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Identifying a diffusion coefficient in a time-fractional diffusion equation

MATHEMATICS AND COMPUTERS IN SIMULATION 2018年 151卷 77-95页

作者： Wei, T. Li, Y. S. Lanzhou Univ Sch Math & Stat Lanzhou 730000 Gansu Peoples R China GanSu Polit Sci & Law Inst Sch Cyber Secur Lanzhou 730000 Gansu Peoples R China

In this paper, we propose a conjugate gradient algorithm for identifying a space-dependent diffusion coefficient in a time-fractional diffusion equation from the boundary Cauchy data in one-dimensional case. The existence and uniqueness of the solution for a weak form of the direct problem are obtained. The identification of diffusion coefficient is formulated into a variational problem by the Tikhonov-type regularization. The existence, stability and convergence of a minimizer for the variational problem approach to the exact diffusion coefficient are provided. We use a conjugate gradient method to solve the variational problem based on the deductions of a sensitive problem and an adjoint problem. We test three numerical examples and show the effectiveness of the proposed method. (C) 2018 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Inverse diffusion coefficient problem Fractional diffusion equation conjugate gradient algorithm

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COMPARISON OF STANDARD AND MATRIX-FREE IMPLEMENTATIONS OF SEVERAL NEWTON-KRYLOV SOLVERS

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AIAA JOURNAL 1994年第12期32卷 2394-2400页

作者： MCHUGH, PR KNOLL, DA LOCKHEED IDAHO TECHNOL CO IDAHO NATL ENGN UBDEPT ENGN ANALIDAHO FALLSID 83415

Fully coupled Newton's method is combined with conjugate gradient-like iterative algorithms to form inexact Newton-Krylov algorithms for solving the steady, incompressible, Navier-Stokes and energy equations in primitive variables. Finite volume differencing is employed using the power law convection-diffusion scheme on a uniform but staggered mesh. The well-known model problem of natural convection in an enclosed cavity is solved. Three conjugate gradient-like algorithms are selected from a class of algorithms based upon the Lanczos biorthogonalization procedure;namely, the conjugate gradients squared algorithm, the transpose-free quasi-minimal-residual algorithm, and a more smoothly convergent version of the biconjugate gradients algorithm. A fourth algorithm is based upon the Arnoldi process, namely the popular generalized minimal residual algorithm (GMRES). The performance of a standard inexact Newton's method implementation is compared with a matrix-free implementation. Results indicate that the performance of the matrix-free implementation is strongly dependent upon grid size (number of unknowns) and the selection of the conjugate gradient-like method. GMRES appeared to be superior to the Lanczos based algorithms within the context of a matrix-free implementation.

关键词： Newton's Method conjugate gradient algorithm Natural Convection conjugate gradient Method Continuity Equation Buoyancy Force Boussinesq Approximation Finite Difference Approximation Navier Stokes Equations Characteristic Velocity

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Uniformizing field distribution along optical axis for volume holographic data storage

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OPTICS COMMUNICATIONS 2001年第1-2期192卷 19-26页

作者： Yang, JW Wang, MR Univ Miami Dept Elect & Comp Engn Coral Gables FL 33124 USA

The conjugate gradient method is adopted to design one phase mask for each stored pattern to improve the uniformity of transverse and axial field distributions in recording medium volume for holographic data storage system. Simulation results demonstrate that almost constant field amplitude of the object beam can be obtained in the medium volume. The reconstruction error is found to be the lowest compared to that of using other types of masks or no masks. Using the phase mask allows effective use of the medium volume and its dynamic range and improves reconstruction performances of stored holograms. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： optical holographic data storage phase mask conjugate gradient algorithm

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Fast robust quasi-Newton algorithm for adaptive arrays

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IEE PROCEEDINGS-COMMUNICATIONS 1999年第4期146卷 231-239页

作者： Klemes, M Nortel Networks Dept R412 Microwave Radio Syst Dev Ottawa ON K1Y 4H7 Canada

A stable, fast (order-of-N) quasi-Newton (QN) algorithm (FRQN) applicable to arbitrary at-ray signals is presented. Its complexity is only twice that of the normalised least mean squares (NLMS) algorithm, yet its convergence is faster and smoother, proceeding along the optimal QN path as that of the order N-2 recursive least squares (RLS) algorithm, albeit more slowly. The development of its recursive update equation is outlined and compared to those of the NLMS and RLS algorithms, as well as variations of the conjugate gradient (CG) algorithm. Analytic expressions for its excess mean squared error in stationary and non-stationary scenarios are presented and compared with those of the LMS algorithm. Simulations of an adaptive array in a mobile wireless base-station show that the FRQN performance falls between that of the NLMS and RLS algorithms for a wide range of signal scenarios.

关键词： mean square error methods stable quasi-Newton algorithm normalised least mean squares adaptive signal processing computational complexity Antenna arrays radiofrequency interference mean squared error mobile wireless base-station array signals Signal processing and detection convergence recursive least squares algorithm recursive update equation Mobile radio systems nonstationary signals Electromagnetic compatibility and interference Newton method numerical stability complexity conjugate gradient algorithm NLMS algorithm interference cancellation land mobile radio Interpolation and function approximation (numerical analysis) adaptive antenna arrays digital adaptive array algorithm stationary signals fast robust quasi-Newton algorithm RLS algorithm interference suppression

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Inverse methodology to determine mold set-point temperature in resin transfer molding process

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2010年第11期49卷 2138-2147页

作者： Sobotka, Vincent Lefevre, Nicolas Jarny, Yvon Delaunay, Didier Nantes Atlantique Univ Ecole Polytech Univ Nantes Lab Thermocinet Nantes UMR CNRS 6607 F-44306 Nantes 03 France

