Constrained Moving Least Square Method for SolvingPoisson's Equations

• Main Authors: Ying-XuanLai, 賴穎暄
• Other Authors: Yung-Ming Wang
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/84089357149357350454

碩士 === 國立成功大學 === 土木工程學系碩博士班 === 101 === In this thesis, the constrained moving least square method is adopted to solve the two-dimensional Poisson’s equations, including the steady-state heat transfer and ideal fluid problems. The feature of this approach is that, by adding suitable constraints with the help of the moving least square approach, the approximate function is constrained to fit the governing equation and boundary conditions. Moreover, the weighted sum of the residuals, which results from the approximation of the field variable, is attempted to be minimized so that the process leads to an interpolation function which is expressed in terms of nodal value of the field variable. The point collocation technique is then introduced to determine the unknown nodal values. In the numerical examples, the Poisson’s equations with different boundary conditions are solved and compared with the exact solutions to examine the accuracy and the rate of convergence of the present method. Moreover the influences of boundary conditions to the numerical accuracy are discussed.