A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid

A conservative multi-tracer transport algorithm on the cubed-sphere based on the semi-Lagrangian approach (CSLAM) has been developed. The scheme relies on backward trajectories and the resulting upstream cells (polygons) are approximated with great-circle arcs. Biquadratic polynomial functions are used for approximating the density distribution in the cubed-sphere grid cells. The upstream surface integrals associated with the conservative semi-Lagrangian scheme are computed as line-integrals by employing the Gauss–Green theorem. The line-integrals are evaluated using a combination of exact integrals and high-order Gaussian quadrature. The upstream cell (trajectories) information and computation of weights of integrals can be reused for each additional tracer.The CSLAM scheme is extensively tested with various standard benchmark test cases of solid-body rotation and deformational flow in both Cartesian and spherical geometry, and the results are compared with those of other published schemes. The CSLAM scheme is accurate, robust, and moreover, the edges and vertices of the cubed-sphere (discontinuities) do not affect the overall accuracy of the scheme. The CSLAM scheme exhibits excellent convergence properties and has an option for enforcing monotonicity. The advantages of introducing cross-terms in the fully two-dimensional biquadratic density distribution functions are also examined in the context of Cartesian as well as the cubed-sphere grid which has six local sub-domains with discontinuous edges and corners.     

High-performance high-resolution semi-Lagrangian tracer transport on a sphere

Current climate models have a limited ability to increase spatial resolution because numerical stability requires the time step to decrease. We describe a semi-Lagrangian method for tracer transport that is stable for arbitrary Courant numbers, and we test a parallel implementation discretized on the cubed sphere. The method includes a fixer that conserves mass and constrains tracers to a physical range of values. The method shows third-order convergence and maintains nonlinear tracer correlations to second order. It shows optimal accuracy at Courant numbers of 10–20, more than an order of magnitude higher than explicit methods. We present parallel performance in terms of strong scaling, weak scaling, and spatial scaling (where the time step stays constant while the resolution increases). For a 0.2° test with 100 tracers, the implementation scales efficiently to 10,000 MPI tasks.     

多边形交错网格的守恒重映算法

提出基于细分和数值积分思想的一种离散的守恒重映方法——质点重映方法.密度分布可采用一阶精度的分片常数分布,或二阶精度的分片线性分布.分片线性密度分布函数采用面平均方法构造.重映过程中,借助四边形辅助网格,实现了交错网格节点量的重映.质点重映方法既适用于结构网格,也适用于非结构网格,且不要求新旧网格之间一一对应.数值结果表明,一阶精度重映算法健壮性好,但会产生较大的扩散效应;二阶精度重映算法可较好地保持密度分布的特性,但存在单调性问题.为改善二阶精度重映方法单调性,将结构网格质量守恒调整算法推广到非结构网格上,以限制新网格的质量密度.给出了一些重映的例子,并进行了误差分析.     

网络计算机模型下海量大数据存储系统设计

对网络计算机模型下海量大数据进行安全稳定的存储,可以提高网络计算机的使用价值,增加其使用周期。但目前的海量大数据存储方法在存储过程中,无法做到对其进行灵活高效的存储,存在大数据存储分布密度较低,存储开销较大等问题。为此,以网络计算机模型体系结构为基础,提出了一种基于ARM的海量大数据存储系统设计方法。该设计方法先利用ARM芯片对网络计算机模型下海量大数据存储系统进行硬件构造,将网络海量大数据中的可利用与不可利用数据进行分类处理,采用VISA结构根据数据分类结果对大数据存储系统软件部分进行设计,依据大数据调度模型和存储相似度特征对大数据存储的时间,质量等方面进行计算,利用计算结果对大数据传输的阈值以及分布密度进行记录,最后根据循环分段的计算方式进行冗余大数据特性压缩,并对海量大数据的常规数据和冗余数据进行存储。实验仿真证明,所提方法提高了海量大数据存储的兼容性,增强了大数据存储的精确性和灵活性。     

基于改进维纳逆滤波的衍射成像光谱仪数据误差分析与重构

衍射成像光谱仪探测到的高光谱数据需要进行计算与反演才可以得到成像光谱数据,本文对衍射成像光谱仪的成像过程及数据误差产生的原理从空间维和光谱维两方面进行了分析,并针对其光谱重构过程中系统点扩散函数标准差较大时重构结果清晰度较低、存在振铃等问题,提出了基于改进维纳逆滤波的光谱数据重构算法,该方法在分析衍射成像光谱仪数据特点与误差的基础上,将每一次维纳逆滤波的重构结果视为新的模糊图像,利用成像过程及维纳逆滤波的基本原理确定新的模糊图像对应的点扩散函数,反复进行维纳逆滤波达到提高图像清晰度的效果,再根据图像自身的空间和光谱特征分布,进行自适应性的噪声去除.利用模拟的衍射成像光谱数据进行验证,在系统点扩散函数的标准差为2.5的情况下,能得到无振铃的重构结果,且与传统维纳逆滤波法的重构结果进行比较,清晰度、细节能力等指标均有所提高,满足了衍射成像光谱数据应用需求.     

