面向结构网格并行应用的一类快速通信算法

通信算法需要在相邻子区域间传输数据.通过求解子区域间的相交问题可以寻找相邻区域.针对子区域的求交问题,基于区间树,结合结构网格应用的特点,构造近似线性时间复杂度的算法.数值实验表明该算法具有较高的计算效率和可扩展性,能够支持百万量级矩形子区域的并行计算.     

自适应结构网格上扩散方程隐式时间积分算法及其应用

提出一种自适应结构网格(SAMR)上求解扩散方程的隐式时间积分算法.该算法从粗网格到细网格逐层进行时间积分,通过多层迭代同步校正保证粗细界面的流连续和计算区域的扩散平衡.分析算法复杂度,并给出评估算法低复杂度的准则.典型算例表明,相对于一致加密情形,本文算法能够在保持相同计算精度的前提下,大幅度降低网格规模和计算量,且具有低复杂度.将算法应用于辐射流体力学数值模拟中非线性扩散方程组求解,相对于一致加密网格,SAMR计算将计算量下降一个量级以上,计算效率提高33.2倍.     

求解双曲型守恒律方程的一类自适应多分辨方法

针对双曲型守恒律方程问题,发展一种有效的自适应多分辨分析方法.通过对嵌套网格上的数值解构造离散多分辨分析,建立小波系数与多层嵌套网格点之间的对应关系.对于小波系数较大的网格点采用高精度WENO格式计算,其余区域则直接采用多项式插值.数值试验表明,该方法在保持原规则网格方法的精度和分辨率的同时,显著地减少计算的CPU时间.     

3维全电磁粒子软件NEPTUNE中的并行计算方法

 介绍了NEPTUNE软件采用的一些并行计算方法：采用“块-网格片”二层并行区域分解方法,使计算规模能够扩展到上千个处理器核。基于复杂几何特征采用自适应技术并行生成结构网格,在原有规则区域的基础上剔除无效网格,大幅降低了存储量和并行执行时间。在经典的Boris和SOR迭代方法基础上,采用红黑排序和几何约束,提出了非规则区域上的Poisson方程并行求解方法。采用这些方法后,当使用NEPTUNE软件模拟MILO器件时,可在1 024个处理器核上获得51.8%的并行效率。     

基于Tahoe框架的某夹具并行计算

在开源软件Tahoe框架基础上,结合有限元前后处理程序MSC.Patran及Tecplot,对某复杂夹具进行建模.通过区域分解、编制接口和采用PHG中提供的PCG(preconditioned conjugate gradient,预处理共轭梯度法)迭代解法成功实现262×10⁴自由度模型的串、并行计算.结果表明,并行计算收敛速度更快,4进程并行计算时间不到串行计算时间的1/4.通过与商用程序MSC.Nastran比较,验证计算结果的正确性.利用大型并行计算机对该模型并行计算性能进行研究,获得最高32进程的并行计算加速比.研究表明,改进后的Tahoe计算框架对于开展大规模自由度下的结构并行计算分析研究是可行的,并且随计算节点增加,并行计算过程基本呈线性加速.     

非近轴近似多高斯声束模型的相控阵换能器声场计算

针对近轴近似的多高斯声束模犁无法准确计算离轴区域声场的问题,我们提出了一个矩形源的非近轴近似多高斯声束模型,用于计算偏转聚焦时线性相控阵换能器辐射的声场.利用该方法计算了由矩形阵元组成的相控线阵的辐射声场,并与瑞利积分、近轴近似方法及夫琅和费近似方法进行了分析和对比,计算结果表明该方法克服了常规近轴近似条件的限制,可以准确、快速地计算较大偏转范围内的换能器辐射声场,在计算相控阵换能器偏转聚焦声场中具有独特的优势.     

