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An interpolated stochastic algorithm for quasi-linear PDEs

MATHEMATICS OF COMPUTATION 2008年第261期77卷 125-158页

作者： Delarue, Francois Menozzi, Stephane Univ Paris 07 UFR Math F-75251 Paris 05 France

In this paper, we improve the forward-backward algorithm for quasi-linear PDEs introduced in Delarue and Menozzi (2006). The new discretization scheme takes advantage of the standing regularity properties of the true solution through an interpolation procedure. For the convergence analysis, we also exploit the optimality of the square Gaussian quantization used to approximate the conditional expectations involved. The resulting bound for the error is closely related to the Holder exponent of the second order spatial derivatives of the true solution and turns out to be more satisfactory than the one previously established.

关键词： DIFFERENTIAL-EQUATIONS numerical algorithms APPROXIMATION UNIQUENESS EXISTENCE

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HIGH-PERFORMANCE SIGNAL PROCESSING ON RECONFIGURABLE PLATFORMS

HIGH-PERFORMANCE SIGNAL PROCESSING ON RECONFIGURABLE PLATFOR...

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作者： Kim, Jung Sub PennState University Libraries

学位级别：Doctor of Philosophy

Reconfigurable platforms have become a promising solution for highperformance signal processing applications due to their flexibleresources, high operating frequency, and low power. However, therequired knowledge of such a reconfigurable platform is growing asthe complexities to use these platforms continue to increase. Thiswork simplifies the use of reconfigurable platforms for targetedsignal processing applications. The first contribution is the designof TANOR, a tool for accelerating applications utilizing numericalalgorithms with large-size data sets. TANOR is targeted at solving arange of N-body interaction problems spanning from astrophysics tomolecular dynamics. The TANOR design flow starts with a MATLABdescription of a particular interaction function and parameterselection from a graphical user interface. Subsequently, TANORautomatically generates a configuration bitstream for a target FPGAalong with associated drivers and control software necessary toexecute the application on a host computer. Architecturalexploration is facilitated through support for standard numberrepresentations such as single precision floating point in additionto support for fully custom fixed-point and floating pointrepresentations. Moreover, TANOR enables joint exploration ofalgorithmic and architectural variations in realizing efficienthardware accelerators. TANOR's effectiveness and adaptability isdemonstrated by generating kernels for three different applications:namely, the gravitational kernel (used in astrophysics), theGaussian kernel (common in image processing applications), and aforce calculation kernel (applied in molecular dynamics). Theresults show that TANOR is capable of achieving identical accuracywith lower resource utilization, making it competitive with existingmanually-designed custom *** second contribution focuses on designing an accelerator for FastFourier Transforms (FFT), which are used extensively in signal anddigital image processing. Since FFT

关键词： Two Dimensional Decomposition Field Programmable Gate Array Fast Fourier Transform numerical algorithms System Generator Hierarchical Memory Controller

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A unified framework for the numerical solution of general quadratic matrix equations

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2007年第2期24卷 259-287页

作者： Tsachouridis, Vassilios A. Karcanias, Nicos Postlethwaite, Ian City Univ London Sch Engn & Math Sci London EC1V 0HB England Univ Leicester Dept Engn Leicester LE1 7RH Leics England

Algebraic quadratic equations are special cases of a single generalized algebraic quadratic matrix equation (GQME). This paper focuses on the numerical solution of the GQME using probability-1 homotopy methods. A synoptic review of these methods and their application to algebraic matrix equations is provided as background. A large variety of analysis and design problems in systems and control are reported as special cases of the presented framework and some of them are illustrated via numerical examples from the literature.

关键词： numerical algorithms homotopy methods matrix equations Riccati equations control systems

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Event and Apparent Horizon Finders for 3+1 numerical Relativity

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LIVING REVIEWS IN RELATIVITY 2007年第1期10卷 1页

作者： Thornburg, Jonathan Univ Southampton Sch Math Southampton SO17 1BJ Hants England Max Planck Inst Gravitat Phys Albert Einstein Inst D-14476 Potsdam Germany

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numeric ally-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotic ally-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time: it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Theta. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well

关键词： .slice spacetimes Black Holes numerical algorithms null geodesics numerical relativity event horizons future-pointing apparent horizons Horizon Finders Finders for numerical

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Objective molecular dynamics

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2007年第10期55卷 2206-2236页

作者： Dumitrica, Traian James, Richard D. Univ Minnesota Dept Mech Engn Minneapolis MN 55455 USA Univ Minnesota Dept Aerosp Engn & Mech Minneapolis MN 55455 USA

We introduce a generalization of periodic molecular dynamics that we term objective molecular dynamics. It is a method of doing molecular dynamics for a restricted set of atoms, nonperiodically mapping the time-dependent displacements of this small set of atoms onto the full, typically infinite structure, such that the full structure satisfies exactly the full, unconstrained set of equations of molecular dynamics subject to certain group-invariant initial conditions. The method is applicable to a wide variety of interesting molecular structures including the tails, capsids and other parts of many viruses, carbon nanotubes, many of the common proteins, C-60 and many other nanostructures now being synthesized, especially via the process of self-assembly. The method is illustrated by simulations of carbon nanotubes. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： atomistic structures numerical algorithms buckling structures dynamics

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Discrete element simulation of shock wave propagation in polycrystalline copper

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2007年第3期55卷 589-614页

作者： Case, Simon Horie, Yasuyuki Atom Weapons Establishment Reading RG7 4PR Berks England USA Res Lab Eglin AFB FL USA

