悬浮随机行走电容提取中多介质格林函数表的快速生成

为加速悬浮随机行走预刻画,利用了多介质格林函数本身的对称性,通过增加虚拟齐次纽曼边界,将有限差分空间离散区域缩减至原本的1/4,从而显著减小了差分矩阵的规模,加速了多介质格林函数表的生成.一般多介质格林函数表的对称性在理论上得到了证明.所提出的数值计算方法基于C++编程实现,其效率和正确性在一台32核服务器上通过数值实...     

An upscaling method using coefficient splitting and its applications to elliptic PDEs

In this paper, we develop an upscaling method using coefficient splitting techniques. Green’s function is constructed using the differential operator associated with the first part of the splitting. An effective upscaling coefficient is recursively calculated by Green’s function. The computation of the upscaling process involves some independent steps. Combining the proposed upscaling method with the stochastic collocation method, we present a stochastic space reduction collocation method, where the stochastic collocation method is performed on a lower dimension stochastic space than the full-dimension stochastic space. We thoroughly analyze the convergence of the proposed upscaling method for both deterministic and stochastic elliptic PDEs. Computation complexity is also addressed for the stochastic upscaling method. A number of numerical tests are presented to confirm the convergence analysis.     

Boundary element method based on preliminary discretization

A new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementation significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.     

Tri-cubic polynomial natural spline interpolation for scattered data

In this paper an interpolation problem for 3D scattered data defined on a rectangular parallelepiped with natural boundary conditions is considered. By using spline function theory in Hilbert space, we discuss the existence, uniqueness and characterization of the solution of the interpolation problem as well as its convergence. We show that the solution can be constructed in a simple way without using reproducing kernel semi-Hilbert space theory. Moreover, the solution can be written as the sum of tri-linear polynomials and piecewise tri-cubic polynomials and its coefficients can be determined by solving a positive semi-definite linear system. Numerical examples are presented to illustrate the proposed approach.     

Solution of Dirichlet problem for a rectangular region in terms of elliptic functions

In this study, the Green function of the (interior) Dirichlet problem for the Laplace (also Poisson) differential equation in a rectangular domain is expressed in terms of elliptic functions and the solution of the problem is based on the Green function and therefore on the elliptic functions. The method of solution for the Dirichlet problem by the Green function is presented; the Green function and transformation required for the solution of the Dirichlet problem in the rectangular region is found and the problem is solved in the rectangular region. An example for the problem in the rectangular region is given in order to present an application of the solution of Dirichlet problem. The equation is solved first by the known method of separation of variables and then in terms of elliptic functions; the results of both methods are compared. The results are found to be consistent but the advantage of this method is that the solution is obtained in terms of elementary functions.     

A novel inverse procedure for load identification based on improved artificial tree algorithm

This paper presents an accurate and effective method, namely, the improved artificial tree algorithm based on the Green’s kernel function method (IAT-GKFM), to identify the load in time domain. The forward problem of load identification is constructed by using the Green’s kernel function method. The forward problem is discretized using the time domain Galerkin method, where a matrix form for load identification is formed. The IAT algorithm is proposed to solve the inverse multi-dimensions problem in the inverse stage, which aims to minimize the measuring dispersion between the calculated response and the actual response. Several numerical examples are conducted. It is demonstrated that the IAT with high performance can provide more optimum results than those of other compared algorithms. Using this optimized strategy, the loads acting on a simple plate and a vehicle roof are reconstructed successfully. The superiority of IAT-GKFM may motivate the improvement of the other inverse problems.

     

The displacement field associated with line forces in a cracked orthotropic body

An explicit result is presented for the two-dimensional Green function for an orthotropic body containing a crack along an orthotropic plane and with its tip in an orthotropic direction. A formal solution and a numerical program for its calculation are presented for a crack on a plane rotated about an orthotropic direction. The use of such Green functions to couple a finite element mesh to a surrounding elastic continuum, thereby shortening finite element calculations for composite bodies with macroscopic orthotropic symmetry, is discussed.     