并行自适应结构网格应用支撑软件框架研制进展

JASMIN框架全称为“并行自适应结构网格应用支撑软件框架（Jparallel Adaptive Structured Mesh Applications Infrastructure）”。该框架面向科学与工程计算的（自适应）结构网格应用,支持应用领域专家在无需了解并行计算和共性数值算法细节的前提下,通过编写串行数值计算程序,     

三维湍流Rayleigh-Bénard热对流的高效并行直接求解方法

高Ra数Rayleigh-Bénard热对流的湍流特性研究是当前国际上的一个热门研究课题, DNS模拟计算是研究该课题的重要手段之一. 当计算规模增大而网格数巨大时计算工作难以实现, 高Ra湍流热对流的数值模拟研究面临重大挑战. 本文创建了大规模高效并行计算的三维湍流热对流直接求解方法. 采用FFT变换解耦压力泊松方程, 将其变换成沿z方向上的块三对角方程组, 并利用块三对角方程的MPI与OpenMP联立的大规模高效并行近似解求解方案, 创建了可以高效并行计算的热对流直接求解方法. 通过对该方法并行效率的验证计算, 证明新的直接求解并行计算方法具有很好的并行效率和计算时效. 三维窄方腔热对流的计算结果表明, 本文方法计算的三维热对流特性是合理的. 本文创建的可大规模高效并行计算的三维湍流热对流直接求解方法, 也很可能是关于计算流体力学不可压NS方程大规模高效并行计算在特殊情况中计算技术上的一个突破.     

自适应间断有限元方法求解双曲守恒律方程

研究自适应Runge-Kutta间断Galerkin (RKDG)方法求解双曲守恒律方程组,并提出两种生成相容三角形网格的自适应算法.第一种算法适用于规则网格,实现简单、计算速度快.第二种算法基于非结构网格,设计一类基于间断界面的自适应网格加密策略,方法灵活高效.两种方法都具有令人满意的计算效果,而且降低了RKDG的计算量.     

块结构自适应网格上任意区域和任意界面的数值积分

研究块结构自适应网格上计算任意界面上和任意区域内的数值积分方法,其中任意界面和任意区域通过一个水平集函数表示.首先介绍在一致网格上任意界面上和任意区域内的数值积分方法.然后,将该方法推广到块结构的自适应网格上.数值算例表明,自适应网格方法有二阶精度.同一致网格方法相比,自适应网格方法显著地减少了计算机存储量的需求.     

基于ERB尺度划分的多子带语声信号抗噪谱减算法

为了研究心理声学在语声增强方面的应用,本文提出了一种基于等效矩阵带宽(ERB)尺度划分的多子带语声信号抗噪谱减算法。此算法根据ERB尺度将带噪信号的频谱划分成多个子带,然后再根据每个子带的分段信噪比以及心理声学掩蔽原则分别计算每个子带的谱减参数,最后在每个子带中分别进行谱减算法处理。实验结果表明,应用新算法所获得的语声增强结果在信噪比、IS失真以及PESQ方面均优于之前提出的多子带语声信号抗噪谱减算法。     

Invariant amplitudes and double dispersion relations for electron-muon scattering

For electron-muon scattering, a set of six invariant amplitudes free from kinematical singularities is determined. A simple proof of this freedom is given. Projection operators for this set are constructed. Double dispersion relations using natural subtraction points are derived for the box diagram.     

Blood vessel enhancement for DSA images based on adaptive multi-scale filtering

Digital subtraction angiography (DSA) plays a significant role in the diagnosis, treatment planning and assessment of diseases. However, because of the geometrical complexity and fine characteristics of blood vessel structures, accurate and robust detection of blood vessels still remains a problem. In this paper, a blood vessel enhancement algorithm is proposed. The main purpose of this work is to improve the visual quality of blood vessels in DSA images. The new blood vessel enhancement algorithm is based on the multi-scale space theory and Hessian matrix. Not only the eigenvalues of Hessian matrix but also the angles between eigenvectors are utilized for the blood vessel enhancement of DSA. The filter parameters and scale factors are decided adaptively. Eigenvalues of the Hessian matrix are also used for the noise elimination. Experimental results show that the proposed algorithm has a good performance in blood vessel enhancement of DSA images. The proposed algorithm filters image background and non-vascular structure effectively. The deformation of blood vessels occurred in the enhancement process is avoided and more small blood vessels are visible in DSA images.     

