We overview our GRAvity PipE (GRAPE) project to develop special-purpose computers for astrophysical N-body simulations. The basic idea of GRAPE is to attach a custom-build computer dedicated to the calculation of grav...
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We overview our GRAvity PipE (GRAPE) project to develop special-purpose computers for astrophysical N-body simulations. The basic idea of GRAPE is to attach a custom-build computer dedicated to the calculation of gravitational interaction between particles to a general-purpose programmable computer. By this hybrid architecture, we can achieve both a wide range of applications and very high peak performance. Our newest machine, GRAPE-6, achieved the peak speed of 32 Tflops, and sustained performance of 11.55 Tflops, for the total budget of about 4 million USD. We also discuss relative advantages of special-purpose and general-purpose computers and the future of high-performance computing for science and technology. (C) 2002 Elsevier Science B.V. All rights reserved.
In MATLAB environment, a new quadrature routine based on Gaussian quadrature rule has been developed. Its performance is evaluated for improper integrals, rapidly oscillating functions and other types of functions req...
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In MATLAB environment, a new quadrature routine based on Gaussian quadrature rule has been developed. Its performance is evaluated for improper integrals, rapidly oscillating functions and other types of functions requiring a. large number of evaluations. This performance is compared against the other quadrature routines written for MATLAB in terms of capability, accuracy and computation time. It is found that our routine rates quite favourably. (c) 2006 Elsevier Inc. All rights reserved.
This paper presents a modified sine-fitting algorithms which can be used for high-accuracy sampling measurements of complex voltage ratio of sinusoidal signals. The proposed algorithms provide a significant reduction ...
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This paper presents a modified sine-fitting algorithms which can be used for high-accuracy sampling measurements of complex voltage ratio of sinusoidal signals. The proposed algorithms provide a significant reduction in the measurement uncertainty of phase shift when synchronizing the sampler and signal source is impossible.
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of closed semialgebraic sets given by Boolean formulas without negations over lax polynomial inequalities. The a...
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We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of closed semialgebraic sets given by Boolean formulas without negations over lax polynomial inequalities. The algorithm works in weak exponential time. This means that outside a subset of data having exponentially small measure, the cost of the algorithm is single exponential in the size of the data. All previous algorithms solving this problem have doubly exponential complexity. Our algorithm thus represents an exponential acceleration over state-of-the-art algorithms for all input data outside a set that vanishes exponentially fast.
The problem of determining an optimal output-feedback controller that forces the aircraft dynamics to evolve as an ideal model with prescribed eigenvalues and eigenvectors is addressed. A mixed linear-quadratic/eigens...
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The problem of determining an optimal output-feedback controller that forces the aircraft dynamics to evolve as an ideal model with prescribed eigenvalues and eigenvectors is addressed. A mixed linear-quadratic/eigenstructure strategy is used, where the matrix gain is chosen by minimizing a standard quadratic performance criterion. This allows one to 1) keep under control the maximum value of the input demand and 2) take into account flying-quality requirements by imposing suitable constraints on the system eigenstructure. It is believed that this optimization procedure provides significant improvements to a standard eigenstructure strategy and that it is well suited in the design of aircraft stability augmentation systems. A discussion of three case studies demonstrates the effectiveness of this procedure by comparing the corresponding results with others given in the literature.
A new simplified algorithm is proposed for numerical simulation of dielectric barrier discharge actuators. It is based on a three-species fluid model and includes five ionic reactions. The reaction rate coefficients a...
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A new simplified algorithm is proposed for numerical simulation of dielectric barrier discharge actuators. It is based on a three-species fluid model and includes five ionic reactions. The reaction rate coefficients are calculated from the Boltzmann equation, and the local field approximation is used. To drastically reduce the computing time, the discharge pulses are artificially damped. Two approximate models for photoionization are implemented and compared. This numerical algorithm is an attempt to compromise two approaches previously proposed: full plasma models, requiring prohibitively long computing time, and phenomenological models, which were based on inadequate physics. The electrical and mechanical characteristics of the electrohydrodynamics flow generated by the discharge are presented and validated by comparing with the experimental data, proving satisfactory accuracy of the model.
The problem of designing a rendezvous guidance maneuver plan robust to thrusting errors is addressed in this paper. The aim of this paper is to develop tractable and robust guidance algorithms. Solving the rendezvous ...
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The problem of designing a rendezvous guidance maneuver plan robust to thrusting errors is addressed in this paper. The aim of this paper is to develop tractable and robust guidance algorithms. Solving the rendezvous guidance problem via a direct approach leads to uncertain optimization problems while accounting for the guidance, navigation, and control systems uncertainties and errors. A worst-case approach is considered in order to obtain tractable robust counterparts. The robustness certificates derived from these guidance algorithms provide the means to analyze the effects of the considered errors on the rendezvous mission. Several types of missions tested in a linear environment are used to illustrate the methodology.
The convergence of inviscid and viscous hypersonic flow calculations using a two-dimensional flux-vector-splitting code is accelerated by applying a Richardson-type overrelaxation method. Successful results are presen...
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The convergence of inviscid and viscous hypersonic flow calculations using a two-dimensional flux-vector-splitting code is accelerated by applying a Richardson-type overrelaxation method. Successful results are presented for various cases, and a 50% savings in computer time (convergence rate is increased by a factor of 2) is usually achieved. An analytical formula for the overrelaxation factor is derived, and the performance of this scheme is confirmed numerically. Moreover, application of this overrelaxation scheme produces a favorable preconditioning for Wynne's epsilon-algorithm. Both techniques have been extended to viscous three-dimensional flows and applied to accelerate the convergence of the compressible Navier-Stokes code. A savings of 40% in computer time is achieved in this case.
Crack growth resistance of shape memory alloys (SMAs) is dominated by the transformation zone in the vicinity of the crack tip. In this study, the transformation toughening behavior of a slowly propagating crack in an...
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Crack growth resistance of shape memory alloys (SMAs) is dominated by the transformation zone in the vicinity of the crack tip. In this study, the transformation toughening behavior of a slowly propagating crack in an SMA under plane strain conditions and mode I deformation is numerically investigated. A small-scale transformation zone is assumed. A cohesive zone model is implemented to simulate crack growth within a finite element scheme. Resistance curves are obtained for a range of parameters that specify the cohesive traction-separation constitutive law. It is found that the choice of the cohesive strength to has a great influence on the toughening behavior of the material. Moreover, the reversibility of the transformation can significantly reduce the toughening of the alloy. The shape of the initial transformation zone, as well as that of a growing crack is determined. The effect of the Young's moduli ratio of the martensite and austenite phases is examined. (c) 2007 Elsevier Ltd. All rights reserved.
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. Th...
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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.
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