308 research outputs found
FMM-Yukawa: An Adaptive Fast Multipole Method for Screened Coulomb Interactions
No full text1 online resource (PDF, 19 pages, includes illustrations)Huang, Jingfang; Jia, Jun; Zhang, Bo. (2009). FMM-Yukawa: An Adaptive Fast Multipole Method for Screened Coulomb Interactions. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/180140
Semi-implicit Krylov deferred correction methods for differential algebraic equations
No full text1 online resource (PDF, 24 pages, includes illustrations)Bu, Sunyoung; Huang, Jingfang; Minion, Michael L.. (2009). Semi-implicit Krylov deferred correction methods for differential algebraic equations. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/180301
Huang qin guo qi
No full textSide A. 1. 芳草青青晨風爽 ; 2. 梳洗打扮 ; 3. 打开了洒金扇 ; 4. 听媽講明成破利害 ; 5. 休傷心來休抱怨 (ca. 25 min.) -- Side B. 1. 花开花落几度春 ; 2. 滴滴鮮血往下淌.Live recording."黑龙江省龙江剧院祁景方赠送 一九八三年七月四日"--Memo.Electronic reproduction from Rulan Chao Pian Audio Cassette Collection.編剧: 王毅 ; 編曲: 祁景方, 苏寿华(执筆)演唱: 白淑賢 [and others] ; 伴奏: 黑龙江省龙江剧院乐隊.Sung in Chinese."Heilongjiang Sheng Longjiang ju yuan Qi Jingfang zeng song yi jiu ba san nian qi yue si ri"--Memo.Bian ju: Wang Yi ; bian qu: Qi Jingfang, Su Shouhua (zhi bi)Yan chang: Bai Shuxian [and others] ; ban zou: Heilongjiang Sheng Longjiang ju yuan yue dui.Detailed contents in vernacular field only
Thoughts on Coronavirus Disease 2019 Based on JingFang Medicine (Classical Chinese Formula) Solutions for COVID-19
No full textThis article aims to provide some thoughts on the prevention and treatment of Coronavirus Disease 2019 (COVID-19) from the perspective of JingFang Medicine (Classical Chinese Formula). It is believed that the vague theoretical understanding of COVID-19 in Traditional Chinese Medicine does not hinder the precise treatment of the disease by following the rule of “With this Zheng, prescribe this Fang.” According to the principle of “Fang-Zheng Correlation” and the knowledge gained from the thousands of years of experience in treating febrile diseases, Xiao Chai Hu Decoction (小柴胡汤) and its modifications are recommended with the emphasis on individualized treatment. As another form of practicing “Fang-Zheng Correlation,” generalized group treatment should also be paid attention to. Giving considerations to the historical medical data, Jing Fang Bai Du Powder (荆防败毒散) and Shi Shen Decoction (十神汤) are recommended for group prevention treatment. Assisting the Zheng (Upright) Qi and using tonic formulas are two entirely different concepts. According to the principle of “Fang-Zheng Correlation,” tonics abuse should be avoided in the prevention of COVID-19, and the using of Huang Qi (黄芪 Radix Astragali seu Hedysari) should also be very carefully done
Integral-equation-based fast algorithms and graph-theoretic methods for large-scale simulations
No full textIn this dissertation, we extend Greengard and Rokhlin's seminal work on fast multipole method (FMM) in three aspects. First, we have implemented and released open-source new-version of FMM solvers for the Laplace, Yukawa, and low-frequency Helmholtz equations to further broaden and facilitate the applications of FMM in different scientific fields. Secondly, we propose a graph-theoretic parallelization scheme to map the FMM onto modern parallel computer architectures. We have particularly established the critical path analysis, exponential node growth condition for concurrency-breadth, and a spatio-temporal graph partition strategy. Thirdly, we introduce a new kernel-independent FMM based on Fourier series expansions and discuss how information can be collected, compressed, and transmitted through the tree structure for a wide class of kernels
Krylov deferred correction methods for differential equations with algebraic constraints
No full textIn this dissertation, we introduce a new class of spectral time stepping methods for efficient and accurate solutions of ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs). The methods are based on applying spectral deferred correction techniques as preconditioners to Picard integral collocation formulations, least squares based orthogonal polynomial approximations are computed using Gaussian type quadratures, and spectral integration is used instead of numerically unstable differentiation. For ODE problems, the resulting Krylov deferred correction (KDC) methods solve the preconditioned nonlinear system using Newton-Krylov schemes such as Newton-GMRES method. For PDE systems, method of lines transpose (MoLT ) couples the KDC techniques with fast elliptic equation solvers based on integral equation formulations and fast algorithms. Preliminary numerical results show that the new methods are of arbitrary order of accuracy, extremely stable, and very competitive with existing techniques, particularly when high precision is desired
Recursive Tree Algorithms for Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations
No full textIn this paper, we study a numerical linear algebra problem arising from the efficient simulation of Brownian dynamics with hydrodynamics interactions where molecules are modeled as ensembles of rigid bodies. Given the first 6 rows of a matrix Q of size 3n x 3n describing how the force on each of the n particles in a rigid body P can be mapped to the 6 entries in P’s resultant force and torque, we show how the remaining 3n − 6 rows of vectors can be constructed explicitly using O(nlog(n)) operations and storage, so that (1) they form an orthonormal basis and (2) they are orthogonal to each of the first 6 vectors. For applications where only the matrix-vector multiplications are needed, without forming Q, we introduce O(n) recursive tree algorithms for computing both Q · v and QT · v for an arbitrary vector v. Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms.Bachelor of Scienc
Compressible Features: Mathematical Foundations and Applications
