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Algorithmic Aspects (algorithmic + aspect)

Distribution by Scientific Domains
Mathematics and Statistics28%
Engineering28%

Selected Abstracts

Constitutive model for quasi-static deformation of metallic sandwich cores

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2004
Zhenyu Xue
Abstract All-metal sandwich construction holds promise for significant improvements in stiffness, strength and blast resistance for built-up plate structures. Analysis of the performance of sandwich plates under various loads, static and dynamic, requires modelling of face sheets and core with some fidelity. While it is possible to model full geometric details of the core for a few selected problems, this is unnecessary and unrealistic for larger complex structures under general loadings. In this paper, a continuum constitutive model is proposed as an alternative means of modelling the core. The constitutive model falls within the framework of a compressible rate-independent, anisotropic elastic,plastic solid. The general form of the model is presented, along with algorithmic aspects of its implementation in a finite element code, and selected problems are solved which benchmark the code against existing codes for limiting cases and which illustrate features specific to compressible cores. Three core geometries (pyramidal truss, folded plate, and square honeycomb) are considered in some detail. The validity of the approach is established by comparing numerical finite element simulations using the model with those obtained by a full three-dimensional meshing of the core geometry for each of the three types of cores for a clamped sandwich plate subject to uniform pressure load. Limitations of the model are also discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source]

The harmonic adjoint approach to unsteady turbomachinery design

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3-4 2002
M. C. Duta
Abstract In recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint flow analysis to efficiently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic flow unsteadiness. The paper introduces the key engineering concepts and discusses the derivation of the adjoint analysis at the algebraic level. The emphasis is on the algorithmic aspects of the analysis, on the iterative solution method and on the role played by the strong solid wall boundary condition, in particular. The novel ideas are exploited to reveal the potential of the approach in the minimization of the unsteady vibration of turbomachinery blades due to incident wakes. Copyright © 2002 John Wiley & Sons, Ltd. [source]

An annotated bibliography of GRASP,Part II: Applications

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 2 2009
Paola Festa
Abstract A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic, have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the second of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. In the companion paper, algorithmic aspects of GRASP are surveyed. In this paper, we cover the literature where GRASP is applied to scheduling, routing, logic, partitioning, location, graph theory, assignment, manufacturing, transportation, telecommunications, biology and related fields, automatic drawing, power systems, and VLSI design. [source]

An annotated bibliography of GRASP , Part I: Algorithms

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2009
Paola Festa
Abstract A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the first of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. This paper covers algorithmic aspects of GRASP. [source]

Orthogonal signal correction: algorithmic aspects and properties

JOURNAL OF CHEMOMETRICS, Issue 11 2002
Baibing Li
Abstract The objective of this paper is to present a modified algorithm for the orthogonal signal correction (OSC) filter based on the approaches proposed by Wold, Antti, Lindgren and Öhman (Chemometrics Intell. Lab. Syst. 1998; 44: 175,185) and Fearn (Chemometrics Intell. Lab. Syst. 2000; 50: 47,52). An OSC filter consists of a trio of building blocks: weights, components and loadings, . The original OSC filter of Wold et al. was based on the framework of the non-linear iterative partial least squares (NIPALS) algorithm. Adopting this approach enabled the mathematical justification for the selection of the loading vectors pj and components tj, but there was no theoretical foundation for the selection of wj. In contrast, the approach of Fearn described an objective function for the selection of the weight vectors wj, but in this case there is no theoretical justification for either pj or tj. Combining both approaches, within a NIPALS framework, enables a clear theoretical basis for the selection of all three building blocks to be established. A number of orthogonal and optimal properties of the NIPALS-based OSC algorithm, although previously reported, are also theoretically proven. Finally, it is shown that the modified OSC algorithm is equivalent to Fearn's OSC but is interpretable as a consequence of it being presented from a NIPALS perspective. This enables the possible extension of OSC to dynamic and non-linear systems. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Numerical analysis of the stochastic Stokes equations of Wick type

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2007
H. Manouzi
Abstract We propose a finite element method for the numerical solution of the stochastic Stokes equations of the Wick type. We give existence and uniqueness results for the continuous problem and its approximation. Optimal error estimates are derived and algorithmic aspects of the method are discussed. Our method will reduce the problem of solving stochastic Stokes equations to solving a set of deterministic ones. Moreover, one can reconstruct particular realizations of the solution directly from Wiener chaos expansions once the coefficients are available. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source]

The geometric minimum action method: A least action principle on the space of curves

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2008
Matthias Heymann
Freidlin-Wentzell theory of large deviations for the description of the effect of small random perturbations on dynamical systems is exploited as a numerical tool. Specifically, a numerical algorithm is proposed to compute the quasi-potential in the theory, which is the key object to quantify the dynamics on long time scales when the effect of the noise becomes ubiquitous: the equilibrium distribution of the system, the pathways of transition between metastable states and their rate, etc., can all be expressed in terms of the quasi-potential. We propose an algorithm to compute these quantities called the geometric minimum action method (gMAM), which is a blend of the original minimum action method (MAM) and the string method. It is based on a reformulation of the large deviations action functional on the space of curves that allows one to easily perform the double minimization of the original action required to compute the quasi-potential. The theoretical background of the gMAM in the context of large deviations theory is discussed in detail, as well as the algorithmic aspects of the method. The gMAM is then illustrated on several examples: a finite-dimensional system displaying bistability and modeled by a nongradient stochastic ordinary differential equation, an infinite-dimensional analogue of this system modeled by a stochastic partial differential equation, and an example of a bistable genetic switch modeled by a Markov jump process. © 2007 Wiley Periodicals, Inc. [source]