HFFT算法的大规模集群性能评估及基于CUDA的并行化探索

近些年来，随着计算机硬件技术的高速发展，大规模并行集群系统被越来越多地用于各种科研应用等活动中，而随着多核CPU芯片的技术成熟，多核集群系统对于科学计算的处理能力得到了空前的提高，如何对科学计算中海量数据进行高效地并行计算，评估影响算法性能的相应因素，成为了一个很重要的研究方向。 快速傅立叶变换作为上个世纪公认的最重要的基础算法之一，在包括大规模科学计算处理，数字信号处理，图形图像仿真等众多领域有着广泛的应用，对此，本文结合了2008年中国最快的超级计算机曙光5000A与大规模非规则区域上的快速傅立叶变换算法，深入研究分析了该算法应用在超大规模多核并行环境下的可扩展性测试及影响性能的因素。测试结果表明，该算法在现有的超大规模并行环境下具有较好的性能，在曙光5000A上，算法在8192核的加速比达到了277倍。 本文的另一部分研究工作集中在探索现有HFFT算法在GPGPU上的并行化应用。GPU在处理能力和存储器带宽上相对CPU有明显优势，在成本和功耗上也不需要付出太大代价，这从而为并行数据处理问题提供了新的解决方案。由于图形渲染的高度并行性，使得GPU可以通过增加并行处理单元和存储器控制单元的方式提高处理能力和存储器带宽。 在实际应用中，Nvidia公司的CUDA是用于GPU计算的并行开发环境，是一个全新的软硬件架构，这个架构可以使用GPU来解决商业、工业以及科学方面的复杂计算问题。CUDA是一个完整的GPGPU解决方案，它提供了直接访问硬件的接口。由于目前GPU已在科研领域中得到广泛研究，为了利用GPU的并行数据处理能力，本文探索了一种通过GPU计算提高现有HFFT算法执行速度的途径。之后，本文对CUDA并行算法进行了实际测试，实验结果表明，GPU对并行FFT部分具有20%的加速比，而除去I/O传输后，程序的加速比是34.4倍。

低温生长砷化镓光电导天线产生太赫兹波的辐射特性

研究了低温生长砷化镓光电导天线(LT-GaAs PCA)产生太赫兹(THz)波的辐射特性。利用太赫兹时域光谱(TDS)技术测量了光电导发射极在飞秒激光作用下辐射的太赫兹脉冲,得到了时域发射光谱,并通过快速傅里叶变换(FFT)得到相应的频域光谱。结果表明,低温砷化镓光电导天线产生的太赫兹波信号比飞秒激光激发半导体表面产生的太赫兹波信号具有更高的强度和信噪比;太赫兹波信号与光电导天线的偏置电压成线性关系;随着抽运激光功率的增强,太赫兹波信号增大并出现饱和。

传输斜移对同步并行光传输系统性能的影响

针对一个具体的链路模型,通过计算机仿真分析了传输斜移对同步并行光传输系统性能的影响.光纤中的信号分析在频域中通过快速傅立叶变换(fast fourier transform,FFT)进行.分别计算了单信道误码率以及没有传输斜移和有传输斜移时并行信道总的误码率.计算结果表明,在噪声不是影响系统性能的主要因素时,传输斜移是决定并行光传输系统最大同步传输速率和传输距离的一个重要因素.

一种计算和分析二维光子晶体缺陷模式的方法

通过改进时域有限差分(FDTD)法,计算和分析了二维光子晶体的缺陷模式。运用一维时域有限差分算法和线性插值法在总场散射场(TF-SF)连接边界引入入射平面波,采用完全匹配层(PML)技术对外行波进行了有效吸收。计算和分析结果表明,在光子晶体非对称方向入射的平面波能激发所有的缺陷模式,选取合适的探测点位置收集电场值,经快速傅里叶变换(FFT)能得到所有的共振峰值。另外,采用该方法研究了二维正方介质柱光子晶体缺陷模的共振频率与缺陷介质柱半径和介电常量之间的关系。结果表明通过改变缺陷的半径和介电常量大小可以在光子晶体禁带中一定的范围内调节缺陷模式的共振频率大小。

Applicatioo of Pade Approximation in Simulating Photonic Crystals

To save finite-difference time-domain(FDTD) computing time, several methods are proposed to convert the time domain FDTD output into frequency domain. The Padé approximation with Baker's algorithm and the program are introduced to simulate photonic crystal structures. For a simple pole system with frequency 160THz and quality factor of 5000,the intensity spectrum obtained by the Padé approximation from a 28-item sequence output is more exact than that obtained by fast Fourier transformation from a 220-item sequence output. The mode frequencies and quality factors are calculated at different wave vectors for the photonic crystal slab from a much shorter FDTD output than that required by the FFT method,and then the band diagrams are obatined. In addition,mode frequencies and Q-factors are calculated for photonic crystal microcavity.

