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A Moving Particle Method for One Dimensional Convection-diffusion Problem

Author: SunMeiLing
Tutor: HuangYunQing
School: Xiangtan University
Course: Computational Mathematics
Keywords: meshfree method finite point method shape function partition of unity method moving point arclength equidistribution
CLC: O241.82
Type: Master's thesis
Year: 2006
Downloads: 73
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Abstract


Recently, meshfree methods have attracted much interest in the science of computing. This new family of numerical methods shares a common feature that no mesh is needed. These methods are designed to handle large deformation , moving boundary and other difficult problems more effectively. In this paper, we introduce two of them. They are finite point method and partition of unity method. The feature of the finite point method we choose is that it is a truely meshless method. No background meshes or elements are needed in the whole calculation process. And it appears to be computationally more simple and efficient. While the feature of partition of unity method is having the ability to include in the finite element space knowledge about the partial differential equation being solved.In this paper, we propose the moving finite point method and moving partition of unity method. We call both of them moving particle method. The main idea of the new method is relating the meshless method to moving mesh methd. First we distribute the points adaptively by equal arc-length in an iterate way. Then we solve the equation by meshless method. We apply these two moving particle methods to two one-dimensional convection-diffusion problems.The results show that the convergence rate of the moving finite point method is one order higher than the upwind moving mesh method and the moving finite point method is more accurate. While the moving partition of unity method is more accurate than the equal distribution partition of unity method, and it is more stable.This paper consists of four chapters.In the second section, we present the theoretical basis of meshless method. In the third section, we propose the moving finite point method and the moving partition of unity method. In the fourth part, we give the numerical results of our moving point methods for two examples. In the end of the paper, we draw a conclusion of this work and make some comments on the prospect of the moving point method.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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