基于分布结构自适应筛选的数据库存储优化设计

通过对数据库的存储结构优化设计,提高数据库的吞吐量。传统方法采用存储节点校验数据适应度分区的数据库存储模型,数据库中存在重复冗余数据,不能自适应滤除,导致数据存储开销较大。提出了一种基于分布结构自适应筛选的数据库存储优化模型,首先进行数据库的存储机制和分布式数据结构分析,采用相空间重构方法进行存储空间的结构分布重组,采用分布结构自适应筛选方法对提取的数据信息流进行重复冗余数据滤波处理,改善数据在数据库存储空间中的结构分布,实现数据库存储优化。仿真结果表明,采用改进的方法进行数据库构建,能提高数据库存储吞吐量,降低数据存储开销,提高数据库的访问和调度性能,展示较好的应用价值。     

Stable reconstruction of the T(2) distribution by low-resolution NMR measurements and the classical markov and hausdorf momentum problem

Assuming that an original distribution is a probabilistic measure and the Laplace transforms are known only for a finite number of points that are affected by errors, we develop a method for reconstructing weak-sense mean values obtained by integrating smooth functions with the measure. Our method is useful in NMR if the NMR signal can be represented as a superposition of exponential terms. In these circumstances, we show how the data processing can be related to the classical Hausdorf momentum problem. First, we clarify the meaning of stable spectrum reconstruction, and then develop stable filtering and a mean value reconstruction algorithm. Our method has been tested on both simulated and real sets of spin–spin relaxation curves with noise. In view of this, our method could provide an efficient and accurate reconstruction of spin–spin relaxation data. For any reader interested in applications, a “practical recipe” that is almost self-consistent has been included.     

Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method

An efficient numerical inverse radiation analysis based on the backward Monte Carlo (BMC) method is presented to determine the three-dimensional (3-D) temperature distribution in a large rectangular enclosure containing the participating medium, using radiative intensities in the visible range received by charge-coupled device (CCD) cameras. For large radiative sources and small detectors, when the radiation onto a small spot and onto a small direction cone is desired, the BMC method is more efficient than the forward Monte Carlo (FMC) method. Because the temperature reconstruction from the measured radiative intensities is an ill-posed inverse problem, least-square QR decomposition (LSQR) method is introduced to determine the meaningful temperature distribution. In order to gain insight into the effects on the accuracy of temperature distribution reconstruction, the detailed analyses are made using numerical simulations. The results show that the temperature distribution can be reconstructed accurately for the exact and noisy data.     

基于扩散滤波的多尺度分解和重构方法及应用初探

从各向异性PM方程出发,推导多维扩散滤波微分方程的离散格式及其稳定性条件,首次构建基于扩散滤波的多尺度分解和重构方法,给出两种具体实施方案及其关键步骤.地震资料应用表明,所提方法分解和重构信号的过程合理可靠,其中方案①的2D傅里叶波数谱能量随尺度的增加而远离谱中心点,其残差信号表现为高波数信号,在随机噪声压制中取得了较好的效果;方案②的2D傅里叶波数谱能量随尺度的增加而靠近谱中心点,其残差信号表现为低波数信号,在低频逆时噪声压制中取得了较好的效果.所提方法计算过程简单易实现,对于信号处理提供了一种多尺度分解和重构方法,在地震信号处理领域具有较高的应用价值.     

