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Lattice Boltzmann method on quadtree grids

Physical Review E 2011年第2期83卷 026707-026707页

作者： Yu Chen Qinjun Kang Qingdong Cai Dongxiao Zhang The State Key Laboratory for Turbulence and Complex Systems (LTCS) Center for Applied Physics and Technology (CAPT) and Department of Mechanics and Aerospace Engineering Peking University Beijing People’s Republic of China Sonny Astani Department of Civil and Environmental Engineering University of Southern California Los Angeles California 90089 USA Earth and Environmental Sciences Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Department of Energy and Resources Engineering Peking University Beijing People’s Republic of China

A lattice Boltzmann method on nonuniform quadtree grids is proposed. Our method employs the interpolation-supplemented lattice Boltzmann model. The advantages of the quadtree grid are preserved by using linear interpolation instead of quadratic interpolation to complete the streaming step in the lattice Boltzmann method. The back-and-forth error compensation and correction (BFECC) method is used to improve the accuracy, so that the second-order accuracy of the conventional lattice Boltzmann method is maintained. Several numerical cases, including a BFECC streaming test, lid-driven cavity flow, and flow over an asymmetrically placed cylinder in a channel, are carried out to demonstrate the accuracy and efficiency of our method.

关键词： BOLTZMANN'S equation QUADTREES interpolation algorithms ERROR analysis (Mathematics) NUMERICAL analysis

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A discrete regression method on manifolds and its application to data on SO( n )

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IFAC Proceedings Volumes 2011年第1期44卷 2284-2289页

作者： Nicolas Boumal P.-A. Absil Center for Systems Engineering and Applied Mechanics (CESAME) and ICTEAM Institute Université catholique de Louvain B-1348 Louvain-la-Neuve Belgium (Tel: (+32) 10 47 80 10)

Abstract The regression problem of fitting a “smooth”, discrete curve to data points on a Riemannian manifold is formulated here as an unconstrained, finite-dimensional optimization problem. Smoothness of a discrete curve, seen as a sequence of close points on the manifold, is assessed and encouraged by a regularity term in the objective function. This term is built upon a generalization of finite differences to manifolds introduced in this work. Tuning of the balance between fitting and regularity (or energy-efficiency) is achieved by adjusting two parameters. The proposed framework is described in detail and is then applied to the special orthogonal group SO( n ), i.e., the set of rotations in n . A Riemannian version of the nonlinear conjugate gradient method is used to minimize the resulting objective. To this end, an explicit formula for the derivative of the matrix logarithm is derived, yielding explicit formulas for the gradient of the objective. Numerical results are presented and show that smooth curves in SO( n ) can be obtained in a few hundred iterations with the proposed algorithm. Copyright © 2011 IFAC

关键词： differential geometric methods non-parametric regression discrete time finite differences conjugate gradient methods interpolation algorithms least-squares approximation rotation

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Fast and accurate interpolation of large scattered data sets on the sphere

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第5期234卷 1505-1521页

作者： Cavoretto, Roberto De Rossi, Alessandra Univ Turin Dept Math I-10123 Turin Italy

In this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented. The solution method is local and involves a modified spherical Shepard's interpolant, which uses zonal basis functions as local approximants. The associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere. Specifically, this technique is mainly based on the partition of the sphere in a suitable number of spherical zones, the construction of spherical caps as local neighbourhoods for each node, and finally the employment of a spherical zone searching procedure. Computational cost and storage requirements of the spherical algorithm are analyzed. Moreover, several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm. (C) 2010 Elsevier BM. All rights reserved.

关键词： Zonal basis functions Spherical Shepard's formula Local methods Scattered data interpolation interpolation algorithms

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A fast frequency-domain interpolation method for the evaluation of the frequency and amplitude of spectral components

A fast frequency-domain interpolation method for the evaluat...

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International Instrumentation and Measurement Technology Conference (I2MTC)

作者： Ferrero, Alessandro Salicone, Simona Politecn Milan Dipartimento Elettrotecn I-20133 Milan Italy

ISBN: (纸本)9781424428335

The evaluation of the spectral components of a signal by means of a DFT or FFT algorithm is subject to leakage errors whenever the sampling frequency is not coherent with the signal frequency. Smoothing windows are used to mitigate these errors, and interpolation methods are applied, in the frequency domain, to reduce these errors further on. However, if cosine windows are employed, closed-form formulas for the evaluation of the harmonic frequencies can be used only with second-order windows, while approximated formulas have to be used in the other cases. In both cases, a high computation burden is required. This paper proposes a fast interpolation method, independent of the window type and order, based on suitable look-up tables. Experimental results are reported and the accuracy is discussed, proving that the method provides results as good as those obtained with other methods, without requiring the same high computation burden.

关键词： interpolation algorithms Cosine windows FFT

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The Fourier series interpolation method for the solution of the SDARE

The Fourier series interpolation method for the solution of ...

