辐射与物质强耦合问题的二维输运数值模拟

分析确定性输运数值方法模拟辐射与物质强耦合问题的难点,给出在任意四边形网格上求解该类问题的简单隅角平衡算法,并应用灰体输运综合加速算法提高输运方程的源迭代收敛速度,最后给出数值例子.     

一种基于角谱理论的改进型相位恢复迭代算法

进行星间激光通信的光学发射天线光束整形器设计时, 首要解决的问题是根据输入光场及理想的输出光场, 确定整形器的相位分布, 其核心就是相位恢复. 基于角谱传播理论, 在传统 Gerchberg-Saxton (G-S)迭代算法的基础上, 提出了一种幅度梯度加成迭代算法, 给出了算法的详细流程与分析. 与G-S相比, 新算法利用迭代过程, 构建光场幅度反馈回路, 利用梯度搜索最佳迭代路径, 两者的联合作用加速其迭代收敛进程. 数值仿真表明, 新算法的单位迭代次数所引起迭代误差下降的速度是G-S算法的1.7倍, 其收敛速度明显优于G-S算法; 对不同的随机初始相位, 新算法都能进行有效迭代, 表现出适应性强, 且收敛一致性好的优点. 幅度梯度加成迭代算法为复杂光场的高效相位恢复提供了一种新思路, 为设计各种衍射光学元件提供了技术支持. 关键词： 相位恢复 迭代算法 角谱理论 光通信     

点目标成像自适应光学随机并行梯度下降算法性能指标与收敛速度

在自适应光学中,随机并行梯度下降(SPGD)算法通过对系统的性能指标直接优化从而校正波前像差,具有很强的应用潜力.在点目标成像自适应光学系统中,SPGD算法经常采用强度分布平方和、平均半径和环围能量作为系统的性能指标进行优化.利用数值仿真分析了三种性能指标与畸变波前的均方根之间的关系.建立了一套实验平台,通过静态波前畸变校正实验,分析了SPGD算法采用以上三种不同的性能指标时的校正效果.实验结果与前面的数值仿真结果一致,表明SPGD取平均半径作为性能指标进行优化时效果较好.实验还分析了控制通道数目对收敛速度的影响.结果表明随着控制通道数目的增加性能指标曲线收敛所需的迭代次数显著增加,与驱动器个数的平方根之间存在一个近似的线性关系.     

混合Krylov子空间算法及其应用

给出了一种适合二维三温辐射流体力学能量方程的大型稀疏线性代数方程组的混合迭代算法.计算结果显示,该算法解二维三温辐射流体力学能量方程的大型稀疏线性代数方程组比原有算法快4倍左右;原有算法不收敛时,该算法收敛;各物理量也符合得很好.     

改进的约束共轭梯度闪光照相图像重建算法

 针对闪光照相图像信噪比低的特点,提出了一种改进的约束共轭梯度闪光照相图像重建算法。该算法在约束共轭梯度迭代重建的基础上,提出了新的预优矩阵选取方案,减小了重建图像的轴线噪声,利用松弛迭代步长代替共轭梯度法中的最优迭代步长,并采用了新的收敛准则,在保证算法收敛的同时,减少了重建算法的计算量。数值试验表明,与传统约束共轭梯度重建算法相比,改进算法稳定收敛,迭代速度更快,并能有效提高重建质量。     

基于联合平行投影迭代的叠栅层析重建

描述了一种新的叠栅层析代数迭代模型,并针对传统代数迭代法中的垂直投影算法收敛速度较慢的问题,结合新模型提出了一种改进了的平行投影重建算法.用该算法进行了数值模拟重建,结果表明：与叠栅层析中的变换类算法相比,对非完全数据问题,新算法具有有效结合先验知识进行重建的能力；与传统的垂直投影算法相比,新算法能在保证重建准确度的前提下大幅度的提高收敛速度.     

由少量投影数据快速重建图像的迭代算法

针对由少最角度的投影数据重建CT图像的问题,提出了一种改进的基于图像总变差最小的迭代重建算法.该算法采用共轭梯度法求图像总变差最小,并在迭代过程中采用了多分辨迭代技术.用模拟的投影数据和实际扫描数据进行了重建数值实验.实验结果表明该算法不但提高了重建图像质量,也同时显著提高了迭代图像的收敛速度.     

一种重构辐射噪声调制谱的方法

在进行辐射噪声信号的仿真研究中,希望利用经滤波、特征提取等处理所得到的反映目标特性的线谱、连续谱、调制谱来重构辐射噪声,以便于研究辐射噪声在声场中的传播特性。本文提出了利用迭代算法估算调制深度谱的算法,给出了时域辐射噪声的重构模型,以实测数据的调制谱为出发点,来重构其时域信号,并对重构前后的调制谱进行了误差分析,取得了较好的效果。     

塑性力学中二次规划算法的研究

针对弹塑性问题数值求解公式,运用二次规划法具体设计了算法,该算法克服了传统求解时冗长的迭代过程,仅有限次的基底交换就达倒收敛的解.文章还具体给出了常见屈服准则的梯度表达式.     

