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fast algorithm for simulation of normal and oblique penetration into limestone targets

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Applied Mathematics and Mechanics(English Edition) 2017年第5期38卷 671-688页

作者： Xuguang CHEN Duo ZHANG Shujian YAO Fangyun LU College of Science National University of Defense TechnologyChangsha 410073China

A fast algorithm is proposed to predict penetration trajectory in simulation of normal and oblique penetration of a rigid steel projectile into a limestone target. The algorithm is designed based on the idea of isolation between the projectile and the target. Corresponding factors of influence are considered, including analytical load model, cratering effect, free surface effect, and separation-reattachment phenomenon. Besides, a method of cavity ring is used to study the process of cavity expansion. Further, description of the projectile＇s three-dimensional gesture is coded for fast calculation, named PENE3D. A presented. As a result, the algorithm is series of cases with selected normal and oblique penetrations are simulated by the algorithm. The predictions agree with the results of tests, showing that the proposed algorithm is fast and effective in simulation of the penetration process and prediction of the penetration trajectory.

关键词： fast algorithm isolation between projectile and target analytical loading model ogive-nosed projectile limestone target

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 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 astrophysics.In 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 type.This 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 surface.Numerical 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 algorithm.The 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

fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations

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Numerical Mathematics(Theory,Methods and Applications) 2022年第1期15卷 200-226页

作者： Jia-Li Zhang Zhi-Wei Fang Hai-Wei Sun Department of Mathematics University of MacaoMacaoSARChina

In this paper,we propose a fast second-order approximation to the variable-order(VO)Caputo fractional derivative,which is developed based on L2-1σformula and the exponential-sum-approximation technique.The fast evaluation method can achieve the second-order accuracy and further reduce the computational cost and the acting memory for the VO Caputo fractional derivative.This fast algorithm is applied to construct a relevant fast temporal second-order and spatial fourth-order scheme(F L2-1σscheme)for the multi-dimensional VO time-fractional sub-diffusion equations.Theoretically,F L2-1σscheme is proved to fulfill the similar properties of the coefficients as those of the well-studied L2-1σscheme.Therefore,F L2-1σscheme is strictly proved to be unconditionally stable and convergent.A sharp decrease in the computational cost and the acting memory is shown in the numerical examples to demonstrate the efficiency of the proposed method.

关键词： Variable-order Caputo fractional derivative exponential-sum-approximation method fast algorithm time-fractional sub-diffusion equation stability and convergence

A fast Cartesian Grid-Based Integral Equation Method for Unbounded Interface Problems with Non-Homogeneous Source Terms

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Communications in Computational Physics 2023年第6期33卷 208-234页

作者： Jiahe Yang Wenjun Ying School of Mathematical Sciences Shanghai Jiao Tong UniversityMinhangShanghai 200240P.R.China Department of Mathematics MOE-LSC and Institute of Natural SciencesShanghai Jiao Tong UniversityMinhangShanghai 200240P.R.China

This work presents a fast Cartesian grid-based integral equation method for unbounded interface problems with non-homogeneous source terms.The unbounded interface problem is solved with boundary integral equation methods such that infinite boundary conditions are satisfied naturally.This work overcomes two difficulties.The first difficulty is the evaluation of singular integrals.Boundary and volume integrals are transformed into equivalent but much simpler bounded interface problems on rectangular domains,which are solved with FFT-based finite difference solvers.The second one is the expensive computational cost for volume integrals.Despite the use of efficient interface problem solvers,the evaluation for volume integrals is still expensive due to the evaluation of boundary conditions for the simple interface problem.The problem is alleviated by introducing an auxiliary circle as a bridge to indirectly evaluate boundary conditions.Since solving boundary integral equations on a circular boundary is so accurate,one only needs to select a fixed number of points for the discretization of the circle to reduce the computational cost.Numerical examples are presented to demonstrate the efficiency and the second-order accuracy of the proposed numerical method.

关键词： Interface problem unbounded domain boundary integral equation kernel-free method auxiliary circle Cartesian grid method fast algorithm

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...

A fast algorithm of the DCT and IDCT for VLSI Implementation

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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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 compression.The DCT algorithms and VLSI architectures for real-time computation capabilities are required urgently.It is known that VLSI implementation of distributed arithmetic is very efficient for computing convolution.Here,an algorithm is presented to convert the DCT and inverse DCT（IDCT） to skew-convolution.VLSI 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...

Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula

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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Communications on Applied Mathematics and Computation 2022年第4期4卷 1313-1350页

作者： Ren-jun Qi Zhi-zhong Sun School of Mathematics Southeast UniversityNanjing 210096JiangsuChina

With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.Three extrapolation formulas are presented,whose temporal convergence orders in L_(∞)-norm are proved to be 2,3-α,and 4-2α,respectively,where 0fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the accuracy.Several numerical experiments confirm the theoretical results.

关键词： L1 formula Asymptotic expansion Fractional sub-diffusion equation Fractional wave equation Richardson extrapolation fast algorithm