Papers by Keyword: Collocation Method

Paper TitlePage

Authors: Zhao Qing Wang, Bing Tao Tang, Wei Zheng
Abstract: A meshless, barycentric interpolation collocation method for numerical approximation of Darcy flows is proposed. The barycentric Lagrange interpolation and its differentiation matrices are basic tool to discretize governing equations, Dirichlet and Neumann boundary conditions. For Darcy flows in irregular domains, embedding the irregular domain into a rectangular, the barycentric interpolation collocation method can be directly applied. The resultant saddle-point systems come from combining the discretized governing equations and boundary conditions, such that we can deal easy with all kinds of boundary condition either regular or irregular domains. Some numerical examples are given to illustrate the accuracy, stability and robust of presented method.
3
Authors: Zhao Qing Wang, Jian Jiang, Bing Tao Tang, Wei Zheng
Abstract: A barycentric interpolation Newton-Raphson iterative method for solving nonlinear beam bending problems is presented in this article. The nonlinear governing differential equation of beam bending problem is discretized by barycentric interpolation collocation method to form a system of nonlinear algebraic equations. Newton-Raphson iterative method is applied to solve the system of nonlinear algebraic equations. The Jacobian derivative matrix in Newton-Raphson iterative method is formulated by the Hadamard product of vectors. Some numerical examples are given to demonstrate the validity and accuracy of proposed method.
41
Authors: Jakub Krzysztof Grabski, Jan Adam Kołodziej
Abstract: Fluid flow in internally finned tubes is a very important problem from a practical point of view. In the literature there are many different numerical methods which were used for analysis this problem. However to the best knowledge of the authors of the present paper there are no so many papers in which meshless methods were applied for this purpose. The main advantages of these methods are: easy implementation, semi-analytical form of the approximate solution and no need for mesh generation. In the paper these meshless methods are compared in application for analysis of incompressible, fully-developed, Newtonian fluid flow in an internally finned tube.
274
Authors: M.R.H. Rudge, D.M. Tiernan
101
Authors: Gorka Urbikain Pelayo, David Olvera, A. Fernández, Adrián Rodríguez, I. Tabernero, Luis Norberto López de Lacalle
Abstract: An accurate prediction of the dynamic stability of a cutting system involves the implementation of tool geometry and cutting conditions on any model used for such purpose. This study presents a dynamic cutting force model based on the collocation method by Chebyshev polynomials taking advantage from its ability to consider tool geometry and cutting parameters. In the paper, a simple 1DOF model is used to forecast chatter vibrations due to the workpiece and tool, which are distinguished in separate sections. The proposed model is verified positively against experimental dynamic tests.
231
Authors: Jian Zhou, Xing Cun Wu
Abstract: This paper starts with the principle and operation approaches of Collocation orbit integration method, analyzing the integration process and initialization value of motion equation and variation equation. Through different integration lengths and polynomial degrees, this paper discussed the impact to orbit precision. It also compares the results to the scientific orbit which were offered by GFZ, through the analysis of this method; we also find the appropriate integration length and polynomial degree and validate the validity of this method.
4435
Authors: Yong Ming Guo
Abstract: In this paper, a forging problem is analyzed by using the overrange collocation method (ORCM), which is a new meshless method. By introducing some collocation points, which are located out of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no overconstrain occurs in partial differential equations on the solved problems.
1675
Authors: Yong Ming Guo, Shunpei Kamitani
Abstract: In this paper, an upsetting problem is analyzed by using a new meshless method called the overrange collocation method (ORCM). By introducing some collocation points, which are located at outside of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no over-constrain condition is imposed into solved boundary value problems.
1396
Authors: Yong Ming Guo, Shunpei Kamitani
Abstract: In this paper, a forging problem is analyzed by using the overrange collocation method (ORCM), which is a new meshless method. By introducing some collocation points, which are located out of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no overconstrain occurs in partial differential equations on the solved problems.
942
Authors: Necdet Bildik, Duygu Dönmez Demir
Abstract: This paper deals with the solutions of lateral heat loss equation by using collocation method with cubic B-splines finite elements. The stability analysis of this method is investigated by considering Fourier stability method. The comparison of the numerical solutions obtained by using this method with the analytic solutions is given by the tables and the figure.
3184
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