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The Gauss-Seidel numerical procedure for Markov stochastic games

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2004年第10期49卷 1779-1782页

作者： Kushner, HJ Brown Univ Dept Appl Math Lefschetz Ctr Dynam Syst Providence RI 02912 USA

Consider the problem of value iteration for solving Markov stochastic games. One simply iterates backward, via a Jacobi-like procedure. The convergence of the Gauss-Seidel form of this procedure is shown for both the discounted and ergodic cost problems, under appropriate conditions, with extensions to problems where one stops when a boundary is hit or if any one of the players chooses to stop, with associated costs. Generally, the Gauss-Seidel procedure accelerates convergence.

关键词： Gauss-Seidel procedure Markov games numerical algorithms stochastic games

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A general approach to waveform relaxation solutions of nonlinear differential-algebraic equations: The continuous-time and discrete-time cases

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2004年第9期51卷 1770-1780页

作者： Jiang, YL Xi An Jiao Tong Univ Inst Informat & Syst Sci Sch Sci Xian 710049 Peoples R China

For a general class of nonlinear differential-algebraic equations of index one, we develop and unify a convergence theory on waveform relaxation (WR). Convergence conditions are achieved for the cases of continuous-time and discrete-time WR approximations. Most of known convergence results in this field can be easily derived from the new theory established here.

关键词： continuous-time and discrete-time waveform relaxation (WR) iterations convergence conditions circuit simulation differential-algebraic equations (DAEs) numerical algorithms WR

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Sound generation by vortex pairing in subsonic axisymmetric jets

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AIAA JOURNAL 2004年第2期42卷 241-248页

作者： Jiang, X Avital, EJ Luo, KH Univ London Queen Mary & Westfield Coll Dept Engn London E1 4NS England

Direct numerical simulation (DNS) and an acoustic analogy are used to investigate the sound generation by vortex pairing in idealized subsonic axisymmetric jets. The detailed sound source structure is provided by the DNS. The acoustic analogy is based on solving the nonlinearized Lilley's third-order wave equation in the time-space domain. A numerical algorithm for solving Lilley's equation is developed, in which the sound field is simulated simultaneously with the source field calculation. The computational domain includes both the near field and a portion of the acoustic far field. Effects of a coaxial secondary jet stream and the jet-to-ambient temperature ratio on the sound generation from an axisymmetric jet are investigated. It is shown that the sound source has a long axial distribution in the streamwise direction with the strongest source located near the end of the jet potential core where vortex pairing/merging occurs, and the radiated sound field is highly directive. It is also found that the secondary jet stream reduces the sound source size;therefore, the sound radiation from the coaxial jets is lower than that from the single jet. The hot jet simulation shows that increasing the jet-to-ambient temperature ratio leads to a smaller and weaker sound source, but does not lead to a weaker sound field. For the sound field a reasonable agreement is observed between the predictions from the axisymmetric Lilley's equation and the DNS results.

关键词： Vortex Breakdown Direct numerical Simulation Jet Stream Temperature Ratio numerical algorithms Shear Layers Conservation of Mass Velocity Profiles Subsonic Jet Axisymmetric Flow

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Convex plastic potentials of fourth and sixth rank for anisotropic materials

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INTERNATIONAL JOURNAL OF PLASTICITY 2004年第8-9期20卷 1505-1524页

作者： Van Houtte, P Van Bael, A Katholieke Univ Leuven Dept MTM B-3001 Heverlee Belgium

It is briefly reminded how the theory of dual plastic potentials has been used in the past to generate analytical expressions for plastic potentials of anisotropic polycrystalline materials with a known crystallographic texture. Such constitutive models are fairly general, and the identification of their parameters can readily be done on the basis of data obtained from a texture measurement. As a result, they are suitable for engineering applications such as elasticplastic finite element models for forming processes. However, the yield loci generated in this way are not automatically convex. Therefore, a new variant of the method has now been developed, which preserves the advantages of the old method, but for which convexity can at least been tested by means of a mathematical criterion. In addition, it has turned out to be possible to slightly modify plastic potentials which do not satisfy the criterion, in order to achieve convexity. An example of a plastic potential modified in this way is discussed. After modification, it was still a good analytical approximation of the plastic potential directly derived from the Taylor-Bishop-Hill theory on the basis of the crystallographic texture of the material. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： anisotropic material polycrystalline material analytic functions finite elements numerical algorithms

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An evaluation of the self-determined probability-weighted moment method for estimating extreme wind speeds

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JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS 2004年第3-4期92卷 219-239页

作者： Whalen, TM Savage, GT Jeong, GD Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA

For the estimation of probability distribution parameters, the method of self-determined probability-weighted moments (SD-PWM) has previously been introduced as a refinement on the original method of probability-weighted moments (PWM). Tables have been created summarizing the solution of the relevant equations for certain probability distributions, but application of these is awkward. In addition, certain associated algorithms are difficult to interpret and contain formulations that do not appear to properly enforce the definitions of self-determined probability-weighted moments. Therefore, new algorithms have been developed to both clarify and simplify the determination of SD-PWM parameter estimates. As an application of the SD-PWM algorithms, the estimation of extreme wind speeds is considered using the Gumbel and generalized extreme value (GEV) distributions. The estimation results are compared to similar results obtained via PWM, the method of moments and the maximum likelihood method. The analyses suggest SD-PWM may be a reasonable tool for analyzing the ability of a particular distribution to describe a sample. Relative to the method of moments and PWM estimates, the SD-PWM estimates compare well based on fits of the cumulative distributions. While the SD-PWM estimates exhibit increased variability relative to the method of moment (MOM) estimates, SD-PWM wind speed estimates are generally conservative relative to the MOM estimates. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： self-determined probability-weighted moments extreme wind speeds parameter estimation numerical algorithms extreme value analysis

