的影响，分别讨论了在观测目标和参考星的斑点数据期间由大气视宁度差异引入的系统误差和探测器严重的附加噪声产生的偏差，并给出了对这些噪声偏差项的补偿方法。     

多群辐射扩散方程组的分裂迭代算法收敛分析

分析了多群辐射扩散方程组的分裂迭代算法的收敛速度,证明其收敛特性,给出迭代矩阵谱半径的解析公式.对谱半径进行数值计算与分析,揭示算法的收敛速度与辐射系数之间的依赖关系,数值算例验证了理论结果,给出了该算法的适用条件.     

Iterative solutions for low lying excited states of a class of SchrSdinger equation

The convergent iterative procedure for solving the groundstate Schr?dinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.     

利用Fernald迭代后向积分法反演低空探测机载激光雷达消光系数

进行低空探测的机载激光雷达消光系数反演存在着标定点选取和标定值确定两大困难.Fernald迭代后向积分法能够在不利用其它辅助没备的情况下,找到进行低空探测机载激光雷达消光系数反演所需的标定点和标定值.利用Fernald迭代后向积分法和Palm et a1.(2002)方法分别对青岛机载激光雷达实验数据进行处理,得到的两条消光系数廓线基本吻合.定蜃分析显示:利用Fernald迭代后向积分法进行机载激光雷达消光系数反演时,激光雷达比对消光系数反演结果影响很大;标定点的消光系数值及迭代判据的取值对机载激光雷达消光系数反演的结果影响较小.Fernald迭代后向积分法为不用其它辅助设备进行低空探测的机载激光雷达消光系数反演提供了一种可行的范例.     

标准对力模型的新迭代方法(英文)

建立了一种求解标准对力模型的新迭代方法。该方法基于标准对力模型的多项式方案,为球形和形变系统提供了方便的初始值预测。特别是对于大尺寸系统,该方法将求解k对多项式的系统方程式简化为分步求解1对多项式系统的迭代过程,并通过快速Newton-Raphson以及Monte Carlo采样算法逐步提供初始值预测。通过扩展,本算法还可用于解决Gaudin型量子多体问题,例如考虑超过100条轨道、50对的大尺寸系统,以及超形变核、核裂变的研究中。A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.     

An Iterative Two-Grid Method of a Finite Element PML Approximation for the Two Dimensional Maxwell Problem

In this paper, we propose an iterative two-grid method for the edge finite element discretizations (a saddle-point system) of Perfectly Matched Layer (PML) equations to the Maxwell scattering problem in two dimensions. Firstly, we use a fine space to solve a discrete saddle-point system of $H(grad)$ variational problems, denoted by auxiliary system 1. Secondly, we use a coarse space to solve the original saddle-point system. Then, we use a fine space again to solve a discrete$\boldsymbol{H}(curl)$-elliptic variational problems, denoted by auxiliary system 2. Furthermore, we develop a regularization diagonal block preconditioner for auxiliary system 1 and use $H$-$X$ preconditioner for auxiliary system 2. Hence we essentially transform the original problem in a fine space to a corresponding (but much smaller) problem on a coarse space, due to the fact that the above two preconditioners are efficient and stable. Compared with some existing iterative methods for solving saddle-point systems, such as PMinres, numerical experiments show the competitive performance of our iterative two-grid method.     

A Fast High Order Iterative Solver for the Electromagnetic Scattering by Open Cavities Filled with the Inhomogeneous Media

The scattering of the open cavity filled with the inhomogeneous media is studied. The problem is discretized with a fourth order finite difference scheme and the immersed interface method, resulting in a linear system of equations with the high order accurate solutions in the whole computational domain. To solve the system of equations, we design an efficient iterative solver, which is based on the fast Fourier transformation, and provides an ideal preconditioner for Krylov subspace method. Numerical experiments demonstrate the capability of the proposed fast high order iterative solver.     

二维三温热传导方程求解中的非线性迭代初值选取

由于二维三温热传导方程具有很强的非线性特性,因此采用全隐格式对该方程离散后,所得非线性代数方程组的求解将变得非常困难.针对二维三温热传导方程离散所得非线性代数方程组的迭代求解,提出了一种有效的选取初值的方法.对两种不同性质的介质进行数值实验,结果表明,所设计的初值选取方法不仅大大提高了计算效率,而且能够降低非线性解法器对时间步长的影响.     

磁场与流场耦合问题中Newton-Laphson方法的收敛性分析(英文)

针对磁场与流场耦合问题的数值分析,提出并证明求解离散化过程所得到的非线性方程组牛顿-拉夫逊方法的-类局部收敛性条件.这-条件不仅给出了时间步长与空间步长、拟压缩因子等之间的关系,而且为数值求解磁场与流场耦合问题的牛顿-拉夫逊方法收敛性提供了理论依据.数值算例表明时间步长的实际取值要比理论值偏大.