一种基于Pade逼近对短时序列频率和品质因数的估计方法

该文提出了一种基于Pade逼近的谱估计方法。由于Pade逼近能够利用有限项很好地逼近对无限项的求和，文中算法适用于短时序列情况。经过实验仿真并与FFT方法和小波变换谱估计方法进行比较表明，该文算法具有较高的频率分辨率和估计精度，并具有较好的品质因数。

Low power design in 100 MHz embedded SRAM

Low power design method is used in a 100MHz embedded SRAM. The embedded SRAM used in a FFT chip is divided into 16 blocks. Two-level decoders are used and only one block can be selected at one time by tristate control circuits, while other blocks are set stand-by. The SRAM cell has been optimized and the cell area has been minimized at the same time.

Period-doubling bifurcations of the thermocapillary convection in a floating half zone

This study experimentally explored the fine structures of the successive period-doubling bifurcations of the time-dependent thermocapillary convection in a floating half zone of 10 cSt silicone oil with the diameter d (0)=3.00 mm and the aspect ratio A=l/d (0)=0.72 in terrestrial conditions. The onset of time-dependent thermocapillary convection predominated in this experimental configuration and its subsequent evolution were experimentally detected through the local temperature measurements. The experimental results revealed a sequence of period-doubling bifurcations of the time-dependent thermocapillary convection, similar in some way to one of the routes to chaos for buoyant natural convection. The critical frequencies and the corresponding fractal frequencies were extracted through the real-time analysis of the frequency spectra by Fast-Fourier-Transformation (FFT). The projections of the trajectory onto the reconstructed phase-space were also provided. Furthermore, the experimentally predicted Feigenbaum constants were quite close to the theoretical asymptotic value of 4.669 [Feigenbaum M J. Phys Lett A, 1979, 74: 375-378].

界面张力引起的流动及界面特征研究

通过对单层流体浮力－热毛细对流和两层流体 B$\acute{\rm e}$nard-Marangoni对流的实验研究，探讨界面张力梯度引起的自然对流的特征及机理问题。考虑到表面张力是温度的函数，对上面是空气(或其蒸汽)的薄液层，加载水平温度梯度将使得气液表面上表面张力分布不均匀，耦合于地面的重力作用，将会驱动薄层流体形成浮力－热毛细对流运动。液层厚度和温度梯度的改变(引起系统长高比、Bond数、Rayleigh数以及Marangoni数的变化)直接影响到薄层流体的对流模式的变化，还可能使得浮力－热毛细对流从稳定发展到不稳定。本研究中以硅油为实验介质，应用高分辨率PIV技术对薄层流体的对流速度场进行了测量，观察到了对流由单胞结构向多胞结构以及由稳定对流向振荡对流的转捩过程，分析给出了对流模式结构变化的规律以及状态转变的临界参数。在浮力－热毛细对流发展过程中，流体表面的变形(形貌)和表面振荡直接反映了热毛细作用与浮力作用的耦合规律以及热毛细对流表面波的基本特征。实验中应用激光干涉技术以及高精度位移传感器对薄液层体系(液层厚度1mm$\sim$5mm)作了系统的研究，获得了微米量级面形形貌变化规律及其亚微米尺度的表面振荡特性。用FFT以及小波分析方法研究了流体自由面振荡的分岔转捩过程及通往混沌的转捩途径。该研究对理解流体热毛细对流的机理具有重要的意义。在自然界里和工程技术中，多层流体体系对流现象更为普遍。近20年来，互不混溶的两层液体体系成为了很多理论和实验研究的重要对象，其主要原因有：(1)在两层流体体系中，由于上下层对流的耦合作用，在临界点上存在HOPF分叉，使得两层模型成为非线性理论研究的理想模型；(2)两层流体模型被应用于地壳运动的研究和空间晶体生长等领域。近年，很多学者通过理论分析和数值模拟对加载垂直温度梯度的上下两层流体B$\acute{\rm e}$nard-Marangoni对流问题进行了研究。上下液层对流的耦合与竞争可以导致上下液层出现多种对流耦合模式和振荡规律，外加温差、液层厚度以及液层厚度比的变化是形成不同对流模式的重要因素。本研究以FC70和KF90-10为实验介质，应用高分辨率PIV技术对两薄层流体B$\acute{\rm e}$nard-Marangoni对流进行了测量，从实验中清晰地观测到了3种临界对流模式：机械耦合、热耦合、临界振荡，分析给出了3种对流转换的临界参数，发现临界振荡可以在峰值液层厚度比附近一个较大的区域范围出现，并且峰值厚度比远离平衡厚度比，这些结果与目前的理论研究有明显的的差异。总之，两种不同外加温度梯度方式，会导致两种不同机制的对流--热毛细对流和Marangoni对流，他们是微重力流体物理研究的重要内容。

