三角域上C^1连续的C-Coons曲面片

在三角形域上利用两类C-Herm ite多项式构造C1连续的两种形式的C-Coons曲面片,构造的三角曲面片均含有形状参数α,调整α的值,可改变曲面的内部形状,而不影响曲面的边界形状;当形状参数α趋于0时,可退化为通常的边—边与边—点方法插值的曲面片。最后,通过例子比较显示了该方法的实际效果。

三角域上C^1连续的T-Coons曲面片

在三角形域上利用两类含形状参数的三角Hermite多项式构造C1连续的两种形式的带形状参数的Coons曲面片。构造的三角曲面片均含有形状参数λ,调整λ的值,可改变曲面的内部形状,而不影响曲面的边界形状。给定的方法是对通常的边-边法和边-点法的扩展。给出的两个实例显示了方法的有效性。

Novel method to optimize the distributed pump powers in a kilowatt ytterbium-doped double-clad fiber laser

The rate equations with multipoint boundary conditions are solved by numerical method accurately.A novel method based on genetic algorithm is proposed to optimize distributed pump powers in kilowatt YDDC fiber laser in this paper.The calculated results show that lower operation temperature and better uniformity can be achieved through an optimized pump arrangement.

Application of cusp catastrophe theory to reliability analysis of slopes in open-pit mines

A method of slope reliability analysis was developed by imposing a state equation on the limit equilibrium theory, given the basis of a fixed safety factor technique. Among the many problems of reliability analysis, the most important problem is to find a performance function. We have created a new method of building a limit state equation for planar slip surfaces by applying the mathematical cusp catastrophe theory. This new technique overcomes the defects in the traditional rigid limit equilibrium theory and offers a new way for studying the reliability problem of planar slip surfaces. Consequently, we applied the technique to a case of an open-pit mine and compared our results with that of the traditional approach. From the results we conclude that both methods are essentially consistent, but the reliability index calculated by the traditional model is lower than that from the catastrophic model. The catastrophe model takes into consideration two possible situations of a slope being in the limit equilibrium condition, i.e., it may or may not slip. In the traditional method, however, a slope is definitely considered as slipping when it meets the condition of a limit equilibrium. We conclude that the catastrophe model has more actual and instructive importance compared to the traditional model.

Solving Linear Fredholm-Stieltjes Integral Equations of the Second Kind by Using the Generalized Midpoint Rule

In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending on the number of subintervals ＂n＂ are calculated by using Maple 18 and presented. These results are demonstrated graphically in a particular numerical example. An algorithm of this application is given by using Maple 18.

An Algorithm for Partitioning Polygons into Convex Parts

An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.

Singular Hybrid Boundary Node Method for Solving Poisson Equation

As a boundary-type meshless method, the singular hybrid boundary node method（SHBNM） is based on the modified variational principle and the moving least square（MLS） approximation, so it has the advantages of both boundary element method（BEM） and meshless method. In this paper, the dual reciprocity method（DRM） is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function（RBF）. Only randomly distributed nodes on the bounding surface of the domain are required and it doesn＇t need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.

Flotation bubble seed image filling algorithm based on boundary point features

Bubble seed image filling is an important prerequisite for the image segmentation of flotation bubble that can be used to improve flotation automatic control. These common image filling algorithms in dealing with complex bubble image exists under-filling and over-filling problems. A new filling algorithm based on boundary point feature and scan lines ~PFSL） is proposed in the paper. The filling a｜gorithm describes these boundary points of image objects by means of chain codes. The features of each boundary point, including convex points, concave points, left points and right points, are defined by the point＇s entrancing chain code and leaving chain code. The algorithm firstly finds out all double-matched boundary points based on the features of boundary points, and fill image objects by these double-matched boundary points on scan lines. Experimental results of bubble seed image filling show that under-filling and over-filling problem can be eliminated by the proposed algorithm.

Analysis of a moving collocation method for one-dimensional partial differential equations

A moving collocation method has been shown to be very effcient for the adaptive solution of second- and fourth-order time-dependent partial differential equations and forms the basis for the two robust codes MOVCOL and MOVCOL4. In this paper, the relations between the method and the traditional collocation and finite volume methods are investigated. It is shown that the moving collocation method inherits desirable properties of both methods： the ease of implementation and high-order convergence of the traditional collocation method and the mass conservation of the finite volume method. Convergence of the method in the maximum norm is proven for general linear two-point boundary value problems. Numerical results are given to demonstrate the convergence order of the method.

Thermal stresses around a circular inclusion with functionally graded interphase in a finite matrix

Based on the theory of the complex variable functions, the analysis of non-axisymmetric thermal stresses in a finite matrix containing a circular inclusion with functionally graded interphase is presented by means of the least square boundary collocation technique. The distribution of thermal stress for the functionally graded interphase layer with arbitrary radial material parameters is derived by using the method of piece-wise homogeneous layers when the finite matrix is subjected to uniform heat flow. The effects of matrix size, interphase thickness and compositional gradient on the interfacial thermal stress are discussed in detail. Numerical results show that the magnitude and distribution of interfacial thermal stress in the inclusion and matrix can be designed properly by controlling these parameters.

Extrapolation methods to compute hypersingular integral in boundary element methods

The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.

Localized collocation schemes and their applications

This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.

ＱＵＡＤＲＩＬＡＴＥＲＡＬ ＭＥＳＨ

Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1+α)-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.

WEAK TRAVELLING WAVE FRONT SOLUTIONS OF GENERALIZED DIFFUSION EQUATIONS WITH REACTION

The author demonstrate that the two-point boundary value problemhas a solution (A,P(8)), where III is the smallest parameter, under the minimal stringent resstrictions oil f(8), by applying the shooting and regularisation methods. In a classic paper)Kolmogorov et. al. studied in 1937 a problem which can be converted into a special case of theabove problem.The author also use the solutioll (A, p(8)) to construct a weak travelling wave front solutionu(x, t) = y((), (= x -- Ct, C = AN/(N + 1), of the generalized diffusion equation with reactionO { 1 O.IN￣1 OUI onde L k(u) i ox: &) ￣ & = g(u),where N > 0, k(8) > 0 a.e. on [0, 1], and f(s):= ac i: g(t)kl/N(t)dt is absolutely continuouson [0, 11, while y(() is increasing and absolutely continuous on (--co, +co) and(k(y(())ly,(OI'), = g(y(()) -- Cy'(f) a.e. on (--co, +co),y(￣oo) ￣ 0, y(+oo) ￣ 1.