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The multiblock method.: A new strategy based on domain decomposition for the solution of wave propagation problems

INTERNATIONAL JOURNAL FOR numerical METHODS IN ENGINEERING 2000年第11期49卷 1353-1376页

作者： Serón, FJ Sabadell, FJ Univ Zaragoza Ctr Politecn Super Dept Comp Sci E-50015 Zaragoza Spain Univ Zaragoza Seismol Grp E-50009 Zaragoza Spain

A novel single-step domain decomposition technique for the elastic wave propagation problem is introduced in this paper, based on the Huygens principle. The method allows an effective and efficient implementation on parallel computers through coarse-grain multiprocessor computations. The various tests and numerical examples let infer that it is very competitive in comparison with classic substructuring techniques, specially for implicit discretization schemes. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： parallelism elastic wave propagation domain decomposition numerical algorithms

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REAL-TIME SIMULATION OF POWER-SYSTEM STABILITY USING PARALLEL DIGITAL SIGNAL PROCESSORS

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MATHEMATICS AND COMPUTERS IN SIMULATION 1995年第4-6期38卷 283-292页

作者： LAVOIE, M QUEDO, V HOULE, JL DAVIDSON, J INST RECH HYDRO QUEBEC VARENNESPQ J3X 1S1CANADA ECOLE POLYTECH MONTREAL MONTREALPQCANADA UNIV QUEBEC MONTREALPQ H2T 2C8CANADA

An electrical power system usually includes machines with their regulators and controls linked through power lines, transformers, capacitor banks, reactors, and loads. In stability analysis, two distinct strategies are possible for solving the differential equations and network equations describing such a system: a simultaneous approach and a partitioned approach. For real-time numerical simulation, the partitioned approach is easier to distribute over parallel processors [2,11] and is therefore more appropriate in this case. In order to demonstrate the feasibility of the real-time simulation of power system stability, this paper presents an implementation of the partitioned approach using parallel digital signal processors (DSP). A network of typical size consisting of 8 machines and 50 buses is simulated. The synchronous machine model has been developed using the block diagram implementation technique. Two algorithms applied to the solution of the network algebraic equations are described and their performances are evaluated on different processors.

关键词： numerical algorithms PARALLEL PROCESSING REAL-TIME SIMULATION TRANSIENT STABILITY numerical STABILITY DIGITAL SIGNAL PROCESSORS

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Convex Approach to Covariance Control with Application to Stochastic Low-Thrust Trajectory Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2022年第11期45卷 2061-2075页

作者： Benedikter, Boris Zavoli, Alessandro Wang, Zhenbo Pizzurro, Simone Cavallini, Enrico Sapienza Univ Rome Dept Mech & Aerosp Engn Via Eudossiana 18 I-00184 Rome Italy Univ Tennessee Dept Mech Aerosp & Biomed Engn Knoxville TN 37996 USA Italian Space Agcy Space Transportat Space Infrastruct & Inorbit Serv Via Politecn snc I-00133 Rome Italy Italian Space Agcy Space Transportat Space Infrastruct & Inorbit Serv Space Transportat Programs Off Via Politecn snc I-00133 Rome Italy

This paper outlines a novel approach to the design of optimal space trajectories under significant uncertainty. Finite-horizon covariance control, i.e., the steering of a system from an initial probability distribution to a desired one at a prescribed time, is employed to plan an optimal nominal path along with a robust feedback controller that compensates for exogenous in-flight disturbances. A mindful convexification strategy is devised to recast the nonlinear covariance control problem as a deterministic convex optimization problem. The convexification is based on a convenient change of variables that allows for relaxing the covariance matrix discrete-time propagation into a set of semidefinite cone constraints. While featuring a larger feasible space, the relaxed problem shares the same optimal solution as the original one. The lossless property of the relaxation is analytically proven by leveraging optimal control theory and discussed on the basis of numerical experiments. Monte Carlo campaigns are carried out to validate the in-flight performance of the attained control policies.

