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QR factorization for the Cell Broadband Engine

SCIENTIFIC PROGRAMMING 2009年第1-2期17卷 31-42页

作者： Kurzak, Jakub Dongarra, Jack Univ Tennessee Dept Elect Engn & Comp Sci Knoxville TN 37996 USA Oak Ridge Natl Lab Div Math & Comp Sci Oak Ridge TN USA Univ Manchester Sch Math Manchester Lancs England Univ Manchester Sch Comp Sci Manchester Lancs England

The QR factorization is one of the most important operations in dense linear algebra, offering a numerically stable method for solving linear systems of equations including overdetermined and underdetermined systems. Modern implementations of the QR factorization, such as the one in the LAPACK library, suffer from performance limitations due to the use of matrix-vector type operations in the phase of panel factorization. These limitations can be remedied by using the idea of updating of QR factorization, rendering an algorithm, which is much more scalable and much more suitable for implementation on a multi-core processor. It is demonstrated how the potential of the cell broadband engine can be utilized to the fullest by employing the new algorithmic approach and successfully exploiting the capabilities of the chip in terms of single instruction multiple data parallelism, instruction level parallelism and thread-level parallelism.

关键词： Cell broadband engine multi-core numerical algorithms linear algebra matrix factorization

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Perspectives for process systems engineering-Personal views from academia and industry

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COMPUTERS & CHEMICAL ENGINEERING 2009年第3期33卷 536-550页

作者： Klatt, Karsten-Ulrich Marquardt, Wolfgang Rhein Westfal TH Aachen Lehrstuhl Prozesstech D-52074 Aachen Germany Bayer Technol Serv GmbH D-51368 Leverkusen Germany

Process systems engineering (PSE) has been an active research field for almost 50 years. Its major achievements include methodologies and tools to support process modeling, simulation and optimization (MSO). Mature, commercially available technologies have been penetrating all fields of chemical engineering in academia as well as in industrial practice. MSO technologies have become a commodity, they are not a distinguishing feature of the PSE field any more. Consequently. PSE has to reassess and to reposition its future research agenda. Emphasis should be put on model-based applications in all PSE domains including product and process design, control and operations. Furthermore, systems thinking and systems problem solving have to be prioritized rather than the mere application of computational problem solving methods. This essay reflects on the past, present and future of PSE from an academic and industrial point of view. It redefines PSE as an active and future-proof research field which can play an active role in providing enabling technologies for product and process innovations in the chemical industries and beyond. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Review Modeling Design Optimization Control Operations numerical algorithms Software Computer-aided process engineering (CAPE)

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A hierarchical model for rate-dependent polycrystals

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INTERNATIONAL JOURNAL OF PLASTICITY 2009年第5期25卷 752-767页

作者： Mahesh, Sivasambu Indian Inst Technol Dept Mech Kanpur 208016 Uttar Pradesh India Indian Inst Technol Dept Aerosp Engn Kanpur 208016 Uttar Pradesh India

A hierarchical model of a polycrystalline aggregate of rigid viscoplastic grains is formulated, and a robust and efficient computational algorithm for its solution is proposed. The polycrystalline aggregate is modeled as a binary tree. The leaves of the binary tree represent grains, and higher tree nodes represent increasingly larger sub-aggregates of grains. The root of the tree represents the entire polycrystalline aggregate. Velocity and traction continuity are enforced across the interface between the children of each non-leaf node in the binary tree. The hierarchical model explicitly models intergranular interactions but is nevertheless comparable in computational effort to the mean field models of polycrystal plasticity. Simulations of tensile, compressive, torsional, and plane strain deformation of copper lead to predictions in good agreement with experiments, and highlight the interconnection between grain deformations and intergranular constraints. It is inferred from the results that a hybrid mean field/hierarchical model represents a computationally efficient methodology to simulate polycrystal deformation while accounting for intergranular interactions. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Crystal plasticity Hierarchical model Texture modeling numerical algorithms

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THE FLEXIBLE GABOR-WAVELET TRANSFORM FOR CAR CRASH SIGNAL ANALYSIS

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INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 2009年第4期7卷 481-490页

