Collocation Method Using Radial Basis Functions And Its Application To The Numerical Simulation In Groundwater Field

Content: Collocation method using radial basis functions is one of thenew numerical analysis methods to solve differential equations,and itwas developed in recent ten years. Mesh is not required in the methodso that the influence of the mesh distortion is reduced evidently. Inthis dissertation,we investigate the basic theory of collocation methodusing radial basis functions.We applied this method to the numericalsimulation in groundwater field.The results of the tests is acceptable.This paper consists of five chapters.In chapter 1,we summarize the his-tory of the meshless method and my main work in this paper. Chaper2 includes the preliminary knowledge. In this section, we introduce themain theory of the radial basis flmctions. In addition to this, we summa-rize the advances of the multiquadric function. In chapter 3, we discussthe theory and approach using radial basis functions by collocation tosolve partial differential equations. In chapter 4,we apply collocationmethod using radial basis functions to the numerical simulation ingroundwater field. We use this method to calculate Darcy's velocity ofunsteady flow and to study confined steady well flow problem. From theresults of the numerical experiments we made, the collocation methodusing radial basis functions has the advantage in easiness and accu-racy compared to the traditional numerical analysis methods. The lastsection we conclude our main results and the work we will put in thefuture.