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PROJECTION METHOD FOR VISCOUS INCOMPRESSIBLE-FLOW ON QUADRILATERAL GRIDS

AIAA JOURNAL 1994年第10期32卷 1961-1969页

作者： BELL, JB SZYMCZAK, WG USN CTR SURFACE WARFAREINFORMAT SCI & SYST BRANCHSILVER SPRINGMD 20903

This paper describes a second-order projection method for the incompressible Navier-Stokes equations on multiply connected domains with a logically rectangular quadrilateral grid. The method uses a second-order fractional step scheme in which one first solves diffusion-convection equations to determine intermediate velocities which are then projected onto the space of divergence-free vector fields. The spatial discretizations are accomplished by formally transforming the equations to a computational space with a uniform grid. The diffusion, pressure gradient, and divergence terms are discretized using standard finite difference approximations. The convection terms are discretized using a second-order Godunov method that provides a robust discretization of these terms at high Reynolds number. Numerical results are presented illustrating the performance of the method.

关键词： Incompressible Flow Reynolds Number Navier Stokes Equations Convection Finite Difference Approximation Strouhal Numbers Computing conjugate gradient algorithm Cartesian Coordinate System Riemann Problem

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Reduced-order compensation using the Hyland-Bernstein optimal projection equations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1996年第2期19卷 407-417页

作者： Collins, EG Haddad, WM Ying, SS FLORIDA STATE UNIV TALLAHASSEEFL 32310 GEORGIA INST TECHNOL ATLANTAGA 30332 COLLINS COMMERCIAL AVION MELBOURNEFL 32934

gradient-based homotopy algorithms have previously been developed for synthesizing H-2 optimal reduced-order dynamic compensators. These algorithms are made efficient and avoid high-order singularities along the homotopy path by constraining the controller realization to a minimal parameter basis. The resultant homotopy algorithms, however, sometimes experience numerical ill conditioning or failure due to the minimal parameterization constraint. A new homotopy algorithm is presented that is based on solving the optimal projection equations, a set of coupled Riccati and Lyapunov equations that characterize the optimal reduced-order dynamic compensator. Path following in the proposed algorithm is accomplished using a predictor/corrector scheme that computes the prediction and correction steps hy efficiently solving a set of four Lyapunov equations coupled by relatively low-rank linear operators. The algorithm does not suffer from ill conditioning because of constraining the controller basis and often exhibits better numerical properties than the gradient-based homotopy algorithms. The performance of the algorithm is illustrated by considering reduced-order control design for the benchmark four disk axial vibration problem and also reduced-order control of the Active Control Technique Evaluation for Spacecraft structure.

关键词： Optimal Projection Equations Linear Time Invariant Spacecraft Structures Numerical Integration Riccati Equations MATLAB Computing conjugate gradient algorithm Taylor Series Robust Design

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A fast Gibbs sampler for synthesizing constrained fractals

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 1997年第4期3卷 337-351页

作者： Vemuri, BC Mandal, C Lai, SH Univ Florida Dept Comp & Informat Sci & Engn Gainesville FL 32611 USA Siemens Corp Res Princeton NJ USA

It is well known that the spatial frequency spectrum of membrane and thin plate splines exhibit self-affine characteristics and, hence, behave as fractals. This behavior was exploited in generating the constrained fractal surfaces, which were generated by using a Gibbs sampler algorithm in the work of Szeliski and Terzopoulos. The algorithm involves locally perturbing a constrained spline surface with white noise until the spline surface reaches an equilibrium state. In this paper, we introduce a fast generalized Gibbs sampler that combines two novel techniques, namely, a preconditioning technique in a wavelet basis for constraining the splines and a perturbation scheme in which, unlike the traditional Gibbs sampler, all sites (surface nodes) that do not share a common neighbor are updated simultaneously. In addition, we demonstrate the capability to generate arbitrary order fractal surfaces without resorting to blending techniques. Using this fast Gibbs sampler algorithm, we demonstrate the synthesis of realistic terrain models from sparse elevation data.