关键词： Trajectory Optimization Thrust Probability Distribution numerical Optimization Flight Performance Linear Quadratic Regulator numerical algorithms Rockets Stochastic Optimization Powered Descent Guidance

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A variational formulation for nonlocal damage models

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INTERNATIONAL JOURNAL OF PLASTICITY 1999年第2期15卷 119-138页

作者： Lorentz, E Andrieux, S Elect France Direct Etud & Rech F-92141 Clamart France Lab Mecan & Technol Cachan F-94235 Cachan France

To control localization phenomena exhibited by strain softening constitutive relations, several issues have been proposed by various authors, based on spatial regularization. In this paper, we define a variational framework, thought to encompass some of these issues: the constitutive relations are written at the structural scale and become minimization problems. Such a framework is not only well-suited to the mathematical study of the boundary value problem, but also leads in a natural way to an efficient numerical algorithm. The formulation is first presented, then applied to several classes of models existing in the literature : a homogenization-based constitutive relation, a porosity model and gradient plasticity. Besides the higher degree of generality confered by the formulation, it will be shown that several proper ties can be obtained for these models. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： fracture constitutive behaviour energy methods numerical algorithms

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Fast Symbolic 3-D Registration Solution

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2020年第2期17卷 761-770页

作者： Wu, Jin Liu, Ming Zhou, Zebo Li, Rui Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong Peoples R China Univ Elect Sci & Technol China Chengdu 611731 Peoples R China

3-D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases. A novel fast symbolic solution is proposed in this article by following our recent publication in this journal. The equivalence analysis shows that our previous solver can be converted to deal with the 3-D registration problem. Rather, the computation procedure is studied for further simplification of computing without complex-number support. Experimental results show that the proposed solver does not loose accuracy and robustness but improves the execution speed to a large extent by almost 50%-80%, on both a personal computer (PC) and an embedded processor. Note to Practitioners-3-D registration usually has a large computational burden in engineering tasks. The proposed symbolic solution can directly solve the eigenvalue and its associated eigenvector. A lot of computation resources can then be saved for better overall system performance. The deterministic behavior of the proposed solver also ensures long-endurance stability and can help an engineer better design thread timing logic.

关键词： Quaternions Eigenvalues and eigenfunctions Estimation Position measurement Microcomputers Robots Integrated circuits 3-D registration fast computation speed numerical algorithms robotics symbolic computation

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Finite strain mean-field homogenization of composite materials with hyperelastic-plastic constituents

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INTERNATIONAL JOURNAL OF PLASTICITY 2016年 81卷 40-62页

作者： Doghri, I. El Ghezal, M. I. Adam, L. UCL iMMC Batiment Euler4 Ave G Lemaitre B-1348 Louvain La Neuve Belgium E Xstream Engn Axis Parc Bldg H9 Rue Emile Francqui B-1435 Mont St Guibert Belgium

A finite strain mean-field homogenization (MFH) formulation is proposed for a class of composites where multiple phases of solid inclusions or cavities are embedded in a continuum matrix. Local constitutive equations of each solid phase are based on a multiplicative decomposition of the deformation gradient onto elastic and inelastic parts and hyperelastic-plastic stress-strain relations. For the special situation of hyperelastic constituents, a mixed variational formulation is presented which handles both compressible and quasi-incompressible cases within the same framework. A special emphasis is put on the proper definition of various macroscopic stress measures and tangent operators. For an extended Mori-Tanaka MFH model, numerical algorithms were developed and implemented. The MFH predictions were extensively tested against direct finite element simulations of representative volume elements or unit cells, for several heterogeneous microstructures under various loadings. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Microstructures Finite strain Inhomogeneous material Elastic-plastic material numerical algorithms

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Application of large-eddy simulation to supersonic compression ramps

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AIAA JOURNAL 2002年第8期40卷 1574-1581页

作者： Rizzetta, DP Visbal, MR USAF Res Lab Computat Sci Branch Aeronaut Sci Div Wright Patterson AFB OH 45433 USA