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On data distributions in the construction of parallel programs

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JOURNAL OF SUPERCOMPUTING 2004年第1期29卷 5-25页

作者： Niculescu, V Univ Babes Bolyai Dept Comp Sci R-3400 Cluj Napoca Romania

Data distributions have a serious impact on time complexity of parallel programs, developed based on domain decomposition. A new kind of distributions-set distributions, based on set-valued mappings, is introduced. These distributions assign a data object to more than one process. The set distributions can be used especially when the number of processes is greater than the data input size, but, sometimes using set distributions can lead to efficient general parallel algorithms. The work-load properties of these distributions and their impact on the number of communications are discussed. In order to illustrate the implications of data distributions in the construction of parallel programs, some examples are presented. Two parallel algorithms for computation of Lagrange interpolation polynomial are developed, starting from simple distributions and set distributions.

关键词： parallel computation distribution complexity correctness numerical algorithms

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On a finite strain viscoplastic theory based on a new internal dissipation inequality

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INTERNATIONAL JOURNAL OF PLASTICITY 2004年第7期20卷 1281-1311页

作者： Lin, RC Brocks, W GKSS Forschungszentrum Geesthacht GmbH Inst Mat Res D-21502 Geesthacht Germany

This work is focused on the theoretical development and numerical implementation of a viscoplastic law. According to the second law of thermodynamics a dissipation inequality described in the rotated material coordinate system is developed. Based on this dissipation inequality and the principle of maximum dissipation a finite strain viscoplastic model described also in the rotated material coordinate system is formulated. The evolution equations are expressed in terms of the material time derivatives of the rotated elastic logarithmic strain, the accumulated plastic strain and the strain-like tensor conjugate to the rotated back stress. The mathematical structure of this theory is concise and similar to that of the infinitesimal viscoplastic theory. These characteristics make the numerical implementation of this theory easy. The stress integration algorithm and the algorithmic tangent moduli for the infinitesimal theory can be applied to the numerical implementation of the present finite strain theory with a little reformulation. The complicated algorithmic formulations for most of other finite plastic laws can be therefore circumvented. In order to check the effectivity of the present finite strain theory a set of numerical examples under strict deformation conditions are presented. These numerical examples prove the excellent performance of the present viscoplastic material law at describing the finite strain elastoplastic and viscoplastic problems. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： constitutive behaviour elastic-viscoplastic material finite strain finite elements numerical algorithms

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H² optimal control for linear stochastic systems

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AUTOMATICA 2004年第7期40卷 1103-1113页

作者： Dragan, V Morozan, T Stoica, A Acad Romana Math Inst RO-70700 Bucharest Romania Univ Politeh Bucharest Fac Aerosp Engn RO-77206 Bucharest Romania

The aim of the present paper is to provide an optimal solution to the H(2) state-feedback and output-feedback control problems for stochastic linear systems subjected both to Markov jumps and to multiplicative white noise. It is proved that in the state-feedback case the optimal solution is a static gain which is also optimal in the class of all higher-order controllers. In the output-feedback case the optimal H(2) controller has the same order as the given stochastic system. The realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of Riccati-type coupled equations. An effective iterative convergent algorithm to compute these stabilizing solutions is also presented. The paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： optimal control stochastic systems Markov parameters white noise Riccati equations numerical algorithms

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Computing the real zeros of hypergeometric functions

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numerical algorithms 2004年第2期36卷 113-134页

作者： Gil, A Koepf, W Segura, J Univ Cantabria Dept Matemat Estadist & Computac E-39005 Santander Spain Univ Kassel FB Math Informat 17 D-34132 Kassel Germany

Efficient methods for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. These methods are based on global fixed point iterations which apply to families of functions satisfying first order linear difference differential equations with continuous coefficients. In order to compute the zeros of arbitrary solutions of the hypergeometric equations, we have at our disposal several different sets of difference differential equations (DDE). We analyze the behavior of these different sets regarding the rate of convergence of the associated fixed point iteration. It is shown how combinations of different sets of DDEs, depending on the range of parameters and the dependent variable, is able to produce efficient methods for the computation of zeros with a fairly uniform convergence rate for each zero.

关键词： zeros hypergeometric functions fixed point iterations numerical algorithms

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Merging, sorting and matrix operations on the SOME-Bus multiprocessor architecture

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FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2004年第4期20卷 643-661页

作者： Katsinis, C Drexel Univ Philadelphia PA 19104 USA

Due to advances in fiber-optics and VLSI technology, interconnection networks which allow multiple simultaneous broadcasts are becoming feasible. This paper presents the multiprocessor architecture of the Simultaneous Optical Multiprocessor Exchange Bus (SOME-Bus), and examines the performance of representative algorithms for matrix operations, merging and sorting. using the message-passing and distributed-shared-memory paradigms. It shows that simple enhancements to the network interface and the cache and directory controllers can result in communication time of 0(l) for the matrix-vector multiplication algorithm using DSM. The SOME-Bus is a low-latency, high-bandwidth, fiber-optic interconnection network which directly links arbitrary pairs of processor nodes without contention, and can efficiently interconnect over 100 nodes. It contains a dedicated channel for the data output of each node, eliminating the need for global arbitration and providing bandwidth that scales directly with the number of nodes in the system. Each of P nodes has an array of receivers, with one receiver dedicated to each node output channel. No node is ever blocked from transmitting by another transmitter or due to contention for shared switching logic. The entire P receiver array can be integrated on a single chip at a comparatively minor cost resulting in O(P) complexity. The SOME-Bus has much more functionality than a crossbar by supporting multiple simultaneous broadcasts of messages, allowing cache consistency protocols to complete much faster. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multiprocessors broadcast architectures numerical algorithms

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