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fast algorithm for viscous Cahn-Hilliard equation

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Frontiers of Mathematics in China 2022年第4期17卷 689-713页

作者： Danxia WANG Yaqian LI Xingxing WANG Hongen JIA College of Mathematics Taiyuan University of TechnologyTaiyuan030024China

The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh(TT-M)finite element(FE)method to ease the problem caused by strong *** TT-M FE algorithm includes the following main computing ***,a nonlinear FE method is applied on a coarse time-meshτ_(c).Here,the FE method is used for spatial discretization and the implicit second-orderθscheme(containing both implicit Crank-Nicolson and second-order backward difference)is used for temporal ***,based on the chosen initial iterative value,a linearized FE system on time fine mesh is solved,where some useful coarse numerical solutions are found by Lagrange’s interpolation *** analysis for both stability and a priori error estimates is made in *** examples are given to demonstrate the validity of the proposed *** algorithm is compared with the traditional Galerkin FE method and it is evident that our fast algorithm can save computational time.

关键词： fast algorithm two time-mesh(TT-M)finite element(FE)method viscous Cahn-Hilliard equation stability CPU time

A fast algorithm for Solving CNOP and Associated Target Observation Tests

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Acta meteorologica Sinica 2009年第4期23卷 387-402页

作者：王斌谭晓伟 LASG Institute of Atmospheric Physics Chinese Academy of Sciences Graduate School of the Chinese Academy of Sciences

Conditional Nonlinear Optimal Perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function （EOF）. The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System （GRAPES）, an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity （target） area is evaluated through two observing system simulation experiments （OSSEs）. The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors （ARPEs） in the verification region are reduced significantly compared with the ＂true state,＂ when the initial conditions （ICs） in the sensitivity area are replaced with the ＂observations.＂ The decrease of the ARPEs can be achieved for even longer prediction times （e.g., 72 h）. Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon＇s initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.

关键词： fast algorithm CNOP (Conditional Nonlinear Optimal Perturbation) target observation OSSE (observing system simulation experiment)

A New Method for Particle Velocity Measurement Based on fast algorithm for Cross-correlation and Filter Interpolation

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A New Method for Particle Velocity Measurement Based on Fast...

fast algorithm for constructing neighbor-joining phylogenetic trees

第25届中国控制与决策会议

作者： Wang Yutao Wang Dayang Yang Gang School of Information Science and Engineering Northeastern University

ISBN: (纸本)9781467355339

Cross-correlation method is a well-known technique in online continuous velocity measurement of particulate solids in pneumatic pipelines, but the low sampling rate and noise will cause inaccuracy in the delay estimates, and the computation of the cross correlation function is expensive which is not suited for real-time implementation. This paper presents a method based on fast algorithm for cross-correlation and filter interpolation to obtain the velocity in real-time and improve the accuracy of the velocity measurement. The real-time DSP-based cross-correlation velocity measurement system is designed and experiments are carried out to evaluate the performance of the proposed method, and the experimental results show that the sampling rate is increased, and system relative error is within ±4% over a velocity range of 2.8-4.0m/s for a moving particle. This method can lower the requirements for data acquisition hardware and improve the estimation accuracy by increasing the sampling rate and eliminate the noise at the same time. It is well suited for real-time implementation in DSP-based velocity measurement system because of the little computation of the cross-correlation function.

关键词： Cross-correlation Particle Velocity Measurement Filter Interpolation Method fast algorithm

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Journal of Southeast University(English Edition) 2006年第2期22卷 176-179页

作者：陈宁涛王能超施保昌华中科技大学计算机科学与技术学院武汉430074 华中科技大学并行计算研究所武汉430074

To improve the performance of Saitou and Nei＇s algorithm （SN） and Studier and Keppler＇s improved algorithm （SK） for constructing neighbor-joining phylogenetic trees and reduce the time complexity of the computation, a fast algorithm is proposed. The proposed algorithm includes three techniques. First, a linear array A[N] is introduced to store the sum of every row of the distance matrix （the same as SK）, which can eliminate many repeated computations. Secondly, the value of A [i] is computed only once at the beginning of the algorithm, and is updated by three elements in the iteration. Thirdly, a very compact formula for the sum of all the branch lengths of operational taxonomic units （OTUs） i and j is designed, and the correctness of the formula is proved. The experimental results show that the proposed algorithm is from tens to hundreds times faster than SN and roughly two times faster than SK when N increases, constructing a tree with 2 000 OTUs in 3 min on a current desktop computer. To earn the time with the cost of the space and reduce the computations in the innermost loop are the basic solutions for algorithms with many loops.

关键词： phylogenetic tree neighbor-joining method fast algorithm progressive multiple alignment

A fast algorithm of the DCT and IDCT for VLSI Implementation

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A Fast Algorithm of the DCT and IDCT for VLSI Implementation

fast algorithm of Parameters Estimation of High Speed Moving Target Based on Conjugate Gradients and Its Test

1996 3rd International Conference on Signal Processing(ICSP’96)

作者： Hong Ying Hou Zhaohuan Institute of Acoustics Chinese Academy of Sciences

ISBN: (纸本)0780329120

＜正＞Since DCT performs very close to the statistically optimal Karhunen-Loeve Transform（KLT）,it is widely used in digital signal processing,especially for speech and image data *** DCT algorithms and VLSI architectures for real-time computation capabilities are required *** is known that VLSI implementation of distributed arithmetic is very efficient for computing ***,an algorithm is presented to convert the DCT and inverse DCT（IDCT） to *** implementation of the algorithm has same advantage as any implementation using distributed arithmetic.