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UKACC International Conference on Control 2010

作者： S. Muhammad J. van der Woude Delft Institute of Applied Mathematics Delft University of Technology Delft Netherlands

ISBN: (纸本)9781627481199

In this paper, we propose the Fourier series interpolation (FSI) method for the solution of the SDARE* in which the state dependency of the coefficient matrices is of periodic nature. In particular, we focus on the SDAREs where the system matrix depends on a single state component in a periodic way. The main advantage of the FSI approach is that the Fourier coefficients are computed offline. This in turn results in significant reduction in online computations for the solution of the SDARE. The implementation and performance of the FSI method is explained by considering the dynamical positioning (DP) problem of a ship. This problem has been studied by using the SDARE controller and observer. This requires online computation of the solution of the SDAREs. We show that the FSI method significantly reduces the online computation time in comparison with the MATLAB routine “care” in a situation where online solution of the SDARE is required. The FSI method can be particularly useful in situations involving the systems having small time constants.

关键词： Riccati equations interpolation algorithms Nonlinear systems Control system design State estimation Kalman filters Solutions Solution Fourier series computational time interpolation Fourier coefficients

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Application of selected statistical coefficients to accuracy analysis on surface interpolation models 7

Application of selected statistical coefficients to accuracy...

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7th International Conference on Environmental Engineering

作者： Gosciewski, Dariusz Univ Warmia & Mazury Olsztyn Fac Geodesy & Land Management Inst Geodesy PL-10957 Olsztyn Poland

ISBN: (纸本)9789955282631

The majority of GIS type software systems allow generating the digital terrain models on the basis of the regular GRID type network of squares. The accuracy of such a model depends mainly on the choice of interpolation algorithms and their computation parameters. Comparison of quality and accuracy of the interpolation models generated by applying different algorithms is becoming an important issue. The paper presents a comparison of accuracy of terrain models generated by application of five interpolation algorithms. The analysis was based on the theoretical model represented by the mathematical surface generated using the function of two variables. Selected statistical coefficients and differential diagram of errors distribution were applied for interpolation models accuracy comparison. The matching accuracy of interpolation surface and the standard surface was also investigated. Results of analysis of the values determined by statistical coefficients supported with differential diagrams allowed comprehensive comparison of accuracy of interpolation algorithms and identification of the most accurate among them.

关键词： interpolation algorithms statistical coefficients differential diagrams accuracy analysis

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The Harmonious Detecting and Analyzing of PV Grid Connected Generation

The Harmonious Detecting and Analyzing of PV Grid Connected ...

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27th Chinese Control Conference

作者： Luo Weiping Wuhan Univ Sci & Engn Coll Elect & Informat Engn Wuhan 430073 Peoples R China

ISBN: (纸本)9787900719706

The method of harmonious detecting is introduced about PV grid connected generation, and the technique is realized to harmonious synchronous sampling based on PLL circuit of hardware, in order that the error is eliminated for non-synchronous sampling at all. It is used to analyze the harmonic of PV system for FFT algorithm based on B-H window function and interpolation, and the error is minished by frequency table giveaway and barrier domino offect effectively, veracity of data processing is advanced.

关键词： Photovoltaic Grid Connected Harmonics Detection Active Power Filter Window Functions interpolation algorithms

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IMPROVING CNC MACHINE TOOLS ACCURACY USING MODELING AND COMPUTER SIMULATION TECHNIQUES

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IFAC Proceedings Volumes 2007年第18期40卷 881-886页

作者： Radu E. Breaz Octavian C. Bologa Gabriel S. Racz “Lucian Blaga” University of Sibiu Engineering Faculty radu.breaz@ulbsibiu.ro

The position was one of the first parameters that required the introduction of automatic control process. One of the most representative applications is represented by the feed drives of the computer numerically controlled (CNC) machine tools. Today, it is possible to use computer simulation techniques in analysing and synthesising position control systems. Thus, the behaviour of the CNC machine tools feed drives can be treated much more realistically. It is the purpose of this paper to show how simulation can be used to accurately represent, predict and improve the performance of a CNC machine tool feed servo drives.

关键词： interpolation algorithms machine tool position control simulation transfer functions

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Study of quintic spline interpolation and generated velocity profile for high speed machining

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Wuhan Ligong Daxue Xuebao/Journal of Wuhan University of Technology 2006年第SUPPL. 1期28卷 507-512页

作者： Zheng, Jinxing Zhang, Mingjun Meng, Qingxin Department of Mechanical Engineering Harbin Engineering University Harbin 150001 China

Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high accelerations, in order to deliver the rapid feed motion. This paper presents an interpolation algorithm to generate continuous quintic spline toolpaths, with a constant travel increment at each step, while the smoother accelerations and jerks of two-order curve are obtained. Then an approach for reducing the feedrate fluctuation in high speed spline interpolation is presented. The presented approach has been validated to quickly, reliably and effective with the simulation.

关键词： interpolation algorithms Quadric jerks profiling Quintic spline

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A Data Treatment System for Water Environmental Hydrodynamics Measurement

A Data Treatment System for Water Environmental Hydrodynamic...

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ICEMI'2005第七届国际电子测量与仪器学术会议

作者： Jiang Fan Chen Wei-ping Li Yuanyuan Zhang Tao (College of Mechanical Engineering, South China University of Technology, GuangZhou 510640 China)

In order to help researcher to understand the measuring data more carefully, and to obtain more valuable and significant information hidden in measuring data of water environmental hydrodynamics, a ne

关键词： Water environmental hydrodynamics measurement measuring data treatment data visualization interpolation algorithms object-oriented program.

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