No full textWith the growing emphasis on analyzing large-scale real-world systems, improving computational efficiency, specifically reducing storage requirements and computational time, has become increasingly important. Although previous studies have introduced various matrix- and tensor-based compression techniques, the behavior of compressible features in special matrix exponentials of the form , where is the sum of a diagonal matrix and a low-rank matrix, remains underexplored as the parameter evolves. Generalized from 2D systems, researchers also employ tensor-based dynamical systems to capture the multilayer relationships that 2D systems cannot. Traditional approaches to verify system properties, such as controllability, stability, and observability, typically involve unfolding the tensor into large block-circulant matrices, followed by the application of classical linear systems theory. However, such unfolding-based methods often result in a dramatic increase in memory usage and computational cost as system dimensions grow, necessitating more scalable solutions. Therefore, this study proposes efficient compression techniques for two-dimensional and higher-order systems by addressing three central challenges: (i) characterizing the evolution of compressible patterns in matrix exponentials of structured operators and proving bounded numerical rank growth in physically relevant systems; (ii) accelerating the analysis of T-product-based dynamical systems (TPDSs) through block diagonalization, significantly reducing computational time and memory; and (iii) improving the computational efficiency of multilinear dynamical systems (MLDSs) using Tucker decomposition and Tensor-Train decomposition (TTD) by leveraging their respective tensor cores. The proposed framework is supported by theoretical guarantees and numerical experiments, all while preserving model interpretability, which is essential for applications in quantum control, video processing, and large-scale network analysis. Overall, our work contributes to the advancement of structured tensor algebra for high-dimensional data analysis and inspires future work related to rank evolution and practical deployment in complex systems.Bachelor of Scienc
Designing Computational tools for high dimensional data with compressible features
No full textIn this paper, we propose a novel approach for dependency testing based on non-standard Haar wavelet expansions. Dependency testing is an important and fundamental problem in statistics, machine learning, and other related fields, where we aim to determine whether two variables in a data set are related to each other or not. In many cases, the variables under consideration exhibit complex, nonlinear relationships that are difficult to capture using traditional polynomial and Fourier basis functions, especially in large noise settings. In such cases, wavelet basis provides a useful alternative. However, traditional wavelet basis functions suffer from certain limitations, such as poor resolution and curse of dimensionality. To overcome these limitations, we propose the use of non-standard Haar wavelet basis functions which are naturally associated with a hierarchical tree structure to allow adaptive resolution of the underlying probability density function and fast computation of the expansion coefficients. The greater adaptivity of the “sparse grid" non-standard Haar wavelet basis enables better resolution when compared to traditional Walsh functions and standard Haar wavelets, and allows its application to extremely high-dimensional datasets (with compressible features) arising from a wide range of problems in Biostatistics, machine learning, and business. Unfortunately, our preliminary numerical experiments also show that when only one of the non-standard Haar expansion coefficient is used in dependency testing (e.g., maximum coefficient test), because of the local properties of the non-standard Haar basis, the statistical power of the resulting testing strategy compares poorly with other basis choices. The main contributions of this paper are two strategies to improve the statistical power of the non-standard Haar wavelet basis based dependency test algorithms. First, we introduce the concept of “skeleton" of the non-standard Haar expansion coefficients which captures most (if not all) of the statistically important features; and second, we apply the technique of “cross validation" to further improve the statistical power of the method. In the cross validation (cross checking) technique, the original data set is randomly separated into two groups, and we learn the statistical features from the first group and validate these features using data from the second group, in order to better determine if the variables are dependent. By employing these two techniques, we established a novel approach for analyzing dependencies between variables. Numerical results are presented to demonstrate the efficiency, accuracy, and statistical power of this new approach, showing that our method has the potential to surpass traditional methods. We believe that our approach represents a significant advance in the field of dependency testing and wavelet analysis.Bachelor of Scienc
Semi-implicit Krylov deferred correction algorithms, applications, and parallelization
No full textIn this dissertation, we introduce several strategies to improve the efficiency of the Krylov deferred correction (KDC) methods for special structured ordinary and partial differential equations with algebraic constraints. We first study the semi-implicit KDC (SI-KDC) technique which splits stiff differential equation systems into different components and applies different low-order time marching schemes to these components. Compared with the fully implicit KDC (FI-KDC) method, our analysis and preliminary numerical results for differential algebraic equations show that the SI-KDC schemes are more efficient due to the reduced number of operations in each spectral deferred correction (SDC) iteration. Next, we apply the SI-KDC scheme to simulate a two-scale model describing the mass transfer processes in drinking water treatment applications, in which some set of chemical species move from one distinct phase to a second distinct phase. We also present an improved effective model to further advance the efficiency of the multiscale modeling. Finally, we investigate the parareal method to parallelize the KDC techniques, and present some preliminary numerical results to show its potential in large scale simulations
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