Finite element solutions of convective diffusion problems

Three weighted residual methods are used to analyse several linear and nonlinear model problems related to the stream function–vorticity formulation of the Navier–Stokes equations. These methods are then used to solve the driven cavity problem. The results obtained at Reynolds numbers of 100 and 400 compare very favourably with those obtained by finite difference and spline methods on meshes using at least four times as many mesh points.     

Solution of a fully fuzzy multi-item economic order quantity problem by using fuzzy ranking functions

In this study, a fuzzy multi-item economic order quantity (EOQ) problem is solved by employing four different fuzzy ranking methods. All of the parameters of the multi-item EOQ problem are defined as triangular fuzzy numbers. Fuzzy ranking methods are used to rank the fuzzy objective values and to handle the constraints in the model. The results obtained by employing different fuzzy ranking methods are also compared.     

Multiobjective optimization with an adaptive weight determination scheme using the concept of hyperplane

Finding an optimum design that satisfies all performances in a design problem is very challenging. To overcome this problem, multiobjective optimization methods have been researched to obtain Pareto optimum solutions. Among the different methods, the weighted sum method is widely used for its convenience. However, since the different weights do not always guarantee evenly distributed solutions on the Pareto front, the weights need to be determined systematically. Therefore, this paper presents a multiobjective optimization using a new adaptive weight determination scheme. Solutions on the Pareto front are gradually found with different weights, and the values of these weights are adaptively determined by using information from the previously obtained solutions' positions. For an n-objective problem, a hyperplane is constructed in n -dimensional space, and new weights are calculated to find the next solutions. To confirm the effectiveness of the proposed method, benchmarking problems that have different types of Pareto front are tested, and a topology optimization problem is performed as an engineering problem. A hypervolume indicator is used to quantitatively evaluate the proposed method, and it is confirmed that optimized solutions that are evenly distributed on the Pareto front can be obtained by using the proposed method.     

A two-phase computational scheme for solving bang-bang control problems

This paper focuses on numerical methods for solving time-optimal control problems using discrete-valued controls. A numerical Two-Phase Scheme, which combines admissible optimal control problem formulation with enhanced branch-and-bound algorithms, is introduced to efficiently solve bang-bang control problems in the field of engineering. In Phase I, the discrete restrictions are relaxed, and the resulting continuous problem is solved by an existing optimal control solver. The information on switching times obtained in Phase I is then used in Phase II wherein the discrete-valued control problem is solved using the proposed algorithm. Two numerical examples, including a third-order system and the F-8 fighter aircraft control problem, are presented to demonstrate the use of this proposed scheme. Comparing to STC and CPET methods proposed in the literature, the proposed scheme provides a novel method to find a different switching structure with a better minimum time for the F-8 fighter jet control problem.     

变分方法在时标上一类边值问题中的应用

本文研究时标T上一类非自治的二阶周期边值问题周期解的存在性.我们综合利用临界点理论和变分方法,先利用变分方法将研究边值问题解的存在性问题转化为研究一个算子临界点问题,再借助于广义山路引理得到所研究边值问题存在至少一个周期解,所得结果在相应的微分方程,差分方程以及通常的时标上都是新的,作为应用,给出了一个例子验证了所得结论.     

位移障碍下变分不等式问题的各向异性非协调有限元方法

本文研究位移障碍下二阶变分不等式问题在各向异性网格上的非协调有限元逼近。通过运用新的方法和技巧,得到了与正则网格剖分下相同的最优误差估计,从而扩展了有限元的应用范围。     

Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation

In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the stability, of the numerical methods proposed are analysed. The Cauchy problem for the Helmholtz equation can be regularized by various methods, such as the general regularization methods presented in this paper, but more accurate results are obtained by classical methods, such as the singular value decomposition and the Tikhonov regularization methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Radial basis functions methods for solving Fokker-Planck equation

In this paper two numerical meshless methods for solving the Fokker-Planck equation are considered. Two methods based on radial basis functions to approximate the solution of Fokker-Planck equation by using collocation method are applied. The first is based on the Kansa's approach and the other one is based on the Hermite interpolation. In addition, to conquer the ill-conditioning of the problem for big number of collocation nodes, two time domain Discretizing schemes are applied. Numerical examples are included to demonstrate the reliability and efficiency of these methods. Also root mean square and N_e errors are obtained to show the convergence of the methods. The errors show that the proposed Hermite collocation approach results obtained by the new time-Discretizing scheme are more accurate than the Kansa's approach.     

