微波脉冲窄缝耦合的数值并行计算

采用时域有限差分方法（FDTD）对微波脉冲与窄缝耦合过程进行了数值模拟计算,分析了数值模拟计算过程中的并行性,给出了相应的并行算法,算法中采用消息合并和计算与通信重叠技术来减少通信阳,分析了算法的通信复杂性,给出了在Alpha工作站上的测试结果。     

流动和传热问题的分区并行计算

针对交错网格下的SIMPLE数值算法实施了分区并行计算方法,在小型局域网下实现了流动和传热问题的并行数值计算.对两个经典的流动和传热问题的数值模拟实验表明,所建立的并行计算环境和分区并行算法能够得到正确的和收敛的数值结果.但与串行计算结果相比,并行计算误差明显大于串行计算误差.对并行算法做出的性能分析表明,所给出的并行算法得到了明显的加速效率.随着计算规模的增大,加速比和并行效率提高更显著.     

改进的3维粒子模拟并行算法

 提出了两种改进的3维粒子模拟并行算法,改进的并行算法能在每个时间步减少一次进程同步。算法分析和数值模拟表明,由于粒子运动路径和发射的初始位置与随机函数有关,只有一种改进的并行算法能保证并行计算正确。在3维粒子模拟软件CHIPIC3D上实现了改进的并行算法,应用CHIPIC3D对一种相对论返波管进行了并行模拟,模拟结果表明改进的并行算法能取得更高的加速比和效率。     

隐-显积分因子间断Galerkin方法求解二维辐射扩散方程

提出一种求解二维非平衡辐射扩散方程的数值方法.空间离散上采用加权间断Galerkin有限元方法,其中数值流量的构造采用一种新的加权平均;时间离散上采用隐-显积分因子方法,将扩散系数线性化,然后用积分因子方法求解间断Galerkin方法离散后的非线性常微分方程组.数值试验中在非结构网格上求解了多介质的辐射扩散方程.结果表明:对于强非线性和强耦合的非线性扩散方程组,该方法是一种非常有效的数值算法.     

2(1/2)维等离子体粒子模拟分布式并行程序设计

设计了两种粒子模拟的并行算法,并对其进行了比较,基于消息传递环境开发2(1/2)维粒子模拟并行程序,测试并分析了并行性能.粒子模拟算法中,给出了一个初始化粒子三维Maxwell速度分布的算法,并对常用的电磁场的Lindman吸收边界作了推广.最后对激光钻孔问题作了粒子模拟计算,验证了该并行程序.     

任意四边形网格上解辐射输运方程的一种数值方法

解二维辐射输运问题时,对于矩形网格,用Sn菱形(diamond)格式处理十分简单有效,但该格式不能直接用于非矩形网格,而辐射流体力学计算往往要求在非矩形网格上进行.本文讨论任意四边形网格的辐射输运数值方法,给出一种全正的子网格平衡计算格式,并进行数值计算,与矩形网格Sn菱形格式结果比较,得出本方法可行性结论.     

电荷非平衡super junction结构电场分布

建立了电荷非平衡情况下super junction(SJ)耐压结构的二维电场分布理论模型. 获得了浓度和宽度非平衡、梯形n-/p- 区和横向线性缓变掺杂三种非平衡SJ结构的电场分布. 理论分析结果与二维器件数值仿真软件MEDICI的仿真结果符合良好. 虽然给出的电场分布为三角级数形式, 但仍能从中获得很多重要信息. 特别地, 由此可求出非平衡SJ结构的峰值电场和耐压. 该结果有助于对SJ结构的深入分析. 关键词： super junction 电场分布 电荷非平衡     

三维电磁粒子模拟并行计算的研究

三维电磁粒子模拟基于时域有限差分算法（FDTD）和PIC（particle-in-cell）方法.根据FDTD和PIC方法的特点,可以将整个模拟区域分割为多个子区域,每个计算进程模拟计算一个子区域,通过消息传递交换子区域的边界数据从而实现并行计算这一基本思路,完成了并行算法的设计,并分析了并行加速比的影响因素.在三维电磁粒子模拟软件CHIPIC3D上实现了该并行算法并验证了算法的正确性,最后应用CHIPIC3D并行版本对磁绝缘线振荡器和相对论速调管两种典型的高功率微波源器件进行了模拟,证明了该并行算法能取 关键词： 电磁粒子模拟 时域有限差分 并行计算 高功率微波源     

用于系统模拟的并行电磁粒子模拟计算技术

针对普通并行算法的缺点，给出了连接体与分段建模的基本理论，提出了一种基于分段建模、系统整体模拟的并行电磁模拟计算方法，基于FDTD-PIC方法和消息传递机制在CHIPIC软件中实现了这一算法。并通过一个磁绝线振荡器加天线的简单系统验证了分段建模和解析的正确性，并通过对其的模拟和调试得到了天线系统输出的最大的功率6.2 GW，证实了此算法的可行性。     

非平衡桥式电路等效电阻的一种计算方法

给出了一种计算非平衡桥式电路等效电阻的方法.     