QCF: Quantum Collaborative Filtering Recommendation Algorithm

With the rapid development of the Internet, e-commerce plays an important role in people’s lives, and the recommendation system is one of the most critical technologies. However, as the number of users and the scale of goods increase sharply, the traditional collaborative filtering recommendation algorithm has a large computational complexity in the part of calculating the user similarity, which leads to a low recommendation efficiency. In response to the above problems, this paper introduces the concept of quantum computing theory. The user score vector is first prepared into a quantum state, the similarity score is calculated in parallel, then the similarity information is saved into the quantum bit, and finally the similar user is searched by the Grover search algorithm. Compared with the traditional collaborative filtering recommendation algorithm, the time complexity of the collaborative filtering recommendation algorithm based on Grover algorithm can be effectively reduced under certain conditions.

     

二维保单调保守恒插值算子

基于一个一维保单调保守恒插值算子,利用不完全双二次插值提出一个二维保单调保守恒插值算子.从插值逼近角度,通过几个数值实验验证该插值算子有效.用得到的二维插值算子作为结构网格自适应加密(structured adaptive mesh refinement,SAMR)算法中的细化插值算子,求解几个二维Euler方程数值例子,结果表明,提出的二维插值算子有效.     

一种基于效率矩阵的网络节点重要度评价算法

为了实现对网络节点重要性的有效评价,提出一种基于网络效率矩阵的节点重要度评价算法.该方法综合考虑节点的度值(局部重要度)和网络节点之间的重要性贡献(全局重要度),利用节点的度和效率矩阵表征网络节点的重要度贡献,克服重要性贡献矩阵法中节点只依赖于邻接节点的不足.考虑实际网络的稀疏性,该算法的时间复杂度为O(n²).通过算例分析验证了该算法的可行性和有效性,结果表明:该算法能够更加直观、简单有效地区分节点的重要度差异,并且对于大型复杂网络具有较理想的计算能力.     

An automated algorithm for stability analysis of hybrid dynamical systems

There are many hybrid dynamical systems encountered in nature and in engineering, that have a large number of subsystems and a large number of switching conditions for transitions between subsystems. Bifurcation analysis of such systems poses a problem, because the detection of periodic orbits and the computation of their Floquet multipliers become difficult in such systems. In this paper we propose an algorithm to solve this problem. It is based on the computation of the fundamental solution matrix over a complete period–where the orbit may contain transitions through a large number of subsystems. The fundamental solution matrix is composed of the exponential matrices for evolution through the subsystems (considered linear time invariant in this paper) and the saltation matrices for the transitions through switching conditions. This matrix is then used to compose a Newton-Raphson search algorithm to converge on the periodic orbit. The algorithm–which has no restriction of the complexity of the system–locates the periodic orbit (stable or unstable), and at the same time computes its Floquet multipliers. The program is written in a sufficiently general way, so that it can be applied to any hybrid dynamical system.     

Feature Analysis and Modeling of the Network Community Structure

Community structure has an important influence on the structural and dynamic characteristics of the complex systems.So it has attracted a large number of researchers.However,due to its complexity,the mechanism of action of the community structure is still not clear to this day.In this paper,some features of the community structure have been discussed.And a constraint model of the community has been deduced.This model is effective to identify the communities.And especially,it is effective to identify the overlapping nodes between the communities.Then a community detection algorithm,which has linear time complexity,is proposed based on this constraint model,a proposed node similarity model and the Modularity Q.Through some experiments on a series of real-world and synthetic networks,the high performances of the algorithm and the constraint model have been illustrated.