Non‐reflecting artificial boundaries for transient scalar wave propagation in a two‐dimensional infinite homogeneous layer

This paper presents an exact non‐reflecting boundary condition for dealing with transient scalar wave propagation problems in a two‐dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x →∞ and another extends toward x→‐ ∞, the non‐reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time‐dependent partial differential equation with only one spatial variable, can be further changed into a linear first‐order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non‐reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non‐reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi‐infinite media. Copyright © 2003 John Wiley & Sons, Ltd.     

The evaluation of domain integrals in complex multiply-connected three-dimensional geometries for boundary element methods

The treatment of domain integrals has been a topic of interest almost since the inception of the boundary element method (BEM). Proponents of meshless methods such as the dual reciprocity method (DRM) and the multiple reciprocity method (MRM) have typically pointed out that these meshless methods obviate the need for an interior discretization. Hence, the DRM and MRM maintain one of the biggest advantages of the BEM, namely, the boundary-only discretization. On the other hand, other researchers maintain that classical domain integration with an interior discretization is more robust. However, the discretization of the domain in complex multiply-connected geometries remains problematic. In this research, three methods for evaluating the domain integrals associated with the boundary element analysis of the three-dimensional Poisson and nonhomogeneous Helmholtz equations in complex multiply-connected geometries are compared. The methods include the DRM, classical cell-based domain integration, and a novel auxiliary domain method. The auxiliary domain method allows the evaluation of the domain integral by constructing an approximately C ¹ extension of the domain integrand into the complement of the multiply-connected domain. This approach combines the robustness and accuracy of direct domain integral evaluation while, at the same time, allowing for a relatively simple interior discretization. Comparisons are made between these three methods of domain integral evaluation in terms of speed and accuracy. This work was partially supported by the United States Department of Energy (DOE) grants DE-FG03-97ER14778 and DE-FG03-97ER25332. This financial support does not constitute an endorsement by the DOE of the views expressed in this paper.     

频域吸收边界条件的构造理论

在频域中推导了适用于差分类数值方法的吸收边界条件的构造方法，并通过选取不同参数导出了几种现有的吸收边界条件。在计算了一般形式的吸收边界条件的反射系数之后，提出了一种简单实用的自适应吸收边界条件。     

离心泵叶片边界层方程的解析解

给出了离心泵叶片表面的边界层动量积分方程的解的构造及其计算方法，并以计算实例说明了该解的唯一性和算法的稳定性、收敛性。它是分析离心泵流体在叶片表面边界层参数的基础。     

边梁效应的数值模拟

应用Fourier级数方法分析了具有边梁加固的板的弯曲问题，获得了Levy型的准确解，并利用该解模拟了边梁的效应，给出了板的挠度、糨矩及剪力等受边梁刚度影响的数值结果。结果表明：（1）忽略边梁的抗扭能力将导致显著的误差;(2)边梁的抗弯、抗扭性能应综合考虑，而不应作为两个相互独立的因素，否则将会出现板的挠度、内力等随边梁刚度的增大而增大的不合理现象。     

Efficient preconditioners for boundary element matrices based on grey‐box algebraic multigrid methods

This paper is concerned with the iterative solution of the boundary element equations arising from standard Galerkin boundary element discretizations of first‐kind boundary integral operators of positive and negative order. We construct efficient preconditioners on the basis of so‐called grey‐box algebraic multigrid methods that are well adapted to the treatment of boundary element matrices. In particular, the coarsening is based on an auxiliary matrix that represents the underlying topology in a certain sense. This auxiliary matrix is additionally used for the construction of the smoothers and the transfer operators. Finally, we present the results of some numerical studies that show the efficiency of the proposed algebraic multigrid preconditioners. Copyright © 2003 John Wiley & Sons, Ltd.     

Vibrations of stretched damped beams under non-ideal boundary conditions

A simply supported damped Euler-Bernoulli beam with immovable end conditions are considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections and moments. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.     

Material constant sensitivity boundary integral equation for anisotropic solids

In this paper, the material constant sensitivity boundary integral equation is presented, and its numerical solution proposed, based on boundary element techniques. The formulation deals with plane problems with general rectilinear anisotropy. Expressions for the computation of sensitivities for displacements, tractions, strains and stresses are derived, both for boundary and interior points. The sensitivities can be computed with respect to the bulk material properties or to the properties of part of the domain (inclusions, coatings, etc.). To assess the accuracy of the proposed approach, the computed results are compared to analytical ones derived from exact solutions obtained by complex potential theory, when possible, or finite difference derivatives otherwise. Copyright © 2005 John Wiley & Sons, Ltd.     

可控环量船用翼的数值模拟和试验研究

本文提出一种可控环量船用翼数值模拟方法,其计算结果与最近Mclachlan的试验数据十分吻合。通过本文的计算,对广泛引用的Kind ＆ Maull的二维试验数据提出了修正。根据本文所作的三维可控环量帆翼的试验结果,与二维计算值的比较,指出它们之间所存在的显著差别。