A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

A numerical multi-level optimization methodology is proposed for determining dextrous workspaces of 3-degree-of-freedom (3-dof) planar parallel manipulators, in which it is required that at any point within the workspace, the manipulator is able to assume any orientation in a specified range. The method starts by finding a single initial point on the boundary of the dextrous workspace. This first stage requires the successive solution of three separate optimization sub-problems, where the evaluation of the objective function for the second problem and the constraint functions in the third problem are determined by the solution of appropriate optimization problems at a lower level. Once the boundary point is identified, further successive points along the dextrous workspace boundary are traced by the application of the so-called chord method. In the latter procedure, the determination of each successive boundary point is also obtained via a constrained optimization problem, where the constraint functions are again evaluated via the solution of an optimization problem at a lower level. The proposed method is illustrated by its successful application to three different manipulator design geometries, and for various ranges of dexterity. An abbreviated version of this paper was presented at the 5th ASMO UK/ISSMO conference on Engineering Design Optimization, Stratford upon Avon, UK, July 12–13, 2004.     

Numerical study of temperature distribution in an inverse moving boundary problem using a meshless method

In this paper, we consider the inverse one-phase one-dimensional Stefan problem to study the thermal processes with phase change in a moving boundary problem and calculate the temperature distribution in the given domain, as well as approximate the temperature and the heat flux on a boundary of the region. For this problem, the location of the moving boundary and temperature distribution on this curve are available as the extra specifications. First, we use the Landau’s transformation to get a rectangular domain and then apply the Crank–Nicolson finite-difference scheme to discretize the time dimension and reduce the problem to a linear system of differential equations. Next, we employ the radial basis function collocation technique to approximate the spatial unknown function and its derivatives at each time level. Finally, the linear systems of algebraic equations constructed in this way are solved using the LU factorization method. To show the numerical convergence and stability of the proposed method, we solve two benchmark examples when the boundary data are exact or contaminated with additive noises.

     

An energy-efficient multi-objective integrated process planning and scheduling for a flexible job-shop-type remanufacturing system

This study considers an energy-efficient multi-objective integrated process planning and scheduling (IPPS) problem for the remanufacturing system (RMS) integrating parallel disassembly, flexible job-shop-type reprocessing, and parallel reassembly shops with the goal of realizing the minimization of both energy cost and completion time. The multi-objective mixed-integer programming model is first constructed with consideration of operation, sequence, and process flexibilities in the RMS for identifying this scheduling issue mathematically. An improved spider monkey optimization algorithm (ISMO) with a global criterion multi-objective method is developed to address the proposed problem. By embedding dynamic adaptive inertia weight and various local neighborhood searching strategies in ISMO, its global and local search capabilities are improved significantly. A set of simulation experiments are systematically designed and conducted for evaluating ISMO’s performance. Finally, a case study from the real-world remanufacturing scenario is adopted to assess ISMO’s ability to handle the realistic remanufacturing IPPS problem. Simulation results demonstrate ISMO’s superiority compared to other baseline algorithms when tackling the energy-aware IPPS problem regarding solution accuracy, computing speed, solution stability, and convergence behavior. Meanwhile, the case study results validate ISMO’s supremacy in solving the real-world remanufacturing IPPS problem with relatively lower energy usage and time cost.     

A numerical method for solving a three-dimensional electrical impedance tomography problem in the case of the data given on part of the boundary

A three-dimensional electrical impedance tomography problem in the case of an object with a piecewise constant electrical conductivity is considered. The task is to determine the unknown boundary separating regions of an object with different conductivity values, which are assumed to be known. The initial data for determining the inhomogeneity boundary represents electrical measurements taken on part of the object’s boundary. A numerical method for solving the problem is proposed and the numerical results are presented.     

Neural network modeling of vector multivariable functions in ill-posed approximation problems

A neural network solution of the ill-posed inverse approximation problem of a multivariable vector function based on of a committee of multilayer perceptrons is proposed. A nonlinear adaptive decision-making rule by the committee is developed that improves the accuracy compared with other neural network solutions of the inverse problem. Using a model example, the accuracy characteristics of the method are shown. An applied engineering problem is considered and the results of its solution by the proposed method are presented.     