On comparing the accuracy of some finite difference methods for parabolic partial differential equations

Methods for comparing the accuracy of numerical methods for the solution of parabolic partial differential equations are briefly surveyed. Criteria for a more systematic comparison are proposed and applied to an accuracy comparison of the classical and the modified Saul'yev methods and the Crank–Nicholson method on a simple linear problem. The results obtained, which include observation of the existence of optimal spatial mesh size for the two Saul'yev methods, are discussed.     

基于遗传算法的图关联着色算法

图的着色算法是一种典型的NP-完全问题。给出了一种用于图的关联着色的遗传算法。遗传算法用于进行全局搜索,从而有效的查找解空间。文中对关联色数为6的一个图进行了仿真实验,给出了该图的关联色数以及4种6-关联着色。用本文提出的算法,得到了完全图、完全多部图的关联色数。实验结果表明,本文设计的遗传算法可以很好的对关联着色猜想进行求解,获得问题的高质量的解。     

New methods and technologies for identification of routes of measurements obtained with the use of optical devices traveling on different trajectories

New methods and technologies for the identification of the measurement routes obtained with the use of different trajectories of optical devices are presented. It is shown that simplified mathematical methods of matrix analysis applied to the entire set of measurement results obtained have to be developed to solve this problem.     

Integrated structure and control design of actively controlled structures using substructure decomposition

This paper presents a substructuring based approach to the combined structure and control system design problem for flexible space structures. The proposed approach involves decomposing the structure to be controlled into a number of substructures. The substructure information obtained through finite element analysis is synthesized to reconstruct a reduced order model for the entire structure. Two approaches for controller design based on linear quadratic regulator (LQR) theory are proposed. The first approach involves designing a controller for the entire structure obtained by assembling individual substructures. For the second approach, the global controller is obtained by assembling all subcontrollers designed at the substructure level. The integrated control/structure design problem is solved iteratively until a minimum weight design is achieved. A numerical example which compares the results obtained from both the methods with those obtained by directly synthesizing a global controller for the entire structure is presented. The results indicate that both methods proposed herein provide good agreement with the results obtained by analyzing the structure in its entirety.     

A New Forward-Problem Solver Based on a Capacitor-Mesh Model for Electrical Capacitance Tomography

An electrical-capacitance-tomography sensor consists of a set of measurement electrodes. It is difficult to calculate the capacitance for a given sensor structure and given permittivity distribution, which is called solving the forward problem, theoretically. Therefore, finite-element methods (FEM) and finite-difference methods are commonly used to solve the forward problem and to generate a sensitivity matrix for image reconstruction. This paper presents a new approach to solving the forward problem based on a capacitor-mesh model. It has been used for iterative image reconstruction using an updated sensitivity matrix according to an estimated image. In this paper, some simulation results are presented and compared with the results obtained using an FEM software package from Ansoft Company, showing that the new approach is promising.     

Primal-dual sensitivity analysis of active sets for mixed boundary-value contact problems

The constrained minimization problem of contact mechanics is investigated as a mixed boundary-value problem determined on the active (contact) set of the solution. Using primal-dual methods of the shape sensitivity analysis, asymptotic expansions of the primal and dual state variables and the cost functional of energy are obtained with respect to a perturbation of the active set in the direction of an arbitrary velocity vector field.     

基于向量式有限元的输电塔风致动力响应研究

该文以某大跨越格构式输电塔风致响应为例进行向量式有限元的应用分析,采用C++语言编写杆系结构向量式有限元的计算程序,获得输电塔的响应并与传统有限元结果进行比较,探讨阻尼处理方法和计算步长对计算结果的影响,最后针对输电塔进行风荷载作用下的倒塌分析。研究表明,两种方法算得的位移响应非常接近;向量式有限元法的计算效率比传统有限元高,该文算例中计算时间相差约20倍;计算步长对有限元计算结果有影响,建议计算时进行试算;向量式有限元可以用来求解输电塔的倒塌问题。     

Numerical solution of fuzzy boundary value problems using Galerkin method

This paper proposes a new technique based on Galerkin method for solving nth order fuzzy boundary value problem. The proposed method has been illustrated by considering three different cases depending upon the sign of coefficients with benchmark example problems. To show the applicability of the proposed method, an application problem related to heat conduction has also been studied. The results obtained by the proposed methods are compared with the exact solution and other existing methods for demonstrating the validity and efficiency of the present method.     