作者： Onchis, Darian M. Suarez Sanchez, Esperanza M. Univ Vienna Inst Math Numer Harmon Anal Grp A-1090 Vienna Austria Univ Seville Dept Appl Math 1 E-41012 Seville Spain

This paper is concerned with the spectral decomposition and the adaptive analysis of data coming from car crash simulations. The mathematical ingredient of the proposed signal processing technique is the flexible Gabor-wavelet transform or the alpha-transform that reliably detects both high and low frequency components of such complicated short-time signals. We go from the functional treatment of this wavelet-type transform to its numerical implementation and we show how it can be used as an improved tool for spectral investigations compared to the short-time Fourier transform or the classical wavelet transform.

关键词： Adaptive time-frequency transform alpha-modulation spaces signal processing numerical algorithms short-time Fourier transform

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Quaternion Analysis Tools for Engineering and Scientific Applications

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第2期32卷 686-693页

作者： Turner, James D. Texas A&M Univ Dept Aerosp Engn College Stn TX 77843 USA

QUATERNION algebra has found a number of applications for engineering and scientific problems, including fluid mechanics [1], quantum mechanics [2,3], robotics [4,5], and spacecraft attitude control [5,6]. Unfortunate... 详细信息

关键词： Gaussian Elimination FORTRAN Computing Newton's Method Spacecraft Attitude Lyapunov Equation Search Algorithm numerical algorithms Solution Algorithm Fluid Mechanics

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A robust formulation of the ensemble Kalman filter

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2009年第639期135卷 507-521页

作者： Thomas, S. J. Hacker, J. P. Anderson, J. L. Natl Ctr Atmospher Res Boulder CO 80307 USA

The ensemble Kalman filter (EnKF) can be interpreted in the more general context of linear regression theory. The recursive filter equations are equivalent to the normal equations for a weighted least-squares estimate that minimizes a quadratic functional. Solving the normal equations is numerically unreliable and subject to large errors when the problem is ill-conditioned. A numerically reliable and efficient algorithm is presented, based on the minimization of an alternative functional. The method relies on orthogonal rotations, is highly parallel and does not 'square' matrices ill order to compute the analysis update. Computation of eigenvalue and singular-value decompositions is not required. The algorithm is formulated to process observations serially or in batches and therefore easily handles spatially correlated observation errors. numerical results are presented for existing algorithms with a hierarchy of models characterized by chaotic dynamics. Under a range of conditions, which may include model error and sampling error, the new algorithm achieves the same or lower mean square errors as the serial Potter and ensemble adjustment Kalman filter (EAKF) algorithms. Published in 2009 by John Wiley and Sons, Ltd.

关键词： EnKF numerical algorithms

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A BSP-Based Algorithm for Dimensionally Nonhomogeneous Planar Implicit Curves with Topological Guarantees

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ACM TRANSACTIONS ON GRAPHICS 2009年第2期28卷 1–24页

作者： Gomes, Abel J. P. Morgado, Jose F. M. Pereira, Edgar S. Univ Beira Interior Inst Telecommun Dept Informat P-6200001 Covilha Portugal

Mathematical systems (e. g., Mathematica, Maple, Matlab, and DPGraph) easily plot planar algebraic curves implicitly defined by polynomial functions. However, these systems, and most algorithms found in the literature, cannot draw many implicit curves correctly;in particular, those with singularities (self-intersections, cusps, and isolated points). They do not detect sign-invariant components either, because they use numerical methods based on the Bolzano corollary, that is, they assume that the curve-describing function f flips sign somewhere in a line segment (AB) over bar that crosses the curve, or f (A). f (B) < 0. To solve these problems, we have generalized the False Position ( FP) method to determine two types of zeros: (i) crossing zeros and (ii) extremal zeros (local minima and maxima without function sign variation). We have called this method the Generalized False Position (GFP) method. It allows us to sample an implicit curve against the Binary Space Partitioning (BSP), say bisection lines, of a rectangular region of R-2. Interestingly, the GFP method can also be used to determine isolated points of the curve. The result is a general algorithm for sampling and rendering planar implicit curves with topological guarantees.

