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Application of Newton's Method with Analytical Computation of Jacobian Matrix to Solve Multi-linear Pole Assignment Equations

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IFAC Proceedings Volumes 2014年第1期47卷 706-710页

作者： Gopal Jee Sarabhai Space Centre Thiruvananthapuram Pin 695022 INDIA

Output feedback pole placement problem is not solvable analytically for the plants having either number of inputs or number of outputs, more than two. There is even lack of a good numerical method which solves any general pole assignment problem. Due to the multi-linear nature of the pole placement problem there is a possibility to utilize multi-linear structure and arrive at a better numerical solution. This paper shows that it is possible to compute analytically the Jacobian and Hessian matrix in an easy manner and utilize them in an iterative numerical method to solve the pole-placement problem. Newton-Raphson method is used with analytical solution of Jacobian matrix to give an iterative solution of pole placement equations with better percentage success rate than the other methods quoted in literature.

关键词： Pole assignment output feedback multi-input/multi-output systems numerical algorithms

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New algorithm to test percolation conditions within the Newman-Ziff algorithm

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 2014年第11期25卷 1450064-1450064页

作者： Tronin, I. V. Natl Res Nucl Univ MEPhI Dept Mol Phys Moscow 115409 Russia

A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman-Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman-Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.

关键词： Percolation theory numerical algorithms continuum percolation lattice percolation

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Improvements of the Methods of Radiation Fields numerical Modeling on the Basis of Mirror Reflection Principle

Improvements of the Methods of Radiation Fields Numerical Mo...

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13th International Conference on Computational Science and Its Applications (ICCSA)

作者： Smokty, Oleg I. Russian Acad Sci St Petersburg Inst Informat & Automat St Petersburg 196140 Russia

ISBN: (纸本)9783642396403

Fundamental properties of the angular-spatial symmetry of radiation fields in the uniform slab of a finite optical thickness are used for improvement of the numerical methods and algorithms of the classical radiative transfer theory. A new notion of so called photometrical invariants is introduced. The basic boundary-value problem of the radiative transfer theory is reformulated in new terms for the subsequent simplification of algorithms of numerical modeling methods such as spherical harmonics, discrete ordinates, Gauss-Seidel and Case methods. This simplification leads to two-fold decrease of the ranks of linear algebraic equations with simultaneous reduction of numerical modeling intervals connected with angular and spatial variables.

关键词： mirror refelection principle photometrical invariants boundary-value problem numerical algorithms rank of linear equations system iteration spherical harmonics discrete ordinates Gauss-Seidel and Case methods

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Molecular modeling of cracks at interfaces in nanoceramic composites

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2013年第10期61卷 1971-1982页

作者： Pavia, F. Curtin, W. A. Brown Univ Sch Engn Providence RI 02912 USA Ecole Polytech Fed Lausanne Inst Engn Mech CH-1006 Lausanne Switzerland

Toughness in Ceramic Matrix Composites (CMCs) is achieved if crack deflection can occur at the fiber/matrix interface, preventing crack penetration into the fiber and enabling energy-dissipating fiber pullout. To investigate toughening in nanoscale CMCs, direct atomistic models are used to study how matrix cracks behave as a function of the degree of interfacial bonding/sliding, as controlled by the density of C interstitial atoms, at the interface between carbon nanotubes (CNTs) and a diamond matrix. Under all interface conditions studied, incident matrix cracks do not penetrate into the nanotube. Under increased loading, weaker interfaces fail in shear while stronger interfaces do not fail and, instead, the CNT fails once the stress on the CNT reaches its tensile strength. An analytic shear lag model captures all of the micromechanical details as a function of loading and material parameters. Interface deflection versus fiber penetration is found to depend on the relative bond strengths of the interface and the CNT, with CNT failure occurring well below the prediction of the toughness-based continuum He-Hutchinson model. The shear lag model, in contrast, predicts the CNT failure point and shows that the nanoscale embrittlement transition occurs at an interface shear strength scaling as tau similar to epsilon(f),CNT sigma CNT, rather than tau s similar to sigma CNT typically prevailing for micron scale composites, where epsilon f,CNT and sigma CNT are the CNT failure strain and stress, respectively. Interface bonding also lowers the effective fracture strength in SWCNTs, due to formation of defects, but does not play a role in DWCNTs having interwall coupling, which are weaker than SWCNTs but less prone to damage in the outerwall. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Crack propagation and arrest Strengthening and mechanisms Ceramic material Analytic functions numerical algorithms

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Wall distance search algorithm using voxelized marching spheres

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JOURNAL OF COMPUTATIONAL PHYSICS 2013年 241卷 76-94页

作者： Roget, Beatrice Sitaraman, Jayanarayanan Univ Wyoming Dept Mech Engn Laramie WY 82071 USA

Minimum distance to a solid wall is a commonly used parameter in turbulence closure formulations associated with the Reynolds Averaged form of the Navier Stokes Equations (RANS). This paper presents a new approach to efficiently compute the minimum distance between a set of points and a surface. The method is based on sphere voxelization, and uses fast integer arithmetic algorithms from the field of computer graphics. Using a simple test case where the number of points (N-p) and surface elements (N-b) can be independently specified, the present method is empirically estimated to be O((NpNb0.5)-N-0.8). An unstructured grid around an aircraft configuration (DLR-F6) is chosen as the test case for demonstration and validation. Multi-processor computations (up to 256 processors) are conducted to study efficiency and scalability. Encouraging results are obtained, with the sphere voxelization algorithm demonstrated to be more efficient than all of the alternate methods for computing minimum distances. However, a load imbalance does exist, which negatively impacts the scalability for large number of cores. A simple method for load re-balancing is formulated and tested, which results in significant improvements in both efficiency and scalability. (C) 2013 Elsevier Inc. All rights reserved.