Generalisation of unidirectional loop layout problem and solution by a genetic algorithm

Unidirectional loop layouts (ULLs) are the preferred layouts in manufacturing systems owing to their relative low investment costs, high material handling elasticity and routing flexibility. Existing formulations of the unidirectional loop layout problem are concentrated on the arrangement of workstations under the assumption that the number and location of loading and unloading stations are known. In this study, the unidirectional loop layout problem is generalised by consideration of potentially attachable loading/unloading equipment to each workstation and releasing of the predetermined number of loading and unloading stations. Thus, more efficient and effective loop layout designs are allowed by eliminating some artificial restrictions. The present ULL model is generalised and a genetic algorithm is developed to solve the problem. Solutions obtained by the genetic algorithm outperformed those obtained by conventional methods. Additionally, comparisons of the generalised model with existing models on randomly generated test problems yielded encouraging results.     

Inexact FETI‐DP methods

Inexact FETI‐DP domain decomposition methods are considered. Preconditioners based on formulations of FETI‐DP as a saddle point problem are used which allow for an inexact solution of the coarse problem. A positive definite reformulation of the preconditioned saddle point problem, which also allows for approximate solvers, is considered as well. In the formulation that iterates on the original FETI‐DP saddle point system, it is also possible to solve the local Neumann subdomain problems inexactly. Given good approximate solvers for the local and coarse problems, convergence bounds of the same quality as for the standard FETI‐DP methods are obtained. Numerical experiments which compare the convergence of the inexact methods with that of standard FETI‐DP are shown for 2D and 3D elasticity using GMRES and CG as Krylov space methods. Based on parallel computations, a comparison of one variant of the inexact FETI‐DP algorithms and the standard FETI‐DP method is carried out and similar parallel performance is achieved. Parallel scalability of the inexact variant is also demonstrated. It is shown that for a very large number of subdomains and a very large coarse problem, the inexact method can be superior. Copyright © 2006 John Wiley & Sons, Ltd.     

Photonic bandgap calculations with Dirichlet-to-Neumann maps

A simple and efficient method for computing bandgap structures of two-dimensional photonic crystals is presented. Using the Dirichlet-to-Neumann (DtN) map of the unit cell, the bandgaps are calculated as an eigenvalue problem for each given frequency, where the eigenvalue is related to the Bloch wave vector. A linear matrix eigenvalue problem is obtained even when the medium is dispersive. For photonic crystals composed of a square lattice of parallel cylinders, the DtN map is obtained by a cylindrical wave expansion. This leads to eigenvalue problems for relatively small matrices. Unlike other methods based on cylindrical wave expansions, sophisticated lattice sums techniques are not needed.     

Methods for optimum and near optimum disassembly sequencing

This paper considers disassembly sequencing problems subjected to sequence dependent disassembly costs. In practice, the methods for dealing with such problems rely mainly on metaheuristic and heuristic methods, which intrinsically generate suboptimum solutions. Exact methods are NP-hard and therefore unsuitable to most of the practical problems. Nevertheless, it is useful to have exact methods available that can be applied in order to check, at least medium sized problems, to what extent the heuristically obtained solutions deviate from the optimum solution. The existing exact approaches, which are based on integer linear programming (ILP), become unmanageable, even for the cases of modest product complexity. To alleviate this problem to some extent, the iterative method that has been proposed by Lambert (2006) is applied here. This method is based on repeatedly solving a binary integer linear programming (BILP) problem instead of an ILP problem. The method appears to converge sufficiently quickly to be valuable for dealing with medium sized problems. We then use the iterative method for the validation of a new heuristic method that is also proposed in this paper. Finally, both the heuristic and the iterative BILP methods are implemented on a cellphone from practice consisting of 25 components that are represented, according to a set of precedence relationships, via a disassembly precedence graph.