HIRFL-CSR Tune值测量系统

兰州重离子加速器冷却储存环(HIRFL-CSR)工作点(Tune)测量系统已投入调束运行。采用FFT测量法,用白噪声信号做激励源,经功率放大并通过同轴开关切换将激励信号加载到垂直或水平的对称极板上,通过位置检测器(BPM)采集束流信号。将BPM两极板感应到的束流信号分别经前置放大器放大,再通过相位相差180°的合路器将差信号送入实时频谱仪进行傅里叶分析,从而计算出Tune值。本文主要介绍HIRFL-CSR工作点测量原理、系统构成以及测量结果。

Suppression of phase separation in PC/PMMA blend film by thermoset oligomer

Phase separation of bisphenol A polycarbonate (PC) and poly(methyl methacrylate) (PMMA) thin blend film is suppressed by addition of solid epoxy oligomer. Epoxy has strong intermolecular interactions with both PC and PMMA, while PC and PMMA are quite incompatible with each other. Consequently, phase separation in the PC/PMMA blend film pushes epoxy to the interface; at the same time, PC and epoxy react readily at the interface to form a cross-linking structure, binding PMMA chains together. Therefore, the interface between PC and PMMA is effectively reinforced, and the PC/PMMA thin blend film is stabilized against phase separation. On the other hand, only an optimal content of epoxy (i.e., 10 wt %) can serve as an efficient interfacial agent. In contrast to the traditional reactive compatibilization, here we observed that the cross-linking structure along the interface is much more stable than block or graft copolymers. Atomic force microscopy (AFM) is used to characterize the morphological changes of the blend films as a function of annealing time. Two-dimensional fast Fourier transform (2D-FFT) of AFM data allows quantitative investigation of the scaling behavior of phase separation kinetics.

多卫星测高数据应用于海底构造动力研究——以中国边缘海及邻区为例

论文系统、深入地探讨了多卫星测高数据的误差分析处理、地球重力场推算及地球物理解释方面的原理和方法，形成了一套较完整的卫星测高数据分析、处理、解释方法，并在计算机上编程实现，应用于中国边缘海及邻区的0-45°N、100-150°E范围内的Geosat ERM、ERS-1/2和Topex/Poseidon测高数据处理，提供的4' * 4'网格间距的大地水准面及残差、重力异常、布格/格莱尼/均衡大地水准面及重力异常、海底地形、Moho面埋深、大/中/小尺度地幔流应力场，分层次、多尺度地展示了研究区丰富的海底构造动务信息。论文的研究要点归纳如下：通过解剖ERS-1/2测高数据结构，并在对联Geosat的单星交叠差调差的基础上，实现ERS-1/2相对于T/P的双星交叠差调差，重点利用ERS-1两个168天长周期的分辨率优势；实现适合研究区的平均海平面的海面地形改正；实现无共线平均的所有海面高数据的权重配赋网格插值，在反推重力异常的垂线偏差计算中，共线平均推迟到对轨迹向海面高斜率和角度来作；在推算重力异常、海底地形和Moho面埋深中，均采用参考模型的“移去-恢复”处理技术，实现简化运算的滑动窗口FFT，有效发挥了测高数据的精度和分辨率优势。展示大地水准面在深部构造动力研究方面的优势，实现大地水准面（位）及重力异常的全球性地形/均衡改正、小尺度地幔流应力场推算。引入地幔流位场概念，使地幔流应力场推算与垂线偏差计算获得统一而简化。由获得的各级测高数据数字模型，刻画研究区沟一弧一盆系的构造动力格局和特征，分辨出地形上难以确定的不同于一般配海岭的扩张脊构造特征、沟弧构造形迹和各段沟弧系俯冲作用及反向挤压强度的差异等。反映欧亚板块东南向蠕散、太平洋板块北西向扩张的大尺度地幔流应力场，展现出北端左旋压扭、南端右旋压扭和中间滑移的哑铃状构造动力格局，南强北弱的能量汇聚与印度洋板块北向推挤有关。中尺度和大尺度地幔流应力场的共同作用，可以解释日本海盆弱西向和南海海盆东南向的不对称张特性，及各段沟弧系的构造活动差异。南海海盆往东强度变大和年代趋新的构造活动特征，冲绳海槽和马里亚纳海槽的地幔流作用方式，体现了海盆及海槽演化的地球动力学过程及特点。