关键词： thin-plate-membrane splines fractal surfaces Gibbs sampler preconditioning wavelet basis conjugate gradient algorithm

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A new fast-lock, low-jitter, and all-digital frequency synthesizer for DVB-T receivers

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INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS 2015年第5期43卷 566-578页

作者： Gholami, Mohammad Rahimpour, Hamid Ardeshir, Gholamreza Miar-Naimi, Hossein Babol Noshirvani Univ Technol Babol Sar Iran

Lock time and convergence time are the most important challenges in delay-locked loops (DLLs). In this paper we cover French very high frequency band with a novel all-digital fast-lock DLL-based frequency synthesizer. Because this new architecture uses a digital signal processing unit instead of using phase frequency detector, charge pump, and loop filter in conventional DLL, therefore, it shows better jitter performance, lock time, and convergence speed than previous related works. Optimization methods are used to make input and output signals of the proposed DLL in phase. The proposed architecture is designed to cover all channels of French very high frequency band by choosing number of delay cells in signal path. Simulation has been done for 22-27 delay cells, and f(REF)=16MHz, which can produce output frequency in range of 176-216MHz. Locking time is approximately 0.3 mu s, which is equal to five clock cycles of reference clock. All of the simulation results show superiority of the proposed structure. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： delay locked loop (DLL) conjugate gradient algorithm optimization synthesizer

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Averaging complex subspaces via a Karcher mean approach

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SIGNAL PROCESSING 2013年第2期93卷 459-467页

作者： Hueper, K. Kleinsteuber, M. Shen, H. Tech Univ Munich Dept Elect Engn & Informat Technol D-80333 Munich Germany Univ Wurzburg Dept Math D-97074 Wurzburg Germany

We propose a conjugate gradient type optimization technique for the computation of the Karcher mean on the set of complex linear subspaces of fixed dimension, modeled by the so-called Grassmannian. The identification of the Grassmannian with Hermitian projection matrices allows an accessible introduction of the geometric concepts required for an intrinsic conjugate gradient method. In particular, proper definitions of geodesics, parallel transport, and the Riemannian gradient of the Karcher mean function are presented. We provide an efficient step-size selection for the special case of one dimensional complex subspaces and illustrate how the method can be employed for blind identification via numerical experiments. (C) 2012 Elsevier B.V. All rights reserved.

关键词： conjugate gradient algorithm Grassmannian Complex projective space Complex linear subspaces Karcher mean

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AN EFFICIENT PARALLEL DISCRETE PDE SOLVER

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PARALLEL COMPUTING 1995年第11期21卷 1725-1748页

作者： NOTAY, Y Service de Métrologie Nucléaire Université Libre de Bruxelles (C.P. 165) 50 Av. F.D. Roosevelt B-1050 Brussels Belgium

We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently developed parallelization technique to avoid communication bottle-neck for the computation associated to the internal boundary nodes. Numerical results are given for a transputer network with up to 512 processors and a few workstation cluster.

关键词： PARTIAL DIFFERENTIAL EQUATION conjugate gradient algorithm INCOMPLETE FACTORIZATION PRECONDITIONING DISTRIBUTED MEMORY MULTIPROCESSOR

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Scattered data approximation by regular grid weighted smoothing

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2018年第1期43卷 1-16页

作者： Francis, Bibin Viswanath, Sanjay Arigovindan, Muthuvel Indian Inst Sci Dept Elect Engn ISL Bangalore 560012 Karnataka India

Scattered data approximation refers to the computation of a multi-dimensional function from measurements obtained from scattered spatial locations. For this problem, the class of methods that adopt a roughness minimization are the best performing ones. These methods are called variational methods and they are capable of handling contrasting levels of sample density. These methods express the required solution as a continuous model containing a weighted sum of thin-plate spline or radial basis functions with centres aligned to the measurement locations, and the weights are specified by a linear system of equations. The main hurdle in this type of method is that the linear system is ill-conditioned. Further, getting the weights that are parameters of the continuous model representing the solution is only a part of the effort. Getting a regular grid image requires re-sampling of the continuous model, which is typically expensive. We develop a computationally efficient and numerically stable method based on roughness minimization. The method leads to an algorithm that uses standard regular grid array operations only, which makes it attractive for parallelization. We demonstrate experimentally that we get these computational advantages only with a little compromise in performance when compared with thin-plate spline methods.

