Explicit formulations for evaluation of velocity gradients using boundary‐domain integral equations in 2D and 3D viscous flows

In this paper, explicit boundary‐domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer. Meth. Fluids 2004; 45 :463–484; Int. J. Numer. Meth. Fluids 2005; 47 :19–43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer. Meth. Fluids 2004; 45 :463–484) for 2D and in (Int. J. Numer. Meth. Fluids 2005; 47 :19–43) for 3D problems constitutes a complete boundary‐domain integral equation system for solving full Navier–Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright © 2007 John Wiley & Sons, Ltd.     

A space of generalized distributions

In this paper we use a duality method to introduce a new space of generalized distributions. This method is exactly the same introduced by Schwartz for the distribution theory. Our space of generalized distributions contains all the Schwartz distributions and all the multipole series of physicists and is, in a certain sense, the smallest space containing all these series. To The Memory of Laurent Schwartz     

Higher Electric Multipole Moments for Some Polyatomic Molecules from Accurate SCF Calculations

Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical andexperimental ones.     

扩散方程基本解的积分处理

详细讨论了时间相关热交换问题扩散方程基本解的时间积分特性，给出了完整的解析处理及相应级数展开表达式，并提出采用按时段构造的时间单元局部化基本解作为边界元法的加权函数，从而显著减少可动边界问题边界元解法的存贮量和计算时间。     

Analytical removal of singularity and direct evaluation of singular integrals in 3-D elastoplastic finite deformation analysis by BEM

As a further development of the present authors' research work [1,2], in this paper a method of the so-called quadratic pentahedron polar co-ordinate transformation and analytical removal of singularity of Cauchy principal value singular integrals is proposed to evaluate the strongly singular integrals in the sense of Cauchy principal values and the weakly singular integrals over quadratic internal cells in 3-D elastoplastic finite deformation analysis by BEM. First, a quadratic pentahedron polar co-ordinate transformation technique is used to reduce the order of singularity of the singular integrals. Then, a form of Gauss' theorem is introduced to remove the singularity in the Cauchy principal value singular integrals analytically. Therefore, the evaluation of all those strongly and weakly singular integrals can be carried out by standard Gaussian quadrature accurately and efficiently. Numerical examples of the 3-D elastoplastic problem and 3-D finite deformation problem are given to demonstrate that the method possesses good accuracy and numerical stability, and is convenient to implement. The method in this paper can be applied extensively to evaluating the singular integrals over cubic and higher order elements.     

Blended kernel approximation in the ℋ︁‐matrix techniques

Several types of ??‐matrices were shown to provide a data‐sparse approximation of non‐local (integral) operators in FEM and BEM applications. The general construction is applied to the operators with asymptotically smooth kernel function provided that the Galerkin ansatz space has a hierarchical structure. The new class of ??‐matrices is based on the so‐called blended FE and polynomial approximations of the kernel function and leads to matrix blocks with a tensor‐product of block‐Toeplitz (block‐circulant) and rank‐k matrices. This requires the translation (rotation) invariance of the kernel combined with the corresponding tensor‐product grids. The approach allows for the fast evaluation of volume/boundary integral operators with possibly non‐smooth kernels defined on canonical domains/manifolds in the FEM/BEM applications. (Here and in the following, we call domains canonical if they are obtained by translation or rotation of one of their parts, e.g. parallelepiped, cylinder, sphere, etc.) In particular, we provide the error and complexity analysis for blended expansions to the Helmholtz kernel. Copyright © 2002 John Wiley & Sons, Ltd.     

气垫船稳态船波势及波阻的边界元法

本文给出了气垫船在静水中航行时稳态船波势问题的边界元数值分析方法，根据本文的数值计算方法，可以得到气垫船行时所兴起的波浪形状以及气垫附近流场情况，由此可计算气垫所受到的兴波阻力，本文的方法适用于任意已知气压分布情况。     

Parallel solvers for the depletion region identification in metal semiconductor field effect transistors

In this work we are interested in a sufficiently accurate approximation of the steady-state potentials in a Metal Semiconductor Field Effect Transistor (MESFET), which can be obtained with the so-called depletion region approximation (see [5]). We propose a robust method based on the shape optimization techniques to analyze and compute the depletion boundary as a function of the applied voltage and the geometry material properties of the device. During the optimization process several intermediate direct problems are solved using the boundary element method (BEM). To accelerate the solutions of of these systems we use a strategy of subdividing the domain into a number of smaller subdomains [11,9]. The scheme is iterative and each subdomain is handled by a separate node in parallel. Test runs comparing the performance of the parallel with the serial code, and other numerical discussions are presented. AMS subject classification 65N55, 65N38, 65K10, 78A55. A. Nachaoui: Corresponding author.