关键词： algorithms Implicit curves binary space partitioning numerical algorithms geometric computing

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Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part II: Computational issues

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2009年第1期46卷 92-124页

作者： Valoroso, Nunziante Rosati, Luciano Univ Napoli Parthenope Dipartimento Tecnol Ctr Direz Isola C4 I-80143 Naples Italy Univ Naples Federico II Dipartimento Ingn Strutturale I-80125 Naples Italy

The implementation of the projected algorithm and of the consistent tangent tensor for general isotropic three-invariant elastoplastic models under plane stress conditions discussed in Part I of this paper [Valoroso, N., Rosati, L., 2008. Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part 1: Theoretical formulation. International journal of Solids and Structures, doi: 10.1016/***.2008.08.012.] is addressed. The connections between the general three-dimensional case and the plane stress problem are analyzed in detail and an algorithmic treatment taking full advantage of the isotropic properties of the model is presented. In particular, intrinsic (matrix-free) expressions are provided for all steps of the stress computation scheme that allow one to carry out the numerical implementation in a way that is completely independent from the matrix representations. The numerical performances of the present solution scheme are evaluated through representative numerical examples. (c) 2008 Elsevier Ltd. All rights reserved.

关键词： numerical algorithms Finite elements Plane stress elastoplasticity Return mapping Consistent tangent

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Gradient-enhanced softening material models

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INTERNATIONAL JOURNAL OF PLASTICITY 2009年第11期25卷 2094-2121页

作者： Poh, L. H. Swaddiwudhipong, S. Natl Univ Singapore Dept Civil Engn Singapore 119260 Singapore

Classical constitutive models exhibit strong mesh dependency during softening and the numerical responses tend towards perfectly brittle behavior upon mesh refinements. Such sensitivity can be avoided by adopting the gradient-enhanced formulation. The implicit approach incorporates the gradient contributions indirectly via an additional Helmholtz equation and requires only C-0 continuity. The explicit approach computes the gradient terms directly from the local field variables. Assuming a weak satisfaction of the yield function, C-1 continuity or C-0 continuity with additional degrees of freedoms in the penalty approach is required. This makes the explicit method less attractive computationally. However, the explicit approach is able to fully regularize some material models where the standard implicit method fails to perform. Drawing analogy to the over-nonlocal integral formulation, the over-implicit-gradient framework is proposed. In addition, an alternative framework for the explicit gradient method requiring only C-0 continuity is proposed. The regularizing effects of the abovementioned two gradient frameworks show promising applications to strain-softening materials. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Yield condition Constitutive behavior Elastic-plastic material Finite elements numerical algorithms

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On electromagnetic forming processes in finitely strained solids: Theory and examples

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2009年第8期57卷 1391-1416页

作者： Thomas, J. D. Triantafyllidis, N. Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

The process of electromagnetic forming (EMF) is a high velocity manufacturing technique that uses electromagnetic (Lorentz) body forces to shape sheet metal parts. EMF holds several advantages over conventional forming techniques: speed, repeatability, one-sided tooling, and most importantly considerable ductility increase in several metals. Current modeling techniques for EMF processes are not based on coupled variational principles to simultaneously account for electromagnetic and mechanical effects. Typically, separate solutions to the electromagnetic (Maxwell) and motion (Newton) equations are combined in staggered or lock-step methods, sequentially solving the mechanical and electromagnetic problems. The present work addresses these issues by introducing a fully Coupled Lagrangian (reference configuration) least-action variational principle, involving magnetic flux and electric potentials and the displacement field as independent variables. The corresponding Euler-Lagrange equations are Maxwell's and Newton's equations in the reference configuration, which are shown to coincide with their current configuration counterparts obtained independently by a direct approach. The general theory is subsequently simplified for EMF processes by considering the eddy Current approximation. Next, an application is presented for axisymmetric EMF problems. It is shown that the proposed variational principle forms the basis of a variational integration numerical scheme that provides an efficient staggered solution algorithm. As an illustration a number of such processes are simulated, inspired by recent experiments of freely expanding uncoated and polyurea-coated aluminum tubes. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Electromechanical processes Finite strain Finite elements numerical algorithms Variational calculus

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