二维三温耦合差分方程组的解法

针对二维三温耦合热传导差分议程组的特点,给出并比较了块G－S算法与ICCG算法,数值结果表明,ICCG算法的收敛速度比块G－S算法的收敛速度可以快数千倍,并且,在二维激光黑腔靶耦合的数值计算中,如果能够实现向量化计算,使用ICCG方法将会大大提高数值模拟的计算效率。     

一种求解三维热辐射输运方程的整体预处理迭代方法及并行计算

为三维灰体热辐射输运方程的隐式离散纵标方法发展一个整体预处理迭代方法并研制并行程序。该方法采用组装线性代数方程组策略,同时求出所有离散方向上的辐射强度。借助预处理的Krylov子空间迭代法,避免复杂网格上扫描算法可能遇到的死锁问题,能够提高健壮性和计算效率。空间离散上采用一阶迎风有限体积格式。数值实验测试变形六面体网格上的收敛率、评估预处理迭代方法的性能并计算辐射和物质的耦合问题,给出三维弯管和黑腔问题的模拟结果,验证程序的正确性和方法的适应性。     

A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation

An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method.     

一种求解大型稀疏对称矩阵(极端)特征值问题的有效算法

提出一种求解大型稀疏对称矩阵几个最大(最小)特征值和相应特征向量的迭代块DL(即Davidson-Lanczos)算法并且讨论了迭代块DL算法的收敛率     

A framework for iterative analysis of non-classically damped dynamical systems

In this paper, we propose a general iterative framework to solve the dynamic problem for linear systems with non-classical viscous damping. A systematic approach is used to derive families of stationary iterative schemes that, as an instance of particular interest, decouple the equations of motion for numerical study of the system response. For such schemes, we present a detailed convergence analysis and propose several solution strategies suitable for a broad class of systems. These techniques are based on spectral analysis of particular iteration matrices arising in the derivation and aim at optimizing the convergence performance of the method. We demonstrate that the proposed systematic framework, based on a novel application of the homotopy analysis method, generalizes iterative schemes previously reported in the literature and, importantly, provides a unified perspective for the study of iterative solutions of dynamic problems. Further, we establish a connection between our results and the theory of iterative schemes for algebraic linear systems, thus providing insights on convergence results and applicability of the method. Numerical examples illustrate the effectiveness of the approach and indicate future research directions.     

High total variation-based method for sparse-view photoacoustic reconstruction

We propose a novel method by combining the total variation（TV） with the high-degree TV（HDTV） to improve the reconstruction quality of sparse-view sampling photoacoustic imaging（PAI）. A weighing function is adaptively updated in an iterative way to combine the solutions of the TV and HDTV minimizations. The fast iterative shrinkage/thresholding algorithm is implemented to solve both the TV and the HDTV minimizations with better convergence rate. Numerical results demonstrate the superiority and efficiency of the proposed method on sparse-view PAI. In vitro experiments also illustrate that the method can be used in practical sparse-view PAI.     

计算流体中一个改进的强隐式格式及迭代的收敛性

本文分析了Stone引入辅助矩阵Ã将五对角阵A变为七对角阵A+Ã的过程,指出Stone引入的辅助阵Ã不具备对称性,由此会给迭代收敛的分析工作带来困难。在此分析的基础上构造了一个对称的辅助矩阵,当A为对称时可使A+Ã对称正定。给出选取最优迭代参数ω的公式和办法。通过典型算例对这种改进的强隐式格式的数值稳定性作了验证。     

Optimal nonmonotonic convergence of the iterative Fourier-transform algorithm

The increase of the monotonic convergence rate is an important issue for iterative Fourier-transform algorithms. However, the steepest monotonic convergence of the iterative Fourier-transform algorithm does not always promise an optimal solution in the design of a diffractive optical element. The optimal nonmonotonic convergence of the iterative Fourier-transform algorithm is investigated by employing a microgenetic algorithm. The proposed hybrid scheme of the iterative Fourier-transform algorithm and the microgenetic algorithm show nonmonotonic convergence, and this results in a superior design.     

Improvement of the recursive projection method for linear iterative scheme stabilization based on an approximate eigenvalue problem

An algorithm for stabilizing linear iterative schemes is developed in this study. The recursive projection method is applied in order to stabilize divergent numerical algorithms. A criterion for selecting the divergent subspace of the iteration matrix with an approximate eigenvalue problem is introduced. The performance of the present algorithm is investigated in terms of storage requirements and CPU costs and is compared to the original Krylov criterion. Theoretical results on the divergent subspace selection accuracy are established. The method is then applied to the resolution of the linear advection–diffusion equation and to a sensitivity analysis for a turbulent transonic flow in the context of aerodynamic shape optimization. Numerical experiments demonstrate better robustness and faster convergence properties of the stabilization algorithm with the new criterion based on the approximate eigenvalue problem. This criterion requires only slight additional operations and memory which vanish in the limit of large linear systems.     

非对称线性代数方程组的并行算法

对五、七和九对角矩阵在并行-向量处理机上建立了解非对称线性代数方程组的PGCR算法,并分析了它的收敛性。本文给出的算法与多处理机的PGCR算法具有相同的选代次数。利用向量机模拟并行向量计算机并做数值实验,数值结果显示此算法很有效。