Large-eddy simulations of supersonic compression-ramp flowfields were performed by a high-order numerical method, utilizing the Smagorinsky dynamic subgrid-scale model to account for spatially underresolved stresses. Computations were carried out at a freestream Mach number of 3.0 for ramp angles of 8, 16, 20, and 24 deg. Extensive comparisons are made between the respective solutions and available experimental data that were collected at higher Reynolds numbers. These include surface pressure, skin friction, and both mean and fluctuating velocity profiles. For the 24-deg case, a number of experimentally measured statistical quantities are compared to the simulation.

关键词： Direct numerical Simulation Freestream Mach Number Skin Friction Reynolds Averaged Navier Stokes Kinetic Energy Boundary Layer Thickness Compressibility Effect numerical algorithms Turbulence Models Vortex Breakdown

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Allocating non-real-time and soft real-time jobs in multiclusters

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2006年第2期17卷 99-112页

作者： He, LG Jarvis, SA Spooner, DP Jiang, H Dillenberger, DN Nudd, GR Univ Warwick Dept Comp Sci Coventry CV4 7AL W Midlands England Univ Nebraska Dept Comp Sci & Engn Lincoln NE 68588 USA IBM Corp TJ Watson Res Ctr Yorktown Hts NY 10598 USA

This paper addresses workload allocation techniques for two types of sequential jobs that might be found in multicluster systems, namely, non-real-time jobs and soft real-time jobs. Two workload allocation strategies, the Optimized mean Response Time (ORT) and the Optimized mean Miss Rate (OMR), are developed by establishing and numerically solving two optimization equation sets. The ORT strategy achieves an optimized mean response time for non-real-time jobs, while the OMR strategy obtains an optimized mean miss rate for soft real-time jobs over multiple clusters. Both strategies take into account average system behaviors (such as the mean arrival rate of jobs) in calculating the workload proportions for individual clusters and the workload allocation is updated dynamically when the change in the mean arrival rate reaches a certain threshold. The effectiveness of both strategies is demonstrated through theoretical analysis. These strategies are also evaluated through extensive experimental studies and the results show that when compared with traditional strategies, the proposed workload allocation schemes significantly improve the performance of job scheduling in multiclusters, both in terms of the mean response time (for non-real-time jobs) and the mean miss rate (for soft real-time jobs).

关键词： scheduling parallel systems distributed systems real-time systems numerical algorithms

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numerically efficient robustness analysis of trajectory tracking for nonlinear systems

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1997年第4期20卷 640-647页

作者： Tierno, JE Murray, RM Doyle, JC Gregory, IM CALTECH PASADENACA 91125 NASA LANGLEY RES CTRDEPT FLIGHT DYNAM & CONTROLHAMPTONVA 23681

A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems that follow a prescribed trajectory, This algorithm provides a computationally efficient means of evaluating the performance of a nonlinear system in the presence of noise, real parametric uncertainty, and unmodeled dynamics, The algorithm is similar in nature and behavior to the power algorithm for the structured singular value (mu) lower bound and does not rely on a descent method, The algorithm is tested on a Eight control example.

关键词： Mathematical Models Computing numerical algorithms Monte Carlo Simulation Aeroplane Linear Time Invariant Ailerons Computing Structures Boundary Value Problems Iterative Algorithm

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Projection-free parallel quadratic programming for linear model predictive control

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INTERNATIONAL JOURNAL OF CONTROL 2013年第8期86卷 1367-1385页

作者： Di Cairano, S. Brand, M. Bortoff, S. A. Mitsubishi Elect Res Labs Cambridge MA USA

A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace, and factory automation is the availability of low-complexity fast optimisation algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper, we introduce a projection-free iterative optimisation algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimised by pre-computing the matrices in a parametric form. We show computational results of the algorithm in three common case studies and we compare such results with the results obtained by other available free and commercial QP solvers.

关键词： model predictive control optimisation numerical algorithms constrained control

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