Absolute Stability of Nonlinear Systems with Two Additive Time-varying Delay Components

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.     

Differential Evolution performances for the solution of mixed-integer constrained process engineering problems

An important number of publications deal with the computational efficiency of a novel Evolutionary Algorithm called Differential Evolution (DE). However, there is still a noticeable lack of studies on DE's performance on engineering problems, which combine large-size instances, constraint-handling and mixed-integer variables issues. This paper proposes the solution by DE of process engineering problems and compares its computational performance with an exact optimization method (Branch-and-Bound) and with a Genetic Algorithm. Two analytical formulations are used to model the batch plant design problem and a set of examples gathering the three above-mentioned issues are also provided.The computational results obtained highlight the clear superiority of DE since its best found solutions always lie very close to the Branch-and-Bound optima. Moreover, for an equal number of objective function evaluations, the results repeatability was found to be much better for the DE method than for the Genetic Algorithm.     

Performance evaluation of efficient multi-objective evolutionary algorithms for design space exploration of embedded computer systems

Multi-objective evolutionary algorithms (MOEAs) have received increasing interest in industry because they have proved to be powerful optimizers. Despite the great success achieved, however, MOEAs have also encountered many challenges in real-world applications. One of the main difficulties in applying MOEAs is the large number of fitness evaluations (objective calculations) that are often needed before an acceptable solution can be found. There are, in fact, several industrial situations in which fitness evaluations are computationally expensive and the time available is very short. In these applications efficient strategies to approximate the fitness function have to be adopted, looking for a trade-off between optimization performance and efficiency. This is the case in designing a complex embedded system, where it is necessary to define an optimal architecture in relation to certain performance indexes while respecting strict time-to-market constraints. This activity, known as design space exploration (DSE), is still a great challenge for the EDA (electronic design automation) community. One of the most important bottlenecks in the overall design flow of an embedded system is due to simulation. Simulation occurs at every phase of the design flow and is used to evaluate a system which is a candidate for implementation. In this paper we focus on system level design, proposing an extensive comparison of the state-of-the-art of MOEA approaches with an approach based on fuzzy approximation to speed up the evaluation of a candidate system configuration. The comparison is performed in a real case study: optimization of the performance and power dissipation of embedded architectures based on a Very Long Instruction Word (VLIW) microprocessor in a mobile multimedia application domain. The results of the comparison demonstrate that the fuzzy approach outperforms in terms of both performance and efficiency the state of the art in MOEA strategies applied to DSE of a parameterized embedded system.     

Adaptive isogeometric analysis by local h-refinement with T-splines

Isogeometric analysis based on non-uniform rational B-splines (NURBS) as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space, which renders a purely local refinement impossible. This paper demonstrates how this difficulty can be overcome by using T-splines instead. T-splines allow the introduction of so-called T-junctions, which are related to hanging nodes in the standard FEM. Obeying a few straightforward rules, rectangular patches in the parameter space of the T-splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry. Furthermore, it is shown how state-of-the-art a posteriori error estimation techniques can be combined with refinement by T-splines. Numerical examples underline the potential of isogeometric analysis with T-splines and give hints for further developments.     

Stable splitting scheme for general form of associated plasticity including different scales of space and time

An efficient implementation of the operator split procedure for boundary value solution with plastic flow computation is presented for a general form of associated plasticity model. We start with the general form of phenomenological model of plasticity where the yield criterion is not restricted to a simple (quadratic) form, and the elasticity tensor does not have constant entries. We then turn to the multi-scale model of plasticity which employs the fine scale representation of the plastic deformation along with the homogenization procedure for stress computation. We also visit the plasticity model with rate sensitive plastic response where plastic flow computation is carried out at fine scale in time. We proved herein the sufficient and necessary conditions for the proposed operator split procedure to converge, for any such general form of associated plasticity. Moreover, we presented a systematic manner for constructing the main ingredients for the plastic flow computation and the global Newton’s iteration, such as the consistent elastoplastic tangent.     

A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation

In this contribution, we present an a posteriori error estimator for the incompressible Stokes problem valid for a conventional mixed FE formulation. Due to the saddle-point property of the problem, conventional error estimators developed for pure minimization problems cannot be utilized straight-forwardly. The new estimator is built up by two key ingredients. At first, a computed error approximation, exactly fulfilling the continuity equation for the error, is obtained via local Dirichlet problems. Secondly, we adopt the approach of solving local equilibrated flux-free problems in order to bound the remaining, incompressible, error. In this manner, guaranteed upper and lower bounds, of the velocity “energy norm” of the error as well as goal-oriented (linear) output functionals, with respect to a reference (overkill) mesh are obtained. In particular, it should be noted that this approach requires no computation of hybrid fluxes. Furthermore, the estimator is applicable to mixed FE formulations using continuous pressure approximations, such as the Mini and Taylor–Hood class of elements. In conclusion, a few simple numerical examples are presented, illustrating the accuracy of the error bounds.     

求解二维随机多区域声波散射问题的快速多极边界元方法

快速多极算法(FMM)是求解大尺度边界元问题的一种很有效的快速算法.应用快速多极算法求解二维随机多区域声散射问题的边界积分方程.首先给出了求解该问题的边界积分方程,进而给出快速多极算法求解的算法实现过程以及积分算子的相应多极展开、局部展开和相应系数的转化关系式.最后通过对数值例子的计算表明快速多极算法在求解随机多区域声散射问题时的可行性及高效性,其求解存储量和计算量都是O(N).     

An efficient parallel implementation of the MSPAI preconditioner

We present an efficient implementation of the Modified SParse Approximate Inverse (MSPAI) preconditioner. MSPAI generalizes the class of preconditioners based on Frobenius norm minimizations, the class of modified preconditioners such as MILU, as well as interface probing techniques in domain decomposition: it adds probing constraints to the basic SPAI formulation, and one can thus optimize the preconditioner relative to certain subspaces. We demonstrate MSPAI’s qualities for iterative regularization problems arising from image deblurring.Such applications demand for a fast and parallel preconditioner realization. We present such an implementation introducing two new optimization techniques: First, we avoid redundant calculations using a dictionary. Second, our implementation reduces the runtime spent on the most demanding numerical parts as the code switches to sparse QR decomposition methods wherever profitable. The optimized code runs in parallel with a dynamic load balancing.     

Linear discriminant projection embedding based on patches alignment

Dimensionality reduction is often required as a preliminary stage in many data analysis applications. In this paper, we propose a novel supervised dimensionality reduction method, called linear discriminant projection embedding (LDPE), for pattern recognition. LDPE first chooses a set of overlapping patches which cover all data points using a minimum set cover algorithm with geodesic distance constraint. Then, principal component analysis (PCA) is applied on each patch to obtain the data's local representations. Finally, patches alignment technique combined with modified maximum margin criterion (MMC) is used to yield the discriminant global embedding. LDPE takes both label information and structure of manifold into account, thus it can maximize the dissimilarities between different classes and preserve data's intrinsic structures simultaneously. The efficiency of the proposed algorithm is demonstrated by extensive experiments using three standard face databases (ORL, YALE and CMU PIE). Experimental results show that LDPE outperforms other classical and state of art algorithms.