求解远场声辐射问题的一种快速边界元法

针对传统边界元法奇异性的固有缺陷,研究一种求解结构辐射声场的间接边界元法。通过在内域虚拟曲面上配置一系列单偶极子源,等效模拟结构外辐射声场,并根据单元体积速度匹配法的边界条件方案,给出数值计算辐射声场的间接边界元模型。结合球冠形辐射器的仿真算例,表明该间接边界元法在求解远场声特性时具有较高的计算效率和精度,为分析设计具有大空间指向性的辐射器提供参考。     

求解二维结构-声耦合问题的一种直接方法

本文基于传递矩阵法(TMM)和虚拟边界元法(VBEM)，提出了一种求解在谐激励作用下二维结构-声耦合问题的直接法。文中对任意形状的二维弹性环建立了一阶非齐次运动微分方程组，便于用齐次扩容精细积分法求解，对于含有任意形状孔穴的无穷域流体介质的Helmholtz外问题，采用复数形式的Burton-Miller型组合层势法建立了虚拟边界元方程，保证了声压在全波数域内存在唯一解。根据叠加原理并结合最小二乘法，提出了一种耦合方程的直接解法，由于该方法不存在迭代过程，因而具有较高的计算精度和效率。文中给出了二个典型弹性环在集中谐激励力作用下声辐射算例，计算结果表明本文方法较通常采用的混合FE／BE法更为有效。     

求解具有长条型内边界的外问题的一种重叠型区域分解算法

以二维调和方程外问题为例，提出一种带椭圆型人工边界的重叠型区域分解算法，理论分析及数值实验表明，用该方法求解带长条型内边界的外问题是十分有效的。     

一种求解JSP问题的混合蚁群算法

提出一种混合蚁群算法,并用其解决经典JSP问题.受转换瓶颈启发式算法的启示,将蚁群算法与禁忌搜索算法相结合,发现这种改进在防止早熟与加速收敛这对矛盾之间找到了一个比较好的结合点.     

一刀切约束下的二维装箱问题高效求解算法

目的 为实现大规模物料的快速剪裁切割,对考虑一刀切约束的二维装箱问题进行研究,并构建相应的改进优先度算法IPH(Improved Priority Algorithm,IPH).方法 IPH能够在不需要任何迭代搜索下,直接进行剩余空间分割与填充.为此,发展PH算法中的优先度放置规则,并以最大化生成大空间面积和最小化生成小空间面积为基础,设计改进砌砖式空间分割策略.结果 针对标准数据集的对比实验表明,IPH能够在较短时间内完成大规模算例的高效求解,并首次获得了多个算例的最优填装效果.结论 基于概率较优的启发式求解方法,能够实现无迭代优选下的一刀切二维装箱问题直接求解,且运算效果令人满意.     

求解混合互补问题的一种内点算法

针对混合互补问题,提出了一种在数值上具有稳健性质的内点算法,并证明了其收敛性定理,数值例子表明这一算法是有效的。     

物流车辆路径问题的混合快速蚂蚁算法

通过分析快速蚂蚁算法的原理和易陷入局部最优的缺点,提出了将贪婪算法和快速蚂蚁算法相结合的混合算法求解物流车辆路径问题.混合算法在最优值未改进次数超过限定次数时,自动调用贪婪算法来寻找一个局部最优解,并调整相应路径上信息素的量.为保证解的多样性,对贪婪算法本身使用随机选择第一个客户的方法进行了调整.用计算实例比较并分析了快速蚂蚁算法、混合算法及其他算法应用到车辆路径问题上的结果,说明了贪婪算法使混合算法跳出局部最优的过程以及混合算法的不足之处.     

一种求解TSP问题的粒子群算法设计

旅行问题(Traveling Salesman Problem,简称TSP)是求一次遍访指定城市并返回出发城市的最短旅行路线的问题,它是图论中一个经典的NP完全问题,用电子计算机需要指数级的时间才能得到解决.尝试用粒子群算法来求解旅行商问题,结合遗传算法的思想,并且给出交叉和变异操作的设计.该算法符合组合优化问题的特点,在求解旅行商问题上有较高的搜索效率.     

一种求解船舶配载问题的混合遗传算法

通过对生产实际中散装货船的多品种、大批量货物的配载问题的分析,总结了散装船舶配载问题的特点和钢铁产品的货物堆装规则;以船舶舱容限制、允许重量和货物堆装规则为约束条件,以提高仓容利用率和装载效率为优化目标,构造了一种混合遗传算法来解决此类多目标、多约束的组合优化问题,即①用启发式算法确定各舱货物的具体摆放方式,满足货物装载质量要求,②遗传算法调用启发式算法,计算配载指标,来确定货物在各舱的分布,以满足各舱的仓容限制,提高仓容利用率和装载效率.     

论Helmholtz方程的一类边界积分方程的合理性

本文导出了Helmholtz 方程超定边值问题有解的一个充要条件,和用非解析开拓法证明了文[1]中的Helmholtz 方程在外域中的解的边界积分表示式的合理性,并将此类边界积分表示式推广用于带空洞的有限域。这样就比较严密而又浅近地证明了基于该表示式建立起来的间接变量和直接变量边界积分方程的合理性。     

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.     

