Numerical analysis and computation of a multi-order laminated microstructure

The mesh transformation method is applied in a finite element approximation to a multi-well problem. It is proved that, compared with standard finite element methods, significantly higher convergence rate for the finite element approximations of multi-level microstructures can be obtained by combining the mesh transformation method with the periodic relaxation technique. Numerical examples are given to show the method can be efficiently implemented in computing multi-level microstructures.     

基于模糊数学和灰色理论的多层次综合评价方法及其应用

针对多层次指标体系的综合评价问题,在模糊综合评判方法的基础上,结合灰色理论,提出了一种新的定量综合评价方法—多层次模糊灰关联聚类分析综合评价方法.应用该方法对油气钻井技术进行综合评价,取得了满意的结果.     

Natural laminar flow shape optimization in transonic regime with competitive Nash game strategy

The Natural Laminar Flow (NLF) airfoil/wing design optimization is an efficient method which can reduce significantly turbulence skin friction by delaying transition location at high Reynolds numbers. However, the reduction of the friction drag is competitively balanced with the increase of shock wave induced drag in transonic regime. In this paper, a distributed Nash Evolutionary Algorithms (EAs) is presented and extended to multi-level parallel computing, namely multi-level parallel Nash EAs. The proposed improved methodology is used to solve NLF airfoil shape design optimization problem. It turns out that the optimization method developed in this paper can easily capture a Nash Equilibrium (NE) between transition delaying and wave drag increasing. Results of numerical experiments demonstrate that both wave drag and friction drag performances of a NE are greatly improved. Moreover, performance of the NE is equivalent to that of cooperative Pareto-optimum solutions, but it is more efficient in terms of CPU time. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.     

A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier–Stokes equations

This paper proposes and analyzes a stabilized multi-level finite volume method (FVM) for solving the stationary 3D Navier?CStokes equations by using the lowest equal-order finite element pair without relying on any solution uniqueness condition. This multi-level stabilized FVM consists of solving the nonlinear problem on the coarsest mesh and then performing one Newton correction step on each subsequent mesh, thus only solving a large linear system. An optimal convergence rate for the finite volume approximations of nonsingular solutions is first obtained with the same order as that for the usual finite element solution by using a relationship between the stabilized FVM and a stabilized finite element method. Then the multi-level finite volume approximate solution is shown to have a convergence rate of the same order as that of the stabilized finite volume solution of the stationary Navier?CStokes equations on a fine mesh with an appropriate choice of the mesh size: ${ h_{j} ~ h_{j-1}^{2}, j = 1,\ldots, J}$ . Finally, numerical results presented validate our theoretical findings.     

A fast wavelet block Jacobi method

In this paper, we develop a fast block Jacobi method for linear systems based on discrete wavelet transform (DWT). Traditional wavelet-based methods for linear systems do not fully utilize the sparsity and the multi-level block structure of the transformed matrix after DWT. For the sake of numerical efficiency, we truncate the transformed matrix to be a sparse matrix by letting the small values be zero. To combine the advantages of the direct method and the iterative method, we solve the sub-systems appropriately based on the multi-level block structure of the transformed matrix after DWT. Numerical examples show that the proposed method is very numerically effective.     

Convergence of multi-level iterative aggregation-disaggregation methods

This paper introduces an error propagation formula of a certain class of multi-level iterative aggregation-disaggregation (IAD) methods for numerical solutions of stationary probability vectors of discrete finite Markov chains. The formula can be used to investigate convergence by computing the spectral radius of the error propagation matrix for specific Markov chains. Numerical experiments indicate that the same type of the formula could be used for a wider class of the multi-level IAD methods. Using the formula we show that for given data there is no relation between convergence of two-level and of multi-level IAD methods.     

改进的多层次分析法的研究及应用

通过结合变权综合原理,改进了多层次综合评价模型,模型可以充分利用所给数据中的隐含信息,根据专家的要求,得出更为科学合理的决策方案,同时基于变权的多层次分析方法可以更好的解决因常权导致评价结果相同的问题.     

MULTI-LEVEL ADAPTIVE CORRECTIONS IN FINITE DIMENSIONAL APPROXIMATIONS

Based on the Boolean sum technique, we introduce and analyze in this paper a class of multi-level iterative corrections for finite dimensional approximations. This type of multi-level corrections is adaptive and can produce highly accurate approximations. For illustration, we present some old and new finite element correction schemes for an elliptic boundary value problem.     

Continuous level anisotropic diffusion for noise removal

This paper presents a new approach to anisotropic diffusion and noise removal. Several functionals are introduced to a variational model. The diffusion behavior is governed by a nonlinear partial differential equation. A dynamic threshold function plays an important role in the continuous level anisotropic diffusion and a related optimization problem is presented. The noise can be removed while the edge well preserved. Multi-level noise or multi-level edge can be handled automatically. Finally, the accuracy and efficiency of the proposed method are verified by several numerical experiments.     

Convergence of multi-level iterative aggregation–disaggregation methods

This paper introduces an error propagation formula of a certain class of multi-level iterative aggregation–disaggregation (IAD) methods for numerical solutions of stationary probability vectors of discrete finite Markov chains. The formula can be used to investigate convergence by computing the spectral radius of the error propagation matrix for specific Markov chains. Numerical experiments indicate that the same type of the formula could be used for a wider class of the multi-level IAD methods. Using the formula we show that for given data there is no relation between convergence of two-level and of multi-level IAD methods.     