The implementation of the characteristic of compressive plasticity into the Discrete Element Code, DM2, while maintaining its quasi-molecular scheme, is described. The code is used to simulate the shock compression of polycrystalline copper at 3.35 and 11.0 GPa. The model polycrystal has a normal distribution of grain sizes, with mean diameter 14 pm, and three distinct grain orientations are permitted with respect to the shock direction;< 100 >, < 110 >, and < 111 >. Particle velocity dispersion (PVD) is present in the shock-induced flow, attaining its maximum magnitude at the plastic wave rise. PVD normalised to the average particle velocity of Delta u(y)/(u) over bar (P) = 0.05 and Delta u(y)/(u) over bar (P) = 0.087 are yielded for the 3.35 and 11.0 GPa shocks, respectively, and are of the same order as those seen in the experiment. Non-planar elastic and plastic wave fronts are present, the distribution in shock front position increasing with propagation distance. The rate of increase of the spread in shock front positions is found to be significantly smaller than that seen in probabilistic calculations on nickel polycrystals, and this difference is attributed, in the main, to grain interaction. Reflections at free surfaces yield a region of tension near to the target free surface. Due to the dispersive nature of the shock particle velocity and the non-planarity of the shock front, the tensile pressure is distributed. This may have implications for the spall strength, which are discussed. Simulations reveal a transient shear stress distribution behind the shock front. Such a distribution agrees with that put forward by Lipkin and Asay to explain the quasi-elastic reloading phenomenon. Simulation of reloading shocks show that the shear stress distribution can give rise to quasi-elastic reloading on the grain scale. Crown Copyright (c) 2006 Published by Elsevier Ltd. All rights reserved.

关键词： shock waves polycrystalline material numerical algorithms microstructures elastic-plastic material

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SU-GG-I-116: Modulation Transfer Function Above Nyquist Frequency: A Robust Algorithm for the Edge Image Method

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Medical Physics 2008年第6PART4期35卷 2668-2668页

作者： M Manciu Physics Department University of Texas at El Paso El Paso TX

Purpose: We present a simple and robust numerical algorithm for the MTF calculation from an edge image, accurate up to frequencies (much) higher than the Nyquist frequency, even in the presence of noise. Method and Materials: The oversampling of the edge image is obtained, as usual, by positioning the edge at a small angle with respect to the detector grid. The angle does not have to be adjusted manually; its value is very accurately calculated using a numeric algorithm, which does not involve recording the Edge Spread Function (ESF) on a sub-sampling grid, and the Fourier coefficients are subsequently calculated numerically. The quality of the MTF calculation is investigated on a simulated ESF, in the presence of the noise due to the quantum nature of the radiation. Results: The numerical algorithm proposed is able to recover the angle between the edge and the detector grid with a relative error of the order of 10 −5 , even for noise-affected data. The center of the Line Spread Function is also detected with an accuracy of the order of 10 −3 pixels. For low levels of noise, the MTF was accurately calculated up to about 10 Nyquist frequencies; for high noise levels, an algorithm that avoids the numerical differentiation, by employing integration by parts, has been suggested. The latter algorithm was shown to provide a good estimation of the MTF up to frequencies much higher than Nyquist frequency. Conclusion: The MTF can be accurately calculated from an edge image, when the edge is slanted with respect to the detector grid. The choice of the best algorithm for calculating the MTF depends on the level of noise; even for relatively large levels of noise the MTF can be accurately calculated up to and above the Nyquist frequency.

关键词： Modulation transfer functions Thermal noise Image sensors numerical algorithms Quantum noise numerical differentiation Integration Position sensitive detectors

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A new quadrature routine for improper and oscillatory integrals

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期189卷 452-461页

作者： Sermutlu, E. Eyyuboglu, H. T. Cankaya Univ Dept Math & Comp Sci TR-06530 Ankara Turkey Cankaya Univ Dept Elect & Commun Engn TR-06530 Ankara Turkey

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.

关键词： quadrature improper integrals numerical algorithms MATLAB

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Crack growth resistance of shape memory alloys by means of a cohesive zone model

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2007年第10期55卷 2157-2180页

作者： Freed, Yuval Banks-Sills, Leslie Tel Aviv Univ Fleischman Fac Engn Dept Solid Mech Mat & Syst Dreszer Fracture Mech Lab IL-69978 Tel Aviv Israel

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.

关键词： phase transformation fracture mechanics finite elements numerical algorithms shape memory alloys

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Tour planning for an unmanned air vehicle under wind conditions

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2007年第5期30卷 1299-1306页

作者： McNeely, Rachelle L. Iyer, Ram V. Chandler, Phillip R. Texas Tech Univ Dept Math & Stat Lubbock TX 79409 USA USAF Res Lab Wright Patterson AFB Wright Patterson AFB OH 45433 USA

A very important subproblem in the task assignment problem for unmanned air vehicles is the evaluation of costs for the state transitions of a directed graph. Usually a Dubins vehicle flying in the absence of wind is considered in the computation of costs. However, when a prevailing wind vector field is considered, the costs taken on very different values and the task assignment problem can have very different solutions. In this paper, we consider the problem of constructing minimum-time trajectories for a Dubins vehicle in the presence of a time-varying wind vector field. We present results on the existence and uniqueness of minimum-time solutions for a Dubins vehicle flying in a general time-varying wind vector field under some technical conditions. These results extend the conclusions of the well-known Dubins theorem. We also propose an algorithm for obtaining the minimum-time solution for an unmanned air vehicle and prove its convergence. We also present the results of numerical experiments that show that the importance of considering wind vector fields while planning the tour for an unmanned air vehicle.

关键词： Air Vehicle Micro Air Vehicle numerical Stability Coordinate Transformations Pontryagin's Maximum Principle Air Force Research Laboratory algorithms Convergence Boundary Value Problems numerical algorithms Euler Equations

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