Boundary knot method for some inverse problems associated with the Helmholtz equation

The boundary knot method is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the solution of partial differential equations. In this paper, the method is applied to the solution of some inverse problems for the Helmholtz equation, including the highly ill‐posed Cauchy problem. Since the resulting matrix equation is badly ill‐conditioned, a regularized solution is obtained by employing truncated singular value decomposition, while the regularization parameter for the regularization method is provided by the L‐curve method. Numerical results are presented for both smooth and piecewise smooth geometry. The stability of the method with respect to the noise in the data is investigated by using simulated noisy data. The results show that the method is highly accurate, computationally efficient and stable, and can be a competitive alternative to existing methods for the numerical solution of the problems. Copyright © 2005 John Wiley & Sons, Ltd.     

各向异性外问题的非均匀网格的自然边界元法及其耦合法

本文对于无界区域上各向异性外问题提出了在椭圆边界非均匀网格上的自然边界元法及其与有限元法的耦合法,证明相应的收敛定理和误差估计式,并且在这两种方法中引入基于等分布原理的移动网格技巧.最后,通过数值结果表明了误差收敛理论的正确性以及所提方法和技巧的有效性.     

Solution of Inverse Boundary Optimization Problem by Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm

The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the generation of mesh grid and numerical integration. In the boundary optimization problem governed by the Helmholtz equation, the numerical solution of TM is expressed as linear combination of the T-complete functions. When this problem is considered by TM, a system of nonlinear algebraic equations will be formed and solved by ECSHA which will converge exponentially. The evolutionary process of ECSHA can acquire the unknown coefficients in TM and the spatial position of the unknown boundary simultaneously. Some numerical examples will be provided to demonstrate the ability and accuracy of the proposed scheme. Besides, the stability of the proposed meshless method will be validated by adding some noise into the boundary conditions.     

二维新型快速多极虚边界元配点法

以二维弹性问题为研究背景, 提出了一种二维新型快速多极虚边界元配点法的求解思想, 即采用新型的快速多极展开和运用广义极小残值法来求解传统的虚边界元配点法方程。相对常规快速多极展开技术, 该文针对二维弹性问题在原有的快速多极虚边界元法展开格式的基础上, 通过引入对角化的概念, 以更新展开传递格式, 欲达到进一步提高计算效率的目的。数值算例说明了该方法的可行性, 计算效率和计算精度。此外, 该文方法的思想具有一般性, 应用上具有扩展性。     

A wideband fast multipole accelerated boundary integral equation method for time‐harmonic elastodynamics in two dimensions

This article presents a wideband fast multipole method (FMM) to accelerate the boundary integral equation method for two‐dimensional elastodynamics in frequency domain. The present wideband FMM is established by coupling the low‐frequency FMM and the high‐frequency FMM that are formulated on the ingenious decomposition of the elastodynamic fundamental solution developed by Nishimura's group. For each of the two FMMs, we estimated the approximation parameters, that is, the expansion order for the low‐frequency FMM and the quadrature order for the high‐frequency FMM according to the requested accuracy, considering the coexistence of the derivatives of the Helmholtz kernels for the longitudinal and transcendental waves in the Burton–Muller type boundary integral equation of interest. In the numerical tests, the error resulting from the fast multipole approximation was monotonically decreased as the requested accuracy level was raised. Also, the computational complexity of the present fast boundary integral equation method agreed with the theory, that is, Nlog N, where N is the number of boundary elements in a series of scattering problems. The present fast boundary integral equation method is promising for simulations of the elastic systems with subwavelength structures. As an example, the wave propagation along a waveguide fabricated in a finite‐size phononic crystal was demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

A fast boundary cloud method for 3D exterior electrostatic analysis

An accelerated boundary cloud method (BCM) for boundary‐only analysis of 3D electrostatic problems is presented here. BCM uses scattered points unlike the classical boundary element method (BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines the weighted least‐squares approach for the construction of approximation functions with a boundary integral formulation for the governing equations. A linear base interpolating polynomial that can vary from cloud to cloud is employed. The boundary integrals are computed by using a cell structure and different schemes have been used to evaluate the weakly singular and non‐singular integrals. A singular value decomposition (SVD) based acceleration technique is employed to solve the dense linear system of equations arising in BCM. The performance of BCM is compared with BEM for several 3D examples. Copyright © 2004 John Wiley & Sons, Ltd.     

Stable Boundary and Internal Data Reconstruction in Two-Dimensional Anisotropic Heat Conduction Cauchy Problems Using Relaxation Procedures for an Iterative MFS Algorithm

We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. The iterative MFS algorithms with relaxation are tested for over-, equally and under-determined Cauchy problems associated with the steady-state anisotropic heat conduction in various two-dimensional geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the method.     

An Optimal Multi-Vector Iterative Algorithm in a Krylov Subspace for Solving the Ill-Posed Linear Inverse Problems

An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth with small error, even under a large noise up to 10%.