Extended multiscale FEM for design of beams and frames with complex topology

A numerical method for design of beams and frames with complex topology is proposed. The method is based on extended multi-scale finite element method where beam finite elements are used on coarse scale and continuum elements on fine scale. A procedure for calculation of multi-scale base functions, up-scaling and downscaling techniques is proposed by using a modified version of window method that is used in computational homogenization. Coarse scale finite element is embedded into a frame of a material that is representing surrounding structure in a sense of mechanical properties. Results show that this method can capture displacements, shear deformations and local stress-strain gradients with significantly reduced computational time and memory comparing to full scale continuum model. Moreover, this method includes a special hybrid finite elements for precise modelling of structural joints. Hence, the proposed method has a potential application in large scale 2D and 3D structural analysis of non-standard beams and frames where spatial interaction between structural elements is important.     

A new discrete filled function method for solving large scale max-cut problems

The global optimization method based on discrete filled function is a new method that solves large scale max-cut problems. We first define a new discrete filled function based on the structure of the max-cut problem and analyze its properties. Unlike the continuous filled function methods, by the characteristic of the max-cut problem, the parameters in the proposed filled function does not need to be adjusted. By combining a procedure that randomly generates initial points for minimization of the proposed filled function, the proposed algorithm can greatly reduce the computational time and be applied to large scale max-cut problems. Numerical results and comparisons with several heuristic methods indicate that the proposed algorithm is efficient and stable to obtain high quality solution of large scale max-cut problems.     

Using groups in the splitting preconditioner computation for interior point methods

Interior point methods usually rely on iterative methods to solve the linear systems of large scale problems. The paper proposes a hybrid strategy using groups for the preconditioning of these iterative methods. The objective is to solve large scale linear programming problems more efficiently by a faster and robust computation of the preconditioner. In these problems, the coefficient matrix of the linear system becomes ill conditioned during the interior point iterations, causing numerical difficulties to find a solution, mainly with iterative methods. Therefore, the use of preconditioners is a mandatory requirement to achieve successful results. The paper proposes the use of a new columns ordering for the splitting preconditioner computation, exploring the sparsity of the original matrix and the concepts of groups. This new preconditioner is designed specially for the final interior point iterations; a hybrid approach with the controlled Cholesky factorization preconditioner is adopted. Case studies show that the proposed methodology reduces the computational times with the same quality of solutions when compared to previous reference approaches. Furthermore, the benefits are obtained while preserving the sparse structure of the systems. These results highlight the suitability of the proposed approach for large scale problems.     

A bi-objective uncapacitated facility location problem

We consider a bi-objective model for uncapacitated facility location where one objective is to maximize the net profit and the other to maximize the profitability of the investment. We first characterize the structure of the model having both a linear and a fractional objective function. In order to generate efficient solutions for the model, we develop a heuristic procedure which has computational advantages over existing methods. A numerical example is presented to illustrate the solution process and computational tests on large scale problems are also provided.     

Data structures to vectorize CG algorithms for general sparsity patterns

We describe an implementation of Conjugate Gradient-type iterative algorithms for problems with general sparsity patterns on a vector processor with a hierarchy of memories, such as the IBM 3090/VF. The implementation relies on the wavefront approach to vectorize the solution of the two sparse triangular systems that arise when using ILU type preconditioners. The data structure is the key to an effective implementation of sparse computational kernels on a vector processor. A data structure is a combination of a layout of the matrix coefficients and ordering schemes for the vectors to increase data locality. With the data structure we describe, we achieve comparable performance on both the matrix-vector product and the solution of the sparse triangular systems on a variety of real problems, such as those arising from large scale reservoir simulation or structural analysis.     

An Augmented Lagrangian Algorithm for Large Scale Multicommodity Routing

The linear multicommodity network flow (MCNF) problem has many applications in the areas of transportation and telecommunications. It has therefore received much attention, and many algorithms that exploit the problem structure have been suggested and implemented. The practical difficulty of solving MCNF models increases fast with respect to the problem size, and especially with respect to the number of commodities. Applications in telecommunications typically lead to instances with huge numbers of commodities, and tackling such instances computationally is challenging.In this paper, we describe and evaluate a fast and convergent lower-bounding procedure which is based on an augmented Lagrangian reformulation of MCNF, that is, a combined Lagrangian relaxation and penalty approach. The algorithm is specially designed for solving very large scale MCNF instances. Compared to a standard Lagrangian relaxation approach, it has more favorable convergence characteristics. To solve the nonlinear augmented Lagrangian subproblem, we apply a disaggregate simplicial decomposition scheme, which fully exploits the structure of the subproblem and has good reoptimization capabilities. Finally, the augmented Lagrangian algorithm can also be used to provide heuristic upper bounds.The efficiency of the augmented Lagrangian method is demonstrated through computational experiments on large scale instances. In particular, it provides near-optimal solutions to instances with over 3,600 nodes, 14,000 arcs and 80,000 commodities within reasonable computing time.     