小波消噪在振动信号处理中的应用

信噪分离是小波分析中的一个有效的信号检测方法。本文在阐述了小波分析及消噪的小波理论的基础上 ,给出了从噪声污染信号中恢复原信号的实例 ,并与傅立叶分析消噪进行了比较 ,结果表明对于非平稳振动信号小波消噪的效果明显优于傅立叶变换。

HHT在电磁信号处理中的应用

In modem signal Processing，non－linear，non－Gaussian and non－stable signals are usually the analyzed and Processed objects，especially non－stable signals. The convention always to analyze and Process non－stable signals are： short time Fourier transform，Wigner－Ville distribution，wavelet Transform and so on. But the above three algorithms are all based on Fourier Transform，so they all have the shortcoming of Fourier Analysis and cannot get rid of the localization of it. Hilbert－Huang Transform is a new non－stable signal processing technology，proposed by N. E. Huang in 1998. It is composed of Empirical Mode Decomposition (referred to as EMD) and Hilbert Spectral Analysis (referred to as HSA). After EMD Processing，any non－stable signal will be decomposed to a series of data sequences with different scales. Each sequence is called an Intrinsic Mode Function (referred to as IMF). And then the energy distribution plots of the original non－stable signal can be found by summing all the Hilbert spectrums of each IMF. In essence，this algorithm makes the non－stable signals become stable and decomposes the fluctuations and tendencies of different scales by degrees and at last describes the frequency components with instantaneous frequency and energy instead of the total frequency and energy in Fourier Spectral Analysis. In this case，the shortcoming of using many fake harmonic waves to describe non－linear and non－stable signals in Fourier Transform can be avoided. This Paper researches in the following parts： Firstly，This paper introduce the history and development of HHT，subsequently the characters and main issues of HHT. This paper briefly introduced the basic realization principles and algorithms of Hilbert－Huang transformation and confirms its validity by simulations. Secondly, This paper discuss on some shortcoming of HHT. By using FFT interpolation, we solve the problem of IMF instability and instantaneous frequency undulate which are caused by the insufficiency of sampling rate. As to the bound effect caused by the limitation of envelop algorithm of HHT, we use the wave characteristic matching method, and have good result. Thirdly, This paper do some deeply research on the application of HHT in electromagnetism signals processing. Based on the analysis of actual data examples, we discussed its application in electromagnetism signals processing and noise suppression. Using empirical mode decomposition method and multi-scale filter characteristics can effectively analyze the noise distribution of electromagnetism signal and suppress interference processing and information interpretability. It has been founded that selecting electromagnetism signal sessions using Hilbert time-frequency energy spectrum is helpful to improve signal quality and enhance the quality of data.

指数矩阵近似计算在地震波场延拓中的应用

Seismic wave field numerical modeling and seismic migration imaging based on wave equation have become useful and absolutely necessarily tools for imaging of complex geological objects. An important task for numerical modeling is to deal with the matrix exponential approximation in wave field extrapolation. For small value size matrix exponential, we can approximate the square root operator in exponential using different splitting algorithms. Splitting algorithms are usually used on the order or the dimension of one-way wave equation to reduce the complexity of the question. In this paper, we achieve approximate equation of 2-D Helmholtz operator inversion using multi-way splitting operation. Analysis on Gauss integral and coefficient of optimized partial fraction show that dispersion may accumulate by splitting algorithms for steep dipping imaging. High-order symplectic Pade approximation may deal with this problem, However, approximation of square root operator in exponential using splitting algorithm cannot solve dispersion problem during one-way wave field migration imaging. We try to implement exact approximation through eigenfunction expansion in matrix. Fast Fourier Transformation (FFT) method is selected because of its lowest computation. An 8-order Laplace matrix splitting is performed to achieve a assemblage of small matrixes using FFT method. Along with the introduction of Lie group and symplectic method into seismic wave-field extrapolation, accurate approximation of matrix exponential based on Lie group and symplectic method becomes the hot research field. To solve matrix exponential approximation problem, the Second-kind Coordinates (SKC) method and Generalized Polar Decompositions (GPD) method of Lie group are of choice. SKC method utilizes generalized Strang-splitting algorithm. While GPD method utilizes polar-type splitting and symmetric polar-type splitting algorithm. Comparing to Pade approximation, these two methods are less in computation, but they can both assure the Lie group structure. We think SKC and GPD methods are prospective and attractive in research and practice.