关键词： Scattered data approximation variational reconstruction conjugate gradient algorithm multi-resolution approach thin-plate splines radial basis functions

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Enhancing k-Space Quantitative Susceptibility Mapping by Enforcing Consistency on the Cone Data (CCD) with Structural Priors

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MAGNETIC RESONANCE IN MEDICINE 2016年第2期75卷 823-830页

作者： Wen, Yan Wang, Yi Liu, Tian MedImageMetric LLC New York NY USA Cornell Univ Dept Biomed Engn Ithaca NY USA Cornell Univ Dept Radiol Weill Med Coll New York NY USA

Purpose: The inversion from the magnetic field to the magnetic susceptibility distribution is ill-posed because the dipole kernel, which relates the magnetic susceptibility to the magnetic field, has zeroes at a pair of cone surfaces in the k-space, leading to streaking artifacts on the reconstructed quantitative susceptibility maps (QSM). A method to impose consistency on the cone data (CCD) with structural priors is proposed to improve the solutions of k-space methods. Methods: The information in the cone region is recovered by enforcing structural consistency with structural prior, while information in the noncone trust region is enforced to be consistent with the magnetic field measurements in k-space. This CCD method was evaluated by comparing the initial results of existing QSM algorithms to the QSM results after CCD enhancement with respect to the COSMOS results in simulation, phantom, and in vivo human brain. Results: The proposed method demonstrated suppression of streaking artifacts and the resulting QSM showed better agreement with reference standard QSM compared with other k-space based methods. Conclusion: By enforcing consistency with structural priors in the cone region, the missing data in the cone can be recovered and the streaking artifacts in QSM can be suppressed. (C) 2015 Wiley Periodicals, Inc. Key words: quantitative susceptibility mapping;conjugate

关键词： quantitative susceptibility mapping conjugate gradient algorithm data fitting

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A new experimental device and inverse method to characterize thermal properties of composite phase change materials

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COMPOSITE STRUCTURES 2015年 133卷 1149-1159页

作者： Didier, Gossard Mustapha, Karkri Mariam, AlMaadeed A. Igor, Krupa Univ Paris Est CERTES F-94010 Creteil France Qatar Univ Ctr Adv Mat Doha 2713 Qatar

A new experimental device has been developed in order to characterize the phase change material (PCM) thermal properties (thermal conductivity k, sensible and latent heat thermal energy storage, c(p) and L-f) in the solid phase, during the solid-liquid transition and in the liquid phase. It allows to measure cylindrical samples of maximum 60 mm radius and 10 mm thick. A typical measurement consists in imposing a vertical temperature gradient through the PCM sample driven by a heat source, monitoring during the experiment time all the boundary conditions (temperatures and heat fluxes) and measuring temperature evolution in three locations within the PCM sample. In this work, we will focus only on the solid thermal conductivity characterization. These experiment data are used to solve the inverse heat conduction problem by applying the conjugate gradient method and finally, to determine the PCM thermal properties. Two types of composite PCM have been thermally characterized: paraffin mixed with synthetic graphite (Timrex SFG75) and paraffin mixed with graphite waste. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Composite PCMs (phase change materials) Thermal conductivity Sensible heat Latent heat Inverse problem conjugate gradient algorithm

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SHAPING OF SYSTEM RESPONSES WITH MINIMAX OPTIMIZATION IN THE TIME DOMAIN

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1993年第1期16卷 40-46页

作者： OHTSUKA, T FUJII, H Tokyo Metropolitan Institute of Technology Tokyo 191 Japan

A minimax problem is introduced for the terminal control of a generic dynamical system without disturbances. The maximum magnitude of the weighted output of the system is minimized over a finite interval by the control input of a prescribed class. Such important characteristics of the controlled system appear explicitly in the proposed problem as the maximum magnitude and settling property of the output. Two numerical examples are shown to illustrate the problem. A slewing experiment is also presented to demonstrate the application of the minimax optimal control.

关键词： Transversality Condition Control System Design Terminal Control Distributed Parameter System Bernoulli Euler Beams Vibration Suppression Feedback Control System Large Angle Maneuver Mathematical Models conjugate gradient algorithm

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