Development of a single-layer finite element and a simplified finite element modeling approach for constrained layer damped structures

A new finite element (FE) is formulated based on an extension of previous FE models for studying constrained layer damping (CLD) in beams. Most existing CLD FE models are based on the assumption that the shear deformation in the core layer is the only source of damping in the structure. However, previous research has shown that other types of deformation in the core layer, such as deformations from longitudinal extension, and transverse compression, can also be important. In the finite element formulated here, shear, extension, and compression deformations are all included. As presented, there are 14 degrees of freedom in this element. However, this new element can be extended to cases in which the CLD structure has more than three layers. The numerical study shows that this finite element can be used to predict the dynamic characteristics accurately. However, there is a limitation when the core layer has a high stiffness, as the new element tends to predict loss factors and natural frequencies that are too high. As a result, this element can be accepted as a general computation model to study the CLD mechanism when the core layer is soft. Because the element includes all three types of damping, the computational cost can be very high for large scale models. Based on this consideration, a simplified finite modeling approach is presented. This approach is based on an existing experimental approach for extracting equivalent properties for a CLD structure. Numerical examples show that the use of these extracted properties with commercially available FE models can lead to sufficiently accurate results with a lower computational expense.     

<Literal>smt</Literal>: a Matlab toolbox for structured matrices

The full exploitation of the structure of large scale algebraic problems is often crucial for their numerical solution. Matlab is a computational environment which supports sparse matrices, besides full ones, and allows one to add new types of variables (classes) and define the action of arithmetic operators and functions on them. The smt toolbox for Matlab introduces two new classes for circulant and Toeplitz matrices, and implements optimized storage and fast computational routines for them, transparently to the user. The toolbox, available in Netlib, is intended to be easily extensible, and provides a collection of test matrices and a function to compute three circulant preconditioners, to speed up iterative methods for linear systems. Moreover, it incorporates a simple device to add to the toolbox new routines for solving Toeplitz linear systems.     

A new nonmonotone adaptive trust region method based on simple quadratic models

Based on simple quadratic models of the trust region subproblem, we combine the trust region method with the nonmonotone and adaptive techniques to propose a new nonmonotone adaptive trust region algorithm for unconstrained optimization. Unlike traditional trust region method, our trust region subproblem is very simple by using a new scale approximation of the minimizing function??s Hessian. The new method needs less memory capacitance and computational complexity. The convergence results of the method are proved under certain conditions. Numerical results show that the new method is effective and attractive for large scale unconstrained problems.     

Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures

In order to design the microstructure of metamaterials showing high toughness in extension (property to be shared with muscles), it has been recently proposed (Dell’Isola et al. in Z Angew Math Phys 66(6):3473–3498, 2015) to consider pantographic structures. It is possible to model such structures at a suitably small length scale (resolving in detail the interconnecting pivots/cylinders) using a standard Cauchy first gradient theory. However, the computational costs for such modelling choice are not allowing for the study of more complex mechanical systems including for instance many pantographic substructures. The microscopic model considered here is a quadratic isotropic Saint-Venant first gradient continuum including geometric nonlinearities and characterized by two Lamé parameters. The introduced macroscopic two-dimensional model for pantographic sheets is characterized by a deformation energy quadratic both in the first and second gradient of placement. However, as underlined in Dell’Isola et al. (Proc R Soc Lond A 472(2185):20150790, 2016), it is needed that the second gradient stiffness depends on the first gradient of placement if large deformations and large displacements configurations must be described. The numerical identification procedure presented in this paper consists in fitting the macro-constitutive parameters using several numerical simulations performed with the micro-model. The parameters obtained by the best fit identification in few deformation problems fit very well also in many others, showing that the reduced proposed model is suitable to get an effective model at relevantly lower computational effort. The presented numerical evidences suggest that a rigorous mathematical homogenization result most likely holds.     

A conjugate gradient algorithm for sparse linear inequalities

This paper presents a conjugate gradient method for solving systems of linear inequalities. The method is of dual optimization type and consists of two phases which can be implemented in a common framework. Phase 1 either finds the minimum-norm solution of the system or detects the inconsistency of the system. In the latter event, the method proceeds to Phase 2 in which an approximate least-squares solution to the system is obtained. The method is particularly suitable to large scale problems because it preserves the sparsity structure of the problem. Its efficiency is shown by computational comparisons with an SOR type method.     