A new symbolic method for solving linear two-point boundary value problems on the level of operators

We present a new method for solving regular boundary value problems for linear ordinary differential equations with constant coefficients (the case of variable coefficients can be adopted readily but is not treated here). Our approach works directly on the level of operators and does not transform the problem to a functional setting for determining the Green’s function.We proceed by representing operators as noncommutative polynomials, using as indeterminates basic operators like differentiation, integration, and boundary evaluation. The crucial step for solving the boundary value problem is to understand the desired Green’s operator as an oblique Moore–Penrose inverse. The resulting equations are then solved for that operator by using a suitable noncommutative Gröbner basis that reflects the essential interactions between basic operators.We have implemented our method as a Mathematica™ package, embedded in the TH$\exists$OREM$\forall$ system developed in the group of Prof. Bruno Buchberger. We show some computations performed by this package.     

Modeling an Inhomogeneous Coating of an Elastic Sphere with the Required Sound Reflecting Properties

We consider the inverse problem of determining the covering inhomogeneity of an elastic sphere characterized by the minimal reflection of a plane sound wave in a preset angular sector and frequency range. Based on an analytic solution to the direct problem, a functional expressing the reflection’s intensity is constructed and an algorithm for its minimization is proposed. The analytic expressions describing the mechanical parameters of an inhomogeneous coating are obtained.     

非线性时滞系统次优控制的逐次逼近法

对状态变量含有时滞的非线性系统的次优控制问题进行了研究，提出了一种次优控制的逐次逼近设计方法．针对由最优控制理论导出的既含有时滞项又含有超前项的非线性两点边值问题，构造了其解序列一致收敛于原问题最优解的非齐次线性两点边值问题序列．从而将两点边值问题解序列的有限次迭代结果作为系统的次优控制律．仿真结果表明了所提出方法的有效性．     

An efficient method for solving elliptic boundary element problems with application to the tokamak vacuum problem

A method for regularizing ill-posed Neumann Poisson-type problems based on applying operator transformations is presented. This method can be implemented in the context of the finite element method to compute the solution to inhomogeneous Neumann boundary conditions; it allows to overcome cases where the Neumann problem otherwise admits an infinite number of solutions. As a test application, we solve the Grad–Shafranov boundary problem in a toroidally symmetric geometry. Solving the regularized Neumann response problem is found to be several orders of magnitudes more efficient than solving the Dirichlet problem, which makes the approach competitive with the boundary element method without the need to derive a Green function. In the context of the boundary element method, the operator transformation technique can also be applied to obtain the response of the Grad–Shafranov equation from the toroidal Laplace n=1 response matrix using a simple matrix transformation.     

Singular perturbation method for initial value problems in two-parameter discrete control systems

A singularly perturbed discrete control system with two small parameters is formulated as an initial value problem. The process of degeneration affects the corresponding two groups of initial conditions. A singular perturbation method is developed based on double asymptotic power series expansions where the approximate solution is sought in terms of an outer solution and two boundary layer correction solutions. Owing to the interplay between the various steps involved in the actual working of the method, an algorithm is presented. An example is provided to illustrate the proposed method.     

Optimal stopping and control with two kinds of boundary conditions: application to dynamic routeing in networks

A stochastic optimal stopping and optimal control problem concerning the dynamic routeing of a randomly perturbed flow is considered. Equations for the solution of the optimal stopping and control problem are given. These equations lead to the solution of an elliptic problem with a given condition on a ‘ free boundary’ within a given domain D and a condition given on the boundary ? D of D. An example is given and a numerical study is conducted on it     

A novel time-marching scheme using numerical Green’s functions: A comparative study for the scalar wave equation

The present paper presents the formulation of a novel time-marching method based on the Explicit Green’s Approach (ExGA) to solve scalar wave propagation problems. By means of the weighted residual method in both time and space, the time integral expression concerning the ExGA is readily established. The arising ExGA time integral expression is spatially discretized in a finite element sense and a recursive scheme that employs time-domain numerical Green’s function matrices is adopted to evaluate the displacement and the velocity vectors. These Green’s matrices are computed by the time discontinuous Galerkin finite element method only at the first time step. The system of coupled equations originated from the time discontinuous Galerkin method is then solved by an iterative predictor–multicorrector algorithm. Once the Green’s matrices are computed, no iterative process is required to obtain the displacement and the velocity vectors at any time level. At the end of the paper, numerical examples are presented in order to compare the proposed approach with other approaches.     

Continuum equilibria and global optimization for routing in dense static ad hoc networks

We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton–Jacobi–Bellman equation, for the global optimization problem, (2) a method based on Green’s Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem.