Applied Mechanics and Materials Vols. 444-445

Abstract: In the paper, by means of Laplace transform the Sobolev differential equations become to the elliptic differential equations, which can be solved by the fourth order finite difference equations in parallel. After getting the approximate solutions of the elliptic differential equations, we can achieve the numerical solutions with high accuracy for the Sobolev differential equations by using the Zakian inversion method. At last, we carry out one numerical experiment to indicate that the method in this paper is effective.

Abstract: A new quadrature method is proposed for numerical integration of integrands with the singularity of 1/r occurring at the computation of stiffness matrix when a singular physical cover is introduced to the numerical manifold method (NMM) for linear fracture problems. The detailed proof is presented, which shows the Jacobian has a factor of r that can be used to eliminate the singularity. Compared with the Duffy transformation, it proves more simple and easier to implement while owning the same precision. A numerical example in elastic fracture by the NMM is presented to illustrate the performance of the proposed method. The result has a good agreement with the reference solution.

Abstract: Fast algorithm for multi-frequency numerical integration in the simulation of acoustic scattering from rigid object by the boundary element method is presented. Normal derivative of the free-space Greens function is partially approximated with the unknown variable by a set of shape functions. As a result, the numerical integral is independent of frequency and need be calculated only at the first frequency step. Singular integral can be computed using the same procedure as that applied in the conventional boundary element method. Computational efficiency and accuracy of the new technique are demonstrated by an example. Numerical results obtained using the new technique are compared with the corresponding analytical solutions and numerical results obtained using the conventional boundary element method. The new technique works well and saves a lot of computational time in the process of generation of coefficient matrices for multi-frequency analysis.

Abstract: Using one known series, We can structure several new series of reciprocals of central binomial coefficients by splitting terms ,these new created denominator of series contain 1 to 4 factors of binomial coefficients. As the result of splitting terms, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial an analysis way and elementary method to create new series.

Abstract: In this paper, we propose a single-interval Legendre-Gauss collocation method for multi-pantograph delay differential equations. Numerical experiments are carried out to illustrate the high order accuracy of the numerical scheme.

Abstract: For the multi-attribute decision making with time series, based on the comprehensive consideration of various indicators of quality and growth degree, with grey relational analysis on less data, uncertain information can be integrated comparison, so we put forward a new decision method considering the decision maker subjective views, and provide a scientific and rational decision-making method. By the example, that method is viable.

Abstract: In recent three decades, the finite element method (FEM) has rapidly developed as an important numerical method and used widely to solve large-scale scientific and engineering problems. In the fields of structural mechanics such as civil engineering , automobile industry and aerospace industry, the finite element method has successfully solved many engineering practical problems, and it has penetrated almost every field of today's sciences and engineering, such as material science, electricmagnetic fields, fluid dynamics, biology, etc. In this paper, we will overview and summarize the development of the p and h-p version finite element method, and introduce some recent new development and our newest research results of the p and h-p version finite element method with quasi-uniform meshes in three dimensions for elliptic problems.

Abstract: In multiple attribute clustering algorithms with uncertain interval numbers, most of the distances between the interval-valued vectors only consider the differences of each interval endpoint ignoring a lot of information. To solve this problem, according to the differences between corresponding points in each interval number, this paper gives a distance formula between interval-valued vectors, extends a FCM clustering algorithm based on interval multiple attribute information. Through an example, we prove the validity and rationality of the algorithm. Keywords: interval-valued vector; FCM clustering algorithm; distance measure; fuzzy partition

Abstract: In this study, two sixth-order compact finite difference schemes have been considered for solving the Burgers equation. The main difference of these schemes lies in the calculation of second-order derivative terms, which is obtained by applying the first-order operator twice and the method of undetermined coefficients. The aim is to comparison these schemes in terms of computational accuracy for solving the Burgers equation with difference viscosity values, especially for very small viscosity values. The results show that both schemes achieve almost the same accuracy for large viscosity values and second method is more accurate for moderate viscosity values, but both schemes are failed for very small viscosity values. However, when both schemes coupled low-pass filter for very small viscosity values, both schemes can well inhibit the problem.

Abstract: When analyzing time series an important issue is to decide whether the time series is stationary or nonstationary. Fixed sample statistical tests for that problem are well studies in the literature. In this paper we propose a moving variance ratio statistic to monitor the stationarity for normal sequence. Our Monte Carlo studies show that the proposed monitoring procedure has satisfactory test power and that the decision can often be made very early.