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Geometrical shape optimization in fluid mechanics using FreeFem plus

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2018年第6期58卷 2761-2788页

作者： Dapogny, Charles Frey, Pascal Omnes, Florian Privat, Yannick Univ Grenoble Alpes CNRS Grenoble INP LJK F-38000 Grenoble France UPMC Univ Paris 06 Sorbonne Univ CNRS Lab Jacques Louis LionsUMR 7598 F-75005 Paris France UPMC Univ Paris 06 Sorbonne Univ ISCD F-75005 Paris France

In this article, we present simple and robust numerical methods for two-dimensional geometrical shape optimization problems, in the context of viscous flows driven by the stationary Navier-Stokes equations at low Reynolds number. The salient features of our algorithm are exposed with an educational purpose;in particular, the numerical resolution of the nonlinear stationary Navier-Stokes system, the Hadamard boundary variation method for calculating the sensitivity of the minimized function of the domain, and the mesh update strategy are carefully described. Several pedagogical examples are discussed. The corresponding program is written in the FreeFem++ environment, and it is freely available. Its chief features-and notably the implementation details of the main steps of our algorithm-are carefully presented, so that it can easily be handled and elaborated upon to deal with different, or more complex physical situations.

关键词： Shape optimization Shape sensitivity Fluid mechanics Educational article numerical algorithm

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On algorithmic Coxeter spectral analysis of positive posets

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APPLIED MATHEMATICS AND COMPUTATION 2020年 386卷 125507-125507页

作者： Gasiorek, Marcin Nicolaus Copernicus Univ Fac Math & Comp Sci Ul Chopina 12-18 PL-87100 Torun Poland

Following a general framework of Coxeter spectral analysis of signed graphs Delta and finite posets I introduced by Simson (SIAM J. Discrete Math. 27:827-854, 2013) we present efficient numerical algorithms for the Coxeter spectral study of finite posets I = ({1,..., n}, <= I) that are positive in the sense that the symmetric Gram matrix G(I) := 1/2 (C-I + C-I(tr)) is an element of M-n (Q) is positive definite, where C-I is an element of M-n(Z) is the incidence matrix of I encoding the relation <= I. In the framework of scientific computing we present a complete Coxeter spectral classification of finite positive posets I of size n = vertical bar I vertical bar < 20. It extends one of the main results obtained in Gasiorek et al. (Eur. J. Comb. 48:127-142, 2015) for posets of size n <= 10. We also show that the connectivity of such posets I is determined by the complex Coxeter spectrum specc I subset of C;equivalently, by the Coxeter polynomial cox(I) (t) is an element of Z[t] od I. One of the main results of the paper is a new technique to compute in a polynomial time a Z-invertible matrix B-I is an element of M-n (Z) such that B-I(tr) center dot C-I center dot B-I = G(DI), where. G(D) is an element of M-n (Z) is a nonsymmetric Gram matrix of a simply-laced Dynkin diagram D-I is an element of {A(n), D-n, E-6, E-7, E-8} associated with a finite positive poset I. (c) 2020 Elsevier Inc. All rights reserved.

关键词： positive poset edge-bipartite graph spectral graph theory Dynkin type Coxeter spectrum numerical algorithm

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Extended Barton-Bandis model for rock joints under cyclic loading: Formulation and implicit algorithm

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INTERNATIONAL JOURNAL FOR numerical AND ANALYTICAL METHODS IN GEOMECHANICS 2023年第3期47卷 349-369页

作者： Fei, Fan Choo, Jinhyun Lawrence Livermore Natl Lab Atmospher Earth & Energy Div Livermore CA 94550 USA Korea Adv Inst Sci & Technol Dept Civil & Environm Engn Daejeon South Korea

In this paper, the Barton-Bandis model for rock joints is extended to cyclic loading conditions, without any new material parameter. Also developed herein is an implicit solution algorithm for the extended Barton-Bandis model, which can also be used for the original Barton-Bandis model for which an implicit algorithm has been unavailable. To this end, we first cast the Barton-Bandis model into an incremental elasto-plastic framework, deriving an expression for the elastic shear stiffness being consistent with the original model formulation. We then extend the model formulation to cyclic loading conditions, incorporating the dependence of shear stress and dilation on the joint position and the shearing direction. The extension is achieved by introducing a few state-dependent variables which can be calculated with the existing material parameters. For robust and accurate utilization of the model, we also develop an implicit algorithm based on return mapping, which is unconditionally stable and guarantees the satisfaction of the strength criterion. We verify that the proposed model formulation and algorithm produce virtually the same results as the original Barton-Bandis model under monotonic shearing conditions. We then validate the extended Barton-Bandis model against experimental data on natural rock joints under cycling loading conditions. The present work thus enables the Barton-Bandis model, which has been exceptionally popular in research and practice, to be applicable to a wider range of problems in rock mechanics and rock engineering.