Numerical simulations to improve the performance of tunable diode laser absorption tomography in a harsh combustion environment

The impact of measurement noise and tomographic methods on reconstruction quality are investigated via simulation studies under a hypothesis harsh flow field environment. Computer tomographic methods based on direct absorption spectroscopy and wavelength modulation spectroscopy are conducted under different measurement noise levels to assess the noise effect quantitatively. It turns out that the wavelength modulation spectroscopy-based tomographic method shows efficient immunity to measurement noise. However, the direct absorption spectroscopy-based tomographic method is found to be susceptible to the measurement noise, which makes the reconstruction quality decline with the increasing noise level. In addition, two kinds of tomographic methods including linear and nonlinear method are investigated under a complex multimodal temperature distribution environment with limited projection data. The reconstructed distribution for the nonlinear tomographic method reveals great fidelity to the original value with a maximum deviation of 51.9?K, while the reconstructed distribution for the linear tomographic method under parallel beam arrangement shows an obvious distortion.     

Eliminate the influence of zero-order diffraction for wavefront reconstruction with selectable magnification in digital holographic

The objective surface is considered as the scattering plane; frequency spectrum of a digital hologram transmission light is studied when the reference light and reconstruction wave are spherical waves. The relation between relevant parameters and the object light, conjugate object light and zero-order diffraction wave frequency spectrum distribution. The research results show that: each frequency spectrum of the diffracted wave broadens to various degrees as the radius of the reconstruction wavefront decreases, and frequency aliasing is generated under certain conditions. Based on the research results, a new method that carries out high-pass filtering processing without zero-order diffraction interference upon digital hologram is proposed and the reconstruction experimental proof for eliminating the interferential changeable magnification wave is given.     

ICF流体力学不稳定性实验中调制传递函数的测量

 在流体力学不稳定性实验中,实际X光强度分布经过成像系统后会发生改变。要准确得到实际的光强分布,必须对系统的调制传递函数进行精确地测量。通过对刀口图像分析得到了系统的线扩散函数,再对其进行傅里叶变换得到调制传递函数,最后通过维纳滤波和约束最小二乘方滤波两种方法对图像进行了重建,得到比较清晰的边界情况和图像轮廓。     

二维弥散介质温度场的快速重建

提出了一种利用电荷耦合器件摄像机获取的辐射信息进行二维弥散介质温度场快速重建的新模型. 与现有的温度场重建模型相比,该模型是以逆向Monte Carlo方法为基础,重建速度更快、效率更高,能更好地描述散射介质. 采用了一个精确的二维温度场作为重建对象,结果表明,即使在存在测量误差的情况下,利用此模型重建出的温度场仍能重现原有精确温度场的特征. 关键词： 温度场重建 逆向Monte Carlo 电荷耦合器件摄像机 反问题     

Role of the null space of the DRM in the performance of modulated polarimeters

Imaging polarimeters infer the spatial distribution of the polarization state of the optical field as a function of time and/or wavelength. A polarimeter indirectly determines the polarization state by first modulating the intensity of the light field and then demodulating the measured data to infer the polarization parameters. This Letter considers passive Stokes parameter polarimeters and their inversion methods. The most widely used method is the data reduction matrix (DRM), which builds up a matrix equation that can be inverted to find the polarization state from a set of intensity measurements. An alternate strategy uses linear system formulations that allow band limited reconstruction through a filtering perspective. Here we compare these two strategies for overdetermined polarimeters and find that design of the null space of the inversion operator provides degrees of freedom to optimize the trade off between accuracy and signal-to-noise ratio. We further describe adaptive filtering techniques that could optimize the reconstruction for a particular experimental configuration. This Letter considers time-varying Stokes parameters, but the methods apply equally to polarimeters that are modulated in space or in wavelength.     

Efficient anisotropic filtering of diffusion tensor images

To improve the accuracy of structural and architectural characterization of living tissue with diffusion tensor imaging, an efficient smoothing algorithm is presented for reducing noise in diffusion tensor images. The algorithm is based on anisotropic diffusion filtering, which allows both image detail preservation and noise reduction. However, traditional numerical schemes for anisotropic filtering have the drawback of inefficiency and inaccuracy due to their poor stability and first order time accuracy. To address this, an unconditionally stable and second order time accuracy semi-implicit Craig-Sneyd scheme is adapted in our anisotropic filtering. By using large step size, unconditional stability allows this scheme to take much fewer iterations and thus less computation time than the explicit scheme to achieve a certain degree of smoothing. Second-order time accuracy makes the algorithm reduce noise more effectively than a first order scheme with the same total iteration time. Both the efficiency and effectiveness are quantitatively evaluated based on synthetic and in vivo human brain diffusion tensor images, and these tests demonstrate that our algorithm is an efficient and effective tool for denoising diffusion tensor images.     