利用改进的符号数算法和光学符号代换实现矩阵计算

本文提出了一种利用改进的符号数算法和多窗口解码光学符号代换法则实现多值矩阵计算的光学方法。并给出两个多比特改进的符号数矩阵外积计算的实验结果。这一方法具有精度高、速度快等特点。     

用非结构网格与欧拉方程计算复杂区域的二维流动

提出用Delaunay三角化方法生成非结构网格的一种过程。所生成的网格可用于复杂多连通域内的可压流计算。采用Euler方程和格心有限体积法,研制出程序,给出了算例。     

光斑环围参量阵列测试法的测量不确定度

 为评定光斑环围参量（包括环围功率和环围尺寸）阵列测试法的测量不确定度,给出了环围参量一般形式的定义和连续形式的计算表达式,归纳并比较了阵列测试法下光斑环围参量的3种常用计算方法,即近似环围功率法、准确环围功率法和等效环围尺寸法,给出了零阶近似下环围参量离散形式的计算表达式。根据不确定度传递律,推导了基于等效环围尺寸法的环围参量测量不确定度的一般表达式,讨论了常见简化条件下的环围参量测量不确定度表达式。建立了光斑环围参量计算及其不确定度评定的一套较完整的方法。以强度为高斯分布的光斑为例,得到了简化条件下的环围参量测量不确定度的解析表达式,并用数值模拟法验证了其正确性。     

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.     

A least squares quantization table method for direct reconstruction of MR images with non-Cartesian trajectory

The direct Fourier transform method is a straightforward solution with high accuracy for reconstructing magnetic resonance (MR) images from nonuniformly sampled k-space data, given that the optimal density compensation function is selected and the underlying magnetic field is sufficiently uniform. The computation however is very time-consuming, making it impractical especially for large-size images. In this paper, the least squares quantization table (LSQT) method is proposed to accelerate the direct Fourier transform computation, similar to the recently proposed methods such as using look-up table (LUT) or equal-phase-line (EPL). With LSQT, all the image pixels are first classified into several groups where the Lloyd-Max quantization scheme is used to ensure the minimal classification error. The representative value of each group is stored in a small-size LSQT in advance to reduce the computational load. The pixels in the same group receive the same contribution, which is calculated only once for each group instead of for each pixel, resulting in the reduction of computation because the number of groups is far smaller than the number of pixels. Finally, each image pixel is mapped into the nearest group and its representative value is used to reconstruct the image. The experimental results show that the LSQT method requires far smaller memory size than the LUT method and fewer multiplication operations than the LUT and EPL methods. Moreover, the LSQT method can perform large-size reconstructions that achieve comparable or higher accuracy as compared to the EPL and gridding methods when the appropriate parameters are given. The inherent parallel structure also makes the LSQT method easily adaptable to a multiprocessor system.     

克尔型非线性薄膜波导的TE模

对于芯区为克尔型非线性介质，覆盖层和衬底为线性介质的平板波导，用Ｋｒｙｌｏｖ－Ｂｏｇｏｌｉｕｂｏｖ－Ｍｉｔｒｏｐｏｌｓｋｙ的渐近法导出了色散方程及场分布的二阶近似数学表达式，计算量大为减少且结果精确。给出了对称和非对称情况的典型实例。     

Analysis of the Three-Dimensional Model of Diffusion of Minority Charge Carriers Generated by an Electron Probe in a Heterogeneous Semiconductor Material by Means of Projection Methods

Algorithms for using the Galerkin projection method and the projection least squares method to analyze the three-dimensional model of the diffusion of minority charge carriers generated by an electron probe in a semiconductor material are presented. The results obtained using these methods are compared with the analytical solution. An estimate of the error is given, and the condition for the computation stability of the projection least squares method in the form of the limiting relation is obtained.     

计算加速度相关Lagrange函数的方法

研究从运动微分方程构造加速度相关Lagrange函数的问题,给出一种由方程的自伴随形式计算加速度相关Lagrange函数的方法.举例说明结果的应用. 关键词： 分析力学 加速度相关Lagrange函数 自伴随性 Lagrange力学逆问题     

具连续分布时滞的抛物型系统的指数镇定

针对一类具分布时滞的抛物型控制系统，提出一种新的镇定设计方法.利用推广的向量Hanalay 微分不等式、Dini导数、结合Green公式及不等式分析技术，在线性反馈控制律的作用下，导出了具分布时滞的抛物型控制系统的镇定的新判据.该镇定性条件不依赖于时滞.最后给了一个算例说明所得结果的可行性.此外，该方法一个明显的优点是所得的镇定性条件容易验证，因而便于应用. 关键词： 抛物型系统 Dini导数 分布时滞 全局指数镇定     

Group-theoretic approach to enhancing the Fourier modal method for crossed gratings with equilateral triangular symmetry

The Fourier modal method for crossed gratings is reformulated by use of a group-theoretic approach when the grating structures have the equilateral triangular symmetry. In the new formulation, a grating problem is first decomposed into four symmetrical basis problems whose field distributions are the symmetry modes (two are nondegenerate and the other two are doubly degenerate) of the grating. Then the symmetry relations of fields in the symmetry modes are used to reduce the number of unknowns in numerical computation. After the symmetrical basis problems are solved, their solutions are superposed to get the solution of the original problem. It is shown that when the grating is at some incident mountings, the memory occupation can be saved by 2/3 and the computation time can be reduced to 1/12 to 1/13.5 of the original one for different incident cases. Numerical examples are given to illustrate the effectiveness of the new formulation and verify the improved computation efficiency.