Niche width and scale in organizational competition: A computational approach

In some organizational applications, the principle of allocation (PoA) and scale advantage (SA) oppose each other. While PoA implies that organizations with wide niches get punished, SA holds that large organizations gain an advantage because of scale efficiencies. The opposition occurs because many large organizations also possess wide niches. However, analyzing these theoretical mechanisms implies a possible trade-off between niche width and size: if both PoA and SA are strong, then organizations must be either focused or large to survive, resulting in a dual market structure, as proposed by the theory of resource partitioning. This article develops a computational model used to study this trade-off, and investigates the properties of organizational populations with low/high SA and low/high PoA. The model generates three expected core “corner” solutions: (1) the dominance of large organizations in the strong SA setting; (2) the proliferation of narrow-niche organizations in the strong PoA setting; and (3) a bifurcated or dual market structure if both SA and PoA are present. The model also allows us to identify circumstances under which narrow-niche (specialists) or wide-niche (generalists) organizations thrive. We also use the model to examine the claim that concentrated resource distributions are more likely to generate partitioned or bifurcated populations. We also investigate the consequences of environments comprised of ordered versus unordered positions.     

求解低秩矩阵填充的改进的交替最速下降法

矩阵填充是指利用矩阵的低秩特性而由部分观测元素恢复出原矩阵,在推荐系统、信号处理、医学成像、机器学习等领域有着广泛的应用。采用精确线搜索的交替最速下降法由于每次迭代计算量小因而对大规模问题的求解非常有效。本文在其基础上采用分离地精确线搜索,可使得每次迭代下降更多但计算量相同,从而可望进一步提高计算效率。本文分析了新算法的收敛性。数值结果也表明所提出的算法更加有效。     

The emergence of large‐scale coherent structure under small‐scale random bombardments

We provide mathematical justification of the emergence of large‐scale coherent structure in a two‐dimensional fluid system under small‐scale random bombardments with small forcing and appropriate scaling assumptions. The analysis shows that the large‐scale structure emerging out of the small‐scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is very small, which explains earlier successful prediction of the large‐scale structure based on equilibrium statistical mechanics. © 2005 Wiley Periodicals, Inc.     

Development of a new method for online parameter identification in seismically excited smart building structures using virtual synchronization and adaptive control design

In this paper a new method for online parameter identification and damage detection in smart building structures that are subjected to arbitrary seismic excitation is proposed. It uses real-time measurements of a structure's motion to identify its unknown constant or piecewise constant parameters such as stiffness, damping and mass over the time. The method is based on elements of system synchronization and adaptive control theories. First, a computational system, called the virtual system, is defined. Next, by using properly designed controller and estimations for the unknown parameters, the state of the virtual system is forced to follow the measured motion of the real structure. The mentioned estimations are computed from a proposed update law which depends on the measured motion of the real structure and the virtual system’s state. A major theoretical novelty of this paper is a proposed convergence condition which is applicable in case of arbitrary external forces or ground acceleration. It is shown that upon the satisfaction of that condition, as the synchronization completes, the computed estimation function converges to the true value of the vector of unknown parameters. In addition, an important practical contribution presented in this study is the introduction of a technique called scale factors. It helps to use available initial guesses of the unknown parameters to improve the speed of online identification. Numerical examples show that the proposed method is promising and has a good performance in both online identification and online damage detection problems.     

An active set strategy based on the multiplier function or the gradient

We employ the active set strategy which was proposed by Facchinei for solving large scale bound constrained optimization problems. As the special structure of the bound constrained problem, a simple rule is used for updating the multipliers. Numerical results show that the active set identification strategy is practical and efficient.     

Stability analysis of switched ARX models and application to learning with guarantees

The main subject of this work is the stability analysis of Switched Auto-Regressive models with eXogenous inputs (SARX), which constitute a reference class for switched and hybrid system identification. The work introduces novel conditions for the arbitrary switching stability of multiple-input multiple-output SARX models which exploit the peculiar structure of their state-space realization. The analysis relies on the properties of block companion matrices, and partly leverages results from the theory of non-negative matrices, without nevertheless asking for an input–output positive behavior of the model. The novel stability conditions have a simple formulation in terms of linear co-positive common Lyapunov functions, and come at a remarkably low computational cost, being solvable by Linear Programming. The low computational burden is particularly attractive in an identification context, as it allows to efficiently constrain learning procedures in order to obtain SARX models with stability guarantees. The latter is itself a contribution of the work, as it fills a gap in the literature on the estimation of SARX models. The results are validated on a particular learning technique based on Regression Trees – a well known machine learning algorithm – which has shown remarkable accuracy in experimental environments.     

Improving Christofides' lower bound for the traveling salesman problem

In 1972 Christofides introduced a lower bound for the Traveling Salesman Problem (TSP). The bound is based on solving repeatedly a Linear Assignment Problem. We relate the bound to the Complete Cycle Problem; as a consequence the correctness of the bound is easier to prove.

Further we give improvements for the bound in the symmetric case and we deal with the influence of the triangle equation together with the identification of non-optimal edges for the TSP. The improvements are illustrated by examples and computational results for large problems.