CT图像“条状”伪影校正方法研究

在CT重建中,当断层射线衰减系数的变化呈非连续性的跳跃变化,如一种材质密度远远大于另一种材质的密度时,CT图像中高密度物质周围就会产生条状伪影。利用重投影技术分别获取高密度物质和低密度物质的正弦图,低密度物质正弦图中的数据缺失区用线性插值技术进行平滑过渡。利用两幅正弦图分别进行CT重建,然后将两幅CT图像进行相加,得到校正后的图像。实验结果表明,该方法能有效抑制条状伪影,同时提高了图像对比度。     

Application of the nonregularization method to solving the inverse problem of passive acoustic thermotomography on the wavelet basis

A comparative analysis of reconstruction quality is performed for the reconstruction of the temperature distribution under hyperthermia by the regularization and nonregularization methods, which are used for solving the systems of linear equations following from the statement of the ill-posed inverse problem of passive acoustic thermotomography. The basis functions are chosen to be wavelets, which allows a compact representation of the temperature peak under reconstruction. It is shown that, when deep-seated parts of tissue are heated, the nonregularization method gives a much smaller systematic error of temperature reconstruction at the focusing point. At the same time, the random error of reconstruction increases. The nonregularization method of reconstruction can be used in combination with regularization for monitoring hyperthermia procedures in oncology to obtain more detailed information on the in-depth temperature.     

基于向量变换的包裹相位场预处理与信息完整性探讨

针对包裹相位场在消除噪声的特别要求,提出了对包裹相位场预处理的向量滤波方法。理论分析了功率谱密度和向量变换的滤波思想。仿真实验研究了滤波模板的大小对滤波效果的影响,比较了在同样模板的选取下向量滤波方法与二次均值滤波法的滤波效果,分析了向量滤波方法与二次均值滤波法的功率谱密度分布。结果表明,相比二次均值滤波法,向量滤波法在降噪的同时,相位图依然清晰,它的功率谱密度分布没有明显变化,预处理后频谱信息的丢失远小于二次均值滤波。向量滤波法在提高信噪比的同时,信息的完整性得到较好保证。     

Non-negativity and stability analyses of lattice Boltzmann method for advection–diffusion equation

Stability is one of the main concerns in the lattice Boltzmann method (LBM). The objectives of this study are to investigate the linear stability of the lattice Boltzmann equation with the Bhatnagar–Gross–Krook collision operator (LBGK) for the advection–diffusion equation (ADE), and to understand the relationship between the stability of the LBGK and non-negativity of the equilibrium distribution functions (EDFs). This study conducted linear stability analysis on the LBGK, whose stability depends on the lattice Peclet number, the Courant number, the single relaxation time, and the flow direction. The von Neumann analysis was applied to delineate the stability domains by systematically varying these parameters. Moreover, the dimensionless EDFs were analyzed to identify the non-negative domains of the dimensionless EDFs. As a result, this study obtained linear stability and non-negativity domains for three different lattices with linear and second-order EDFs. It was found that the second-order EDFs have larger stability and non-negativity domains than the linear EDFs and outperform linear EDFs in terms of stability and numerical dispersion. Furthermore, the non-negativity of the EDFs is a sufficient condition for linear stability and becomes a necessary condition when the relaxation time is very close to 0.5. The stability and non-negativity domains provide useful information to guide the selection of dimensionless parameters to obtain stable LBM solutions. We use mass transport problems to demonstrate the consistency between the theoretical findings and LBM solutions.     

Large-eddy simulation of decaying isotropic turbulence across a grid refinement interface using explicit filtering and reconstruction

This paper explores numerical errors that arise when large-eddy simulation (LES) is used with adaptive mesh refinement (AMR). LES and AMR combined can reduce the computational cost of turbulence simulations compared to direct numerical simulations, but are rarely used together due to complications that arise with the application of the turbulence closure model at different grid resolutions. Errors appear at grid refinement interfaces due to dependence of computed quantities on the LES filter width and insufficient smoothness of the solution at the grid scale. Here, explicit filtering and approximate reconstruction of the unfiltered velocity field are used to mitigate the effects of these errors in a simulation of decaying isotropic turbulence advected past a grid refinement interface. In particular, different explicit filter types and levels of reconstruction are tested. Explicit filtering with zero-level reconstruction is found to produce the best long-term convergence to a uniform grid solution with minimum perturbation at the interface. Higher levels of reconstruction yield better near-interface convergence. When explicit filtering is used, the explicit filter width transition is more important than the grid spacing transition in terms of solution convergence and interface perturbation. These results inform the use of LES on more complicated AMR grids.