This study consists of determining by inverse method the set-point temperature of the fluid flowing through heating plates in a Resin Transfer Molding (RIM) process tool so as to reach a predetermined thermal history in the composite part. Although the described methodology is applied in a specific mold in this paper, it remains general and may be transposed to a large scale of molding configuration. The considered mold is metallic and composed of several parts. Assembling these parts is not possible without introducing imperfect contacts that perturb heat transfer between them. The heat transfer at the interface is modeled by thermal contact resistances (TCR) whose values are unknown. In the case of metallic molds TCR are of the same order of magnitude than the equivalent thermal resistance of the mold. Therefore they cannot be neglected. The influence of these TCR is then a key-point on heat transfer since a bad knowledge of their values implies a wrong estimation of the temperature field. Then before being able to estimate the set-point of the temperature of the thermoregulated fluid, it is necessary in a first stage to evaluate the most influent TCR that are spatially and time dependent. Their determination is achieved by an optimization approach and carried out on a 2D transverse cut of the mold. Experimental temperature measurements in the mold are matched to the computed responses of the heat conduction model. A least square criterion is minimized by using the conjugate gradient algorithm. The gradient of the criterion is determined by solving a set of adjoint equations. After the identification of these parameters, the same optimization method is used to compute the mold set point temperature. It is notable that the same set of adjoint equations is used to solve both problems. (C) 2010 Elsevier Masson SAS. All rights reserved.

关键词： Resin transfer molding Inverse method Adjoint problem Composite material Two dimensional heat transfer Parameter estimation conjugate gradient algorithm Thermal control

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Estimation of dynamic origin-destination trip tables for a general network

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2001年第3期35卷 217-235页

作者： Sherali, HD Park, T Virginia Polytech Inst & State Univ Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA

In this paper, we propose a parametric optimization approach to estimate time-dependent path flows, or origin-destination (OD) trip tables, using available data on link traffic volumes for a general road network. Our model assumes knowledge of certain time-dependent link flow contribution factors that are a dynamic generalization of the path-link incidence matrix for the static case. A least squares model is accordingly formulated to determine the time-dependent trip tables. We develop a column generation approach that uses a sequence of dynamic shortest path subproblems in order to solve this problem. Computational results are presented on several variants of two sample test networks from the literature. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： dynamic origin-destination trip tables time-dependent flows column generation approach conjugate gradient algorithm

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Mixed L²-Wasserstein optimal mapping between prescribed density functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2001年第2期111卷 255-271页

作者： Benamou, JD Brenier, Y INRIA Le Chesnay France Univ Paris 06 Anal Numer Lab F-75252 Paris France

A time-dependent minimization problem for the computation of a mixed L-2-Wasserstein distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal mapping between prescribed initial and final densities. We enforce the final density conditions through a penalization term added to our cost function. A conjugate gradient method is used to solve this relaxed problem. We obtain an algorithm which computes an interpolated L-2-Wasserstein distance between two densities and the corresponding optimal mapping.

关键词： Monge-Kantorovitch mass transfer problem Wasserstein distance least-square distance optimal control conjugate gradient algorithm

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UNIFIED FORMULATION OF DYNAMICS FOR SERIAL RIGID MULTIBODY SYSTEMS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1991年第3期14卷 531-542页

作者： JAIN, A JPL Pasadena CA

There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix.

关键词： Multibody Dynamics conjugate gradient algorithm Computing Kalman Filter conjugate gradient Method D'Alembert's Principle Euler Equations Boundary Value Problems Gaussian Elimination Lyapunov Equation

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An adaptive nonmonotone active set - weight constrained - neural network training algorithm

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NEUROCOMPUTING 2019年 360卷 294-303页

作者： Livieris, Ioannis E. Pintelas, Panagiotis Univ Patras Dept Math GR-26500 Patras Greece

In this work, a new direction for improving the classification accuracy of artificial neural networks is proposed by bounding the weights of the network, during the training process. Furthermore, a new adaptive nonmonotone active set - weight constrained - neural network training algorithm is proposed in order to demonstrate the efficacy and efficiency of our approach. The proposed training algorithm consists of two phases: a gradient projection phase which utilizes an adaptive nonmonotone line search and an unconstrained optimization phase which exploits the box structure of the bounds. Also, a set of switching criteria is defined for efficiently switching between the two phases. Our preliminary numerical experiments illustrate that the classification efficiency of the proposed algorithm outperforms classical neural network training algorithms, providing empirical evidence that it provides more stable, efficient and reliable learning. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Artificial neural networks Constrained optimization Weight bounds ASA method conjugate gradient algorithm Accuracy

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Neural Volterra filter for chaotic time series prediction

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CHINESE PHYSICS 2005年第11期14卷 2181-2188页

作者： Li, HC Zhang, JS Xiao, XC SW Jiaotong Univ Sichuan Prov Key Lab Signal & Informat Proc Chengdu 610031 Peoples R China Univ Elect Sci & Technol China Dept Elect Engn Chengdu 610054 Peoples R China

A new second-order neural Volterra filter (SONVF) with conjugate gradient (CG) algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system in this paper, where the neuron activation functions are introduced to constraint Volterra series terms for improving the nonlinear approximation of second-order Volterra filter (SOVF). The SONVF with CG algorithm improves the accuracy of prediction without increasing the computation complexity. Meanwhile, the difficulty of neuron number determination does not exist here. Experimental results show that the proposed filter can predict chaotic time series effectively, and one-step and multi-step prediction performances are obviously superior to those of SOVF, which demonstrate that the proposed SONVF is feasible and effective.

关键词： chaotic time series adaptive neural Volterra filter conjugate gradient algorithm

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