关键词： numerical algorithms Computational fluid dynamics Turbulence modeling Computer graphics Minimum wall distance Voxel-based methods

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An extension of a shape memory alloy model for large deformations based on an exactly integrable Eulerian rate formulation with changing elastic properties

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INTERNATIONAL JOURNAL OF PLASTICITY 2013年 43卷 153-176页

作者： Teeriaho, J-P Univ Oulu Dept Mech Engn FI-90014 Oulu Finland

A small-displacement, phenomenological 3D model for shape memory alloys is expanded for large deformations. The Eulerian rate type formulation from the large deformation theory is used, with an additive decomposition of the stretching tensor. The expansion is performed by introducing, in the first stage, a thermodynamic frame for an isotropic material with logarithmic strains and scalar-valued internal state variables. The rate type characterisation of the elasticity is derived from the free energy. The relation is exactly integrable to define a free energy-based elastic relation. The formulation presented extends the previously presented ideas to possibly characterise changing elastic behaviours as a result of a phase transformation or other inelastic mechanisms. In the second part, a thermodynamic framework is used to derive the SMA constitutive equations by introducing large deformation counterparts in the small displacement theory for the Gibbs free energy, the transformation flow rule and the criteria for transformation. Then, a compatible integration algorithm is derived and implemented in Abaqus Standard FE software. The simulations presented demonstrate both a path-independent description of the elasticity and the model applicability to describe the unique properties of shape memory alloys. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Phase transformation Constitutive behaviour Finite strain Polycrystalline material numerical algorithms

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Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2013年第9期24卷 1852-1862页

作者： Dehnavi, Maryam Mehri Fernandez, David M. Gaudiot, Jean-Luc Giannacopoulos, Dennis D. MIT Cambridge MA 02139 USA McGill Univ Montreal PQ H3A 0E9 Canada Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92697 USA

Accelerating numerical algorithms for solving sparse linear systems on parallel architectures has attracted the attention of many researchers due to their applicability to many engineering and scientific problems. The solution of sparse systems often dominates the overall execution time of such problems and is mainly solved by iterative methods. Preconditioners are used to accelerate the convergence rate of these solvers and reduce the total execution time. Sparse approximate inverse (SAI) preconditioners are a popular class of preconditioners designed to improve the condition number of large sparse matrices. We propose a GPU accelerated SAI preconditioning technique called GSAI, which parallelizes the computation of this preconditioner on NVIDIA graphic cards. The preconditioner is then used to enhance the convergence rate of the BiConjugate Gradient Stabilized (BiCGStab) iterative solver on the GPU. The SAI preconditioner is generated on average 28 and 23 times faster on the NVIDIA GTX480 and TESLA M2070 graphic cards, respectively, compared to ParaSails (a popular implementation of SAI preconditioners on CPU) single processor/core results. The proposed GSAI technique computes the SAI preconditioner in approximately the same time as ParaSails generates the same preconditioner on 16 AMD Opteron 252 processors.

关键词： numerical algorithms parallel algorithms graphics processors parallel programming conditioning

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Acoustic Velocity Formulation for Sources in Arbitrary Motion

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AIAA JOURNAL 2013年第3期51卷 632-642页

作者： Ghorbaniasl, G. Carley, M. Lacor, C. Vrije Univ Brussel B-1050 Brussels Belgium Univ Bath Bath BA2 7AY Avon England

This paper deals with the acoustic velocity field simulation generated by interaction of flow with moving bodies. Starting from the Ffowcs Williams and Hawkings equation, an analytical formulation of the acoustic velocity is derived for sources in arbitrary motion. This makes the imposition of the boundary condition on a (rigid) scattering surface much more straightforward, as, if the traditional pressure formulation is used, then the pressure gradient must be calculated. Computational results for a pulsating sphere, dipole source, and a propeller case with subsonic tips verify this formulation.

关键词： Acoustic Scattering Propellers Helicopter Blade Thickness Ratio Aerodynamic Loads Green's Function Fluid Density Computational Aeroacoustics numerical Integration numerical algorithms

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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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Using permuted graph bases in H_∞ control

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AUTOMATICA 2013年第6期49卷 1790-1797页

作者： Mehrmann, Volker Poloni, Federico TU Berlin Inst Math D-10623 Berlin Germany Univ Pisa Dipartimento Informat I-56127 Pisa Italy

We present a new numerical method (based on the computation of deflating subspaces) for the gamma-iteration in H-infinity, control in the extended matrix pencil formulation. We introduce a permuted graph representation of these subspaces, which avoids the known difficulties that arise when the iteration is based on the solution of algebraic Riccati equations but at the same time makes use of the special symmetry structures that are present in the problems. We use this representation to perform both the deflation of spurious infinity eigenvalues of the even pencils and the implementation of the inverse-free sign iteration. We show that the new method returns accurate results and is applicable in many situations where conventional methods fail. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Algebraic Riccati equations Robust control numerical algorithms Inverse-free algorithms Matrix sign iteration

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