A Hybrid Meta-Heuristic for the Batching Problem in Just-In-Time Flow Shops

This paper is concerned with a batching problem encountered in the context of production smoothing in just-in-time manufacturing systems. The manufacturing system of interest is a multi-level system with a flow-shop at the final level. We develop a hybrid meta-heuristic method to solve the batching problem, which is known to be NP-hard. We hybridize strategic oscillation (SO) and path re-linking (PR) methods and compare the hybrid method's performance to two benchmark methods: a bounded dynamic programming method developed for the problem earlier and an implementation of robust tabu search (RTS) meta-heuristic. Through a computational study, we show that the proposed hybrid method is effective in solving the problem within several minutes of computer time and yielding near-optimal results.     

具有引导变量的多层递阶方法在黑龙江省哈尔滨市天气预报中的应用

对多层递阶基本问题做了简要的叙述,紧紧围绕多层递阶方法发展的两个新方向,即多模型、多算法的综合预报模式和带有引导变量模型的预报模式,并对其进行改进,利用改进后的模型和算法对黑龙江省哈尔滨市的月平均气温进行了具体的预报,预报的效果令人满意.     

The relaxation of non-quasiconvex variational integrals

We show that the Steepest Descent Algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum of the associated non-quasiconvex variational integrals. We introduce a multi-level infinite dimensional variant of the Steepest Descent Algorithm designed to compute complex microstructures by forming non-smooth minimizers from the smooth initial guesses. We apply this multi-level method to the minimization of the variational problems associated with martensitic branching. Received December 2, 1997 / Revised version received March 13, 1998     

Interpolating Cubic Spline Wavelet Packet on Arbitrary Partitions

In many applications, the splines on an arbitrary partition are very useful. In this paper, a spline wavelet structure is created in the way that it provides a multiresolution approximation of the spline subspaces with arbitrary partition in the space of continuous functions on a finite interval. Based on the wavelet basis and the wavelet packet in this structure, a multi-level interpolation method is developed for decomposing a function into wavelet series and reconstructing it from its wavelet representation.     

Multiscale RBF collocation for solving PDEs on spheres

In this paper, we discuss multiscale radial basis function collocation methods for solving certain elliptic partial differential equations on the unit sphere. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. Two variants of the collocation method are considered (sometimes called symmetric and unsymmetric, although here both are symmetric). A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions.     

On algebraic multi-level methods for non-symmetric systems - Comparison results

We establish theoretical comparison results for algebraic multi-level methods applied to non-singular non-symmetric M-matrices. We consider two types of multi-level approximate block factorizations or AMG methods, the AMLI and the MAMLI method. We compare the spectral radii of the iteration matrices of these methods. This comparison shows, that the spectral radius of the MAMLI method is less than or equal to the spectral radius of the AMLI method. Moreover, we establish how the quality of the approximations in the block factorization effects the spectral radii of the iteration matrices. We prove comparisons results for different approximations of the fine grid block as well as for the used Schur complement. We also establish a theoretical comparison between the AMG methods and the classical block Jacobi and block Gauss-Seidel methods.     

Solution of the Cumulative Assignment Problem With a Well-Structured Tabu Search Method

The Cumulative Assignment Problem is an NP-complete problem obtained by substituting the linear objective function of the classic Linear Assignment Problem, with a non-linear cumulative function. In this paper we present a first attempt to solve the Cumulative Assignment Problem with metaheuristic techniques. In particular we consider two standard techniques, namely the Simulated Annealing and the Multi-Start methods, and we describe the eXploring Tabu Search: a new structured Tabu Search algorithm which uses an iterative multi-level approach to improve the search. The new method is analyzed through extensive computational experiments and proves to be more effective than the standard methods.     

Interactive TOPSIS algorithms for solving multi-level non-linear multi-objective decision-making problems

This paper extended the concept of the technique for order preference by similarity to ideal solution (TOPSIS) to develop a methodology for solving multi-level non-linear multi-objective decision-making (MLN-MODM) problems of maximization-type. Also, two new interactive algorithms are presented for the proposed TOPSIS approach for solving these types of mathematical programming problems. The first proposed interactive TOPSIS algorithm includes the membership functions of the decision variables for each level except the lower level of the multi-level problem. These satisfactory decisions are evaluated separately by solving the corresponding single-level MODM problems. The second proposed interactive TOPSIS algorithm lexicographically solves the MODM problems of the MLN-MOLP problem by taking into consideration the decisions of the MODM problems for the upper levels. To demonstrate the proposed algorithms, a numerical example is solved and compared the solutions of proposed algorithms with the solution of the interactive algorithm of Osman et al. (2003) [4]. Also, an example of an application is presented to clarify the applicability of the proposed TOPSIS algorithms in solving real world multi-level multi-objective decision-making problems.     

基于熵权及国际生产折衷理论的中国煤炭贸易国际竞争优势评价

利用国际生产折衷理论建立了煤炭贸易国际竞争优势评价指标体系,从专属优势、区位优势、内部化优势和国际化程度的角度对各主要煤炭出口国的竞争优势进行基于熵权的多层次综合评价.指出与其他煤炭出口国相比,中国煤炭贸易竞争优势主要来自于专属优势以及部分区位因素,而在国际化程度上明显处于劣势,同时指出了中国煤炭企业的挖潜方向.     

质量符合性评价体系的本体化建模及评价支持实证研究

本文面向质量管理评价领域对精细化和科学性的需求,研究质量符合性评价体系所蕴涵的知识共性,提出了一种构建符合性评价知识系统的多层本体化模型框架,设计了涵盖两种不同粒度水平的评价知识构成元模型,以此获取质量符合性评价在语义层次上的支持。最后,以信息安全产品防火墙质量评价为例实证了一类质量符合性评价体系知识本体的构建,以及基于规则推理的自动评价决策支持应用。