关键词： VLSI discrete cosine transforms inverse problems transform coding digital signal processing chips data compression speech coding image coding digital arithmetic convolution number theory IDCT DCT VLSI implementation fast algorithm digital signal processing statistically optimal Karhunen-Loeve transform image data compression speech compression VLSI architectures real-time computation distributed arithmetic inverse DCT skew-convolution number theoretic transforms

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Fast Algorithm of Parameters Estimation of High Speed Moving...

A fast algorithm for Matching Remote Scene Images

2011 International Conference on Computer Science and Information Technology(ICCSIT 2011)

作者： GAO Zhu Unit 92635 PLA

ISBN: (纸本)9781612848334

Wideband signal processing is always realized by wideband correlative processing which has a time scale and time delay 2-D peak value search calculation structure. Aiming at the relatively high parameters estimation precision, the structure should have a high search density, but it would cause a heavy operation which system cannot afford. Then a fast algorithm of parameters estimation based on conjugate gradients was advanced. The computer simulation of fast algorithm was accomplished and parameters estimation deviation variance curves were calculated by Monte Carlo method. The simulated reflected signal of high-speed moving target was collected in lake test and the fast algorithm were applied on the target detection and parameters estimation under the low SNR. The results of simulation and lake test showed that the fast algorithm based on conjugate gradients could reach the peak value by low operation and relatively high parameters estimation precision by iterative calculation.

关键词： parameters estimation conjugate gradients fast algorithm Monte Carlo lake test

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Geo-Spatial Information Science 2008年第3期11卷 197-200页

作者： LIU Jin YAN Li School of Geodesy and Geomatics Wuhan University 129 Luoyu Road Wuhan 430079 China State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing Wuhan University 129 Luoyu Road Wuhan 430079 China.

An iterative algorithm to calculate mutual correlation using hierarchical key points and the search space mark principle is proposed. An effective algorithm is designed to improve the matching speed. By hi-erarchical key point algorithm and mutual correlation coefficients of the matching images, the important points can be iteratively calculated in the images hierarchically, and the correlation coefficient can be ob-tained with satisfactory precision. Massive spots in the parameter space which are impossible to match can be removed by the search space mark principle. Two approximate continuities in the correlation image matching process, the image gray level distribution continuity and the correlation coefficient value in the parameter space continuity, are considered in the method. The experiments show that the new algorithm can greatly enhance matching speed and achieve accurate matching results.

关键词： image correlation matching fast algorithm iterative algorithm

A fast algorithm for Improving the Visual Distance in Fog

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Semiconductor Photonics and Technology 2009年第4期15卷 241-246页

作者： YANG Wei XIAO Zhi-tao YU Jian YAN Zhi-jie School of Information and Communication Engineering Tianjin Polytechnic University Tianjin 300160 CHN School of Computer Science and Technology Tianjin University Tianjin 300072 CHN

Images captured outdoor usually degenerate because of the bad weather conditions,among which fog,one of the widespread phenomena,affects the video quality *** physical features of fog make the video blurred and the visible distance shortened,seriously impairing the reliability of the video *** order to satisfy the requirement of image processing in real-time,the normal distribution curve fitting technology is used to fit the histogram of the sky part and the region growing method is used to segment the region of *** for the non-sky part,a method of self-adaptive interpolation to equalize the histogram is adopted to enhance the contrast of the *** results show that the method works well and will not cause block effect.

关键词： fog image interpolation region growing histogram equalization fast algorithm normaldistribution

A High-Accurate fast Poisson Solver Based on Harmonic SurfaceMapping algorithm

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Communications in Computational Physics 2021年第6期30卷 210-226页

作者： Jiuyang Liang Pei Liu Zhenli Xu School of Mathematical Sciences Institute of Natural Sciencesand MOE-LSCShanghai Jiao Tong UniversityShanghai 200240China School of Mathematics University of MinnesotaTwin CitiesMinneapolisMN 55455USA

Poisson’s equations in a cuboid are frequently solved in many scientific and engineering applications such as electric structure calculations,molecular dynamics simulations and computational *** this paper,a fast and highly accurate algorithm is presented for the solution of the Poisson’s equation in a cuboidal domain with boundary conditions of mixed *** so-called harmonic surface mapping algorithm is a meshless algorithm which can achieve a desired order of accuracy by evaluating a body convolution of the source and the free-spaceGreen’s function within a sphere containing the cuboid,and another surface integration over the spherical *** quadratures are introduced to approximate the integrals,resulting in the solution represented by a summation of point sources in free space,which can be accelerated by means of the fast multipole *** complexity of the algorithm is linear to the number of quadrature points,and the convergence rate can be arbitrarily high even when the source term is a piecewise continuous function.

关键词： fast algorithm Poisson’s equation boundary integral method image charge mixed boundary condition fast multipole method