变系数偏微分方程的Galerkin KPOD模型降阶方法

研究了变系数偏微分方程的 Galerkin KPOD (Krylov Enhanced Proper Orthogonal Decomposition)模型降阶方法.首先基于Galerkin有限元理论建立变系数偏微分方程的空间离散格式,得到具有时变系数矩阵的常微分方程组,并对该常微分方程组应用KPOD模型降阶方法进行降阶并求解.其次,对降阶投影算子进行了分析,给出了 Galerkin有限元解与Galerkin KPOD降阶解之间的误差界.最后用数值算例验证了变系数偏微分方程的Galerkin KPOD模型降阶求解方法的可行性,通过有限元离散解与Galerkin KPOD降阶解、Galerkin POD降阶解之间的误差比较,体现Galerkin KPOD降阶方法的优势.     

基于对称多项式理论及吴方法求解逆变器选择性消谐多项式

提出了一种利用对称多项式简化求解逆变器选择性消谐多项式的方法.基于余式理论求解逆变器选择性消谐多项式方程组,会出现当要求解多个开关角时,多项式方程的次数较高、计算工作量大的问题.为此,本文首先利用对称多项式理论降低该多项式方程组的次数,然后利用吴方法及置换法求解多项式方程组,结果表明,最后只需计算一些代数表达式就可得到选择性消谐多项式方程组的所有解,大大减少了计算量,提高了在线计算的速度.     

旋转对称矩量法高阶算法研究

直接应用三维矩量法求解旋转对称目标的电磁散射特性计算效率较低,计算机内存耗费大,利用其结构特点可降维获得一种更为有效的计算方式。然而对于电大目标,这种改进依然是不够的。文中根据旋转对称目标矩量法（ BOR-MOM）中电流的分解特征,构建了一种基于切比雪夫近似的高阶基函数,将电流的切向分量和方位角分量分别以该高阶基函数展开后应用矩量法求解。实验结果表明：高阶BOR-MOM算法在低剖分下,具有很高的计算精度,计算效率和存储耗费得到了较大改善。     

Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models. Often, it is known beforehand that the underlying unknown function has certain properties, e.g., nonnegative or increasing on a certain region. However, the approximation may not inherit these properties automatically. We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials, and rational functions that preserve nonnegativity.     

Solving the multi-buyer joint replenishment problem with the RAND method

The multi-buyer joint replenishment problem (MJRP) is the multi-item inventory problem of coordinating the replenishment of a group of items that are jointly ordered from a single supplier. Joint replenishment of a group of items reduces cost by decreasing the number of times that the major ordering cost is charged. The objective of MJRP is to develop inventory policies minimizing the total costs over the planning horizon. The single buyer joint replenishment problem may be solved by techniques using the collectively described as the best available heuristics (e.g. Simulated Annealing, Genetic Procedures, Tabu Search, and others), collectively discussed as the RAND method. In this paper, we propose a new efficient RAND method to solve MJRP.     

Solving fuzzy differential equations by differential transformation method

An extension of the differential transformation method (DTM), which is an analytical-numerical method for solving the fuzzy differential equation (FDE), is given. The concept of generalised H-differentiability is used. This concept is based on an enlargement of the class of differentiable fuzzy mappings; to define this, the lateral Hukuhara derivatives are considered. The proposed algorithm is illustrated by numerical examples, and some error comparisons are made with other methods for solving a FDE.     

0-1背包问题的模糊粒子群算法求解*

针对基本粒子群算法在背包问题上表现的不足,在基本粒子群算法的基础上运用模糊规则表加入了新的扰动因子,提出了一种新的算法——模糊粒子群算法。该算法结合了模糊控制器中输入/输出的模糊化处理和粒子群寻优的特点,为实际问题提供了新的解决手段。将模糊粒子群算法应用于0-1背包问题上,通过多组实例数据进行测试,验证表明了本算法具有良好的有效性和鲁棒性。     

Solving a system of third-order boundary value problem using variational iteration method

In this paper, the variational iteration method is used to solve a system of third-order boundary value problem associated with obstacle, unilateral and contact problems. Numerical solution obtained by the method is of high accuracy. The numerical example compared with those considered by other authors shows that the method is more efficient.     

Solving a sealed-bid reverse auction problem by multiple-criterion decision-making methods

This study presents a model for solving the sealed-bid, multiple-issue reverse auction problem, using multiple-criterion decision-making approaches, such that the interests of both the buyer and the supplier are satisfied. On the supplier side, the bid construction process is formulated as a fuzzy multiple-objective programming problem, and is solved using an exhausted enumeration algorithm which adjusts the production plan in accordance with the buyer’s demand, based on the current master production schedule (MPS) and the available-to-promise (ATP) inventory. The use of the information of MPS and ATP enables the supplier to make accurate estimates of the production costs associated with specific delivery dates, and thus facilitates the construction of a bid which is both profitable and likely to secure the contract. On the buyer side, the winner determination process is treated as a multiple-attribute decision-making problem, and is solved using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. The validity of the proposed approach is demonstrated via an illustrative example.     

Implementation of PEC boundary condition for Laguerre‐RPIM meshless method with novel uniform nodal distribution

The implementation of perfect electric conductor (PEC) boundary condition for meshless radial point interpolation method (RPIM) with the weighted decaying Laguerre polynomial (WLP) is investigated. A novel uniform nodal placement is proposed and the number of H‐nodes reduces to about a half of that for the conventional scheme. There are only E‐nodes scattered on the PEC boundary. The E‐node and H‐node have the same scale of support domain nodes. The image theory is adopted to update the implicit electric equations on the PEC boundary. This scheme is also suitable for nonuniform node distribution. Numerical results have verified the accuracy of the proposed method.     

Solution of initial value problems by the differential quadrature method with Hermite bases

The differential quadrature method (DQM) is used to solve the first-order initial value problem. The initial condition is given at the beginning of the interval. The derivative of a space-independent variable at a sampling grid point within the interval can be defined as a weighted linear sum of the given initial conditions and the function values at the sampling grid points within the defined interval. Hermite polynomials have advantages compared with Lagrange and Chebyshev polynomials, and so, unlike other work, they are chosen as weight functions in the DQM. The proposed method is applied to a numerical example and it is shown that the accuracy of the quadrature solution obtained using the proposed sampling grid points is better than solutions obtained with the commonly used Chebyshev–Gauss–Lobatto sampling grid points.