关键词： constitutive model cyclic loading implicit method numerical algorithm rock joints

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Multi-loop PI/PID controllers design for disturbance rejection based on non-parametric effective model and non-convex optimisation

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IET CONTROL THEORY AND APPLICATIONS 2014年第15期8卷 1499-1512页

作者： Jin, Qibing Liu, Qie Beijing Univ Chem Technol Coll Informat Sci & Technol Inst Automat Beijing 100029 Peoples R China

In this study, the authors address the design of the multi-loop controllers for multi-input and multi-output (MIMO) processes for disturbance rejection. Three types of disturbance rejection are analysed, and they demonstrate that those disturbance responses are directly related to the integral terms of the controllers. A concept of non-parametric effective model is introduced here to decompose a MIMO control system into several equivalent single-input and single-output control systems. Based on the effective model in each loop, a non-convex optimisation problem is established to obtain the optimal controller parameters with certain robustness indices. Considering the drawbacks of using random search algorithm, they develop a numerical algorithm to solve this non-convex optimisation problem. Simulation studies demonstrate that the proposed method improves the disturbance rejection compared with other decentralised controllers.

关键词： MIMO systems three-term control PI control control system synthesis concave programming optimal control search problems numerical analysis multiloop PI-PID controllers design disturbance rejection nonparametric effective model multi-input and multi-output processes disturbance responses MIMO control system nonconvex optimisation problem equivalent single-input and single-output control systems optimal controller parameters certain robustness indices random search algorithm numerical algorithm decentralised controllers

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Inverse design of indoor environment using an adjoint RNG k-ε turbulence model

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INDOOR AIR 2019年第2期29卷 320-330页

作者： Zhao, Xingwang Chen, Qingyan Tianjin Univ Sch Environm Sci & Engn Tianjin Key Lab Indoor Air Environm Qual Control Tianjin Peoples R China Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA

The adjoint method can determine design variables of an indoor environment according to the optimal design objective, such as minimal predicted mean vote (PMV) for thermal comfort. The method calculates the gradient of the objective function over the design variables so that the objective function can be minimized along the fastest direction using an optimization algorithm. Since the objective function is controlled by the Reynolds-averaged Navier-Stokes (RANS) equations with the RNG k-epsilon model during the optimization process, all the corresponding adjoint equations should be solved, rather than the "frozen turbulence" assumption used in previous studies. This investigation developed adjoint equations for the RNG k-epsilon turbulence model and applied it to a two-dimensional ventilated cavity and a three-dimensional, two-person office. Design processes with the adjoint RNG k-epsilon turbulence model led to a near-zero design function for the two cases, while those with the "frozen turbulence" assumption did not. This investigation has successfully used the new method to design a two-person office with optimal thermal comfort level around the two occupants.

关键词： adjoint method indoor environment inverse design numerical algorithm turbulence model validation

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An effective analytical-algorithmic approach to solve diffusion-type differential equations with non-linear sources: Unbounded domains

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COMPUTERS & CHEMICAL ENGINEERING 2007年第9期31卷 1174-1180页

作者： Oyanader, Mario Arce, Pedro Tennessee Technol Univ Cookeville TN 38505 USA Univ Catolica Norte Chem & Environm Engn Dept Antofagasta Chile

Many technological applications need of differential models either for their microscopic or macroscopic description and, frequently, they involve non-linear equations. There is a class of differential models that is the diffusive-reaction type models that have a very large number of applications in different chemical engineering problems. These include transport and reaction in catalytic processes, heat and mass transfer in more than one phase, and electrostatic potentials in many current electrokinetic processes, just to name a few. Solutions to these models are either by linear approximations of the non-linear source, by other approximations of such non-linearity, or by numerical methods that frequently are heavily dependent of the mesh size for a successful convergence. In this contribution, an analytical-logarithmic approach is introduced and applied to unbounded domains of a rectangular, cylindrical, and spherical geometry for the case of electrostatic potential around a particle or an electrode in a given solution. Due to the lack of general methods to derive analytical solutions for differential models with non-linear sources, this study has focused on developing an efficient and economical procedure to obtain a formal analytical solution for such models that is used in a simple predictor-corrector approach to predict the correct solution. The proposed method involves the use of a recursive function,integral(AO), of the non-linear dependable variable that work as a corrector function. The procedure converts the non-linear ordinary differential equation in a simpler pseudo-linear ordinary differential equation whose analytical solution is later modified by means of the integral(AO) correction function to obtain the correct solution. The start of the algorithmic approach uses the case of integral(AO) = 1, that is the "true" solution to the linear approximation. Afterwards, the correction function is updated until convergence to the solution of the original non-

关键词： non-linear differential equations numerical algorithm correction function Poisson-Boltzmann equation

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The α-path of multi-dimensional uncertain differential equations and its applications

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2024年第2期46卷 4761-4776页

作者： Wang, Xiaoli Wang, Chongguo Shi, Gang Xinjiang Univ Sch Comp Sci & Technol Urumqi 830046 Peoples R China

As a complex uncertain differential equation, how to solve the multi-dimensional uncertain differential equation is a complicated and difficult problem. This paper will be devoted to the a-path of some special multi-dimensional uncertain differential equations, namely, multi-factor uncertain differential equations, nested uncertain differential equations and multifactor nested uncertain differential equations. The alpha psi-path method is used to study the numerical solution problems of the above three special multi-dimensional uncertain differential equations. At the same time, the inverse uncertainty distributions and expected values of these three special multi-dimensional uncertain differential equations are also obtained. At last, the numerical algorithm examples are given to verify it.

关键词： Uncertainty theory multi-dimensional uncertain differential equation alpha-path numerical algorithm

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DYNAMIC PERFORMANCE ANALYSIS OF RELUCTANCE MOTORS USING DAMPING AND SYNCHRONIZING TORQUES

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IEE PROCEEDINGS-B ELECTRIC POWER APPLICATIONS 1990年第4期137卷 231-238页

作者： OSHEBA, SM ABDELKADER, FM SUEZ CANAL UNIV FAC ENGN DEPT ELECT POWER & MACHINES PORT SAID EGYPT

The paper analyses the dynamic performance of polyphase reluctance motors using damping and synchronising torques. A numerical algorithm has been applied to obtain these torque components in the time domain using detailed nonlinear models of reluctance motors. The effects of all electrical motor parameters have been examined and the optimum values of parameters, which give maximum damping of hunting oscillations, have been obtained. It has also been demonstrated that these optimum parameters substantially improve the dynamic performance of reluctance motors. The presented results form a guide to the production of reluctance motors with well-damped oscillations and improved dynamic performance.

关键词： torque electrical motor parameters numerical algorithm time-domain analysis Synchronous machines transient response damping nonlinear models well-damped oscillations reluctance motors time domain synchronising torques hunting oscillations dynamic performance polyphase reluctance motors machine theory

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Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems

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APPLIED MATHEMATICS LETTERS 2014年 29卷 36-41页

作者： Wang, Cheng Tang, Tao Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

This letter deals with the identification problem of a class of linear-in-parameters output error moving average systems. The difficulty of identification is that there exist some unknown variables in the information vector. By means of the auxiliary model identification idea, an auxiliary model based recursive least squares algorithm is developed for identifying the parameters of the proposed system. The simulation results confirm the conclusion. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： numerical algorithm Least squares Parameter estimation Recursive identification Linear-in-parameters model Dynamic system

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WIGGLE: A new constrained molecular dynamics algorithm in Cartesian coordinates

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JOURNAL OF COMPUTATIONAL PHYSICS 2005年第1期210卷 171-182页

作者： Lee, SH Palmo, K Krimm, S Univ Michigan Div Biophys Res Ann Arbor MI 48109 USA Univ Michigan Dept Phys Ann Arbor MI 48109 USA

The theory of conventional constrained molecular dynamics (MD) simulations is reexamined based on a projection operator approach. A new algorithm, named WIGGLE, is presented for MD simulations with internal constraints. At each time step, the algorithm utilizes the constrained accelerations derived from velocity adjustments to satisfy the hidden constraints, and provides both initial and final constrained values that are almost an order of magnitude closer to the desired values than does RATTLE. Its performance is compared with those of RATTLE and SHAKE for an octane molecule. Also presented are a formalism to additionally constrain the angular momentum about the center of mass and an expression for the local energy drift during each integration time step. (c) 2005 Elsevier Inc. All rights reserved.

关键词： molecular dynamics constrained dynamics WIGGLE SHAKE RATTLE angular momentum numerical integration numerical algorithm computer simulation

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