The effectiveness of projection methods for solving systems of linear
inequalities is investigated. It is shown that they have a computational
advantage over some alternatives and that this makes them successful in
real-world applications. This is supported by experimental evidence provided in
this paper on problems of various sizes (up to tens of thousands of unknowns
satisfying up to hundreds of thousands of constraints) and by a discussion of
the demonstrated efficacy of projection methods in numerous scientific
publications and commercial patents (dealing with problems that can have over a
billion unknowns and a similar number of constraints).
miércoles, 23 de diciembre de 2009
On the Effectiveness of Projection Methods for Convex Feasibility Problems with Linear Inequality Constraints. (arXiv:0912.4367v1 [math.OC])
Analysis of a finite-volume-finite-element scheme for a nuclear transport model
We consider a problem of nuclear waste contamination, taking into account thermal effects. The temperature and the contaminant's concentration obey convection–diffusion reaction equations. The velocity and the pressure in the flow satisfy the Darcy equation, with a viscosity depending on both concentrations and temperature. The equations are nonlinear and strongly coupled. Using both finite-volume and nonconforming finite-element methods, we introduce a scheme adapted to this problem. We prove the convergence of this scheme and give error estimates.
Verification of the Clauser Technique in Predicting Wall Shear Stress
AIAA Journal Jan. 2010, Vol. 48: 252-256.
Laminar Near Wake of a Circular Cylinder at Hypersonic Speeds
AIAA Journal Jan. 2010, Vol. 48: 236-248.
Mixed-Variable Optimization Strategy Employing Multifidelity Simulation and Surrogate Models
AIAA Journal Jan. 2010, Vol. 48: 215-223.
Computations of Flapping Flow Propulsion for Unmanned Underwater Vehicle Design
AIAA Journal Jan. 2010, Vol. 48: 188-201.
Simulation of Supersonic Combustion Involving H2/Air and C2H4/Air
AIAA Journal Jan. 2010, Vol. 48: 166-173.
Piezoelectric Control of a Partially Propped Cantilever Subjected to a Follower Force
AIAA Journal Jan. 2010, Vol. 48: 144-157.
Optimization of Variable-Stiffness Panels for Maximum Buckling Load Using Lamination Parameters
AIAA Journal Jan. 2010, Vol. 48: 134-143.
Redundant Reactions of Indeterminate Beams by Principle of Quasi Work
AIAA Journal Jan. 2010, Vol. 48: 129-133.
Thermal Force and Moment Determination of an Integrated Thermal Protection System
AIAA Journal Jan. 2010, Vol. 48: 119-128.
Microramps Upstream of an Oblique-Shock/Boundary-Layer Interaction
AIAA Journal Jan. 2010, Vol. 48: 104-118.
Numerical Simulations of Effects of Micro Vortex Generators Using Immersed-Boundary Methods
AIAA Journal Jan. 2010, Vol. 48: 92-103.
Reliability Analysis for Multidisciplinary Systems with Random and Interval Variables
AIAA Journal Jan. 2010, Vol. 48: 82-91.
Finite Element Method Applied to Supersonic Flutter of Circular Cylindrical Shells
AIAA Journal Jan. 2010, Vol. 48: 73-81.
Fast algorithms for hierarchically semiseparable matrices
Semiseparable matrices and many other rank-structured matrices have been widely used in developing new fast matrix algorithms. In this paper, we generalize the hierarchically semiseparable (HSS) matrix representations and propose some fast algorithms for HSS matrices. We represent HSS matrices in terms of general binary HSS trees and use simplified postordering notation for HSS forms. Fast HSS algorithms including new HSS structure generation and HSS form Cholesky factorization are developed. Moreover, we provide a new linear complexity explicit ULV factorization algorithm for symmetric positive definite HSS matrices with a low-rank property. The corresponding factors can be used to solve the HSS systems also in linear complexity. Numerical examples demonstrate the efficiency of the algorithms. All these algorithms have nice data locality. They are useful in developing fast-structured numerical methods for large discretized PDEs (such as elliptic equations), integral equations, eigenvalue problems, etc. Some applications are shown. Copyright © 2009 John Wiley & Sons, Ltd.
Factorized parallel preconditioner for the saddle point problem
The aim of this paper is to apply the factorized sparse approximate inverse (FSAI) preconditioner to the iterative solution of linear systems with indefinite symmetric matrices. Until now the FSAI technique has been applied mainly to positive definite systems and with a limited success for the indefinite case. Here, it is demonstrated that the sparsity pattern for the preconditioner can be chosen in such a way that it guarantees the existence of the factorization. The proposed scheme shows excellent parallel scalability, performance and robustness. It is applicable with short recurrence iterative methods such as MinRes and SymmLQ. The properties are demonstrated on linear systems arising from mixed finite element discretizations in linear elasticity. Copyright © 2009 John Wiley & Sons, Ltd.
Basic displacement functions for centrifugally stiffened tapered beams
Introducing the concept of basic displacement functions (BDFs), free vibration analysis of rotating tapered beams is studied from a mechanical point of view. Holding pure structural/mechanical interpretations, BDFs are obtained by solving the governing static differential equation of flapwise motion of rotating Euler-Bernoulli beams and imposing appropriate boundary conditions. Following the principles of structural mechanics, it is shown that exact shape functions and consequently structural matrices could be derived in terms of BDFs. The new shape functions capture the effects of variation of both cross-sectional area and moment of inertia along the element and the stiffening effect of centrifugal force. The method is employed to determine the natural frequencies of tapered rotating beams with different variations of cross-sectional dimensions and the results are in good agreement with those in the literature. Finally, the effects of rotational speed and taper ratio on the natural frequencies are investigated. Copyright © 2009 John Wiley & Sons, Ltd.
Rocking vibrations of a rigid embedded foundation in a poroelastic half-space
This paper presents an analysis of the rocking vibrations of a rigid cylindrical foundation embedded in poroelastic soil. The foundation is subjected to time-harmonic rocking excitation and is perfectly bonded to the surrounding soil. The soil underlying the foundation base is represented by a homogeneous poroelastic half-space, whereas the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory. The contact surface between the foundation base and the poroelastic soil is assumed to be smooth and either fully permeable or impermeable. The dynamic interaction problem is solved by employing a simplified analytical method. Some numerical results for the nondimensional rocking dynamic impedance and nondimensional angular displacement amplitude of the foundation are presented to show the effect of nondimensional frequency of excitation, poroelastic material parameters, hydraulic boundary condition, depth ratio and mass ratio of the foundation. Copyright © 2009 John Wiley & Sons, Ltd.
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