无单元伽辽金法及其在瞬态温度场中的应用研究

Element-Free Method and Its Application to Study of Transient Heat Transference

无单元伽辽金法(EFGM)采用移动的最小二乘法构造形函数,和有限元相比,它只需结点信息而不需要单元信息.简述了无单元法的基础理论,推导出瞬态温度场的无单元法计算公式,采用罚函数法引入了第一类边界条件,编制了相应的计算程序.通过应用于经典的瞬态温度场例子,和有限元结果作比较,说明了无单元法具有精度高、前后处理简单等优越性,是一种具有较大发展潜力的新数值计算方法.

The element free Galerkin method （EFGM）, which is based on moving least square, is a new numerical method. EFGM requires only nodal data; no element connectivity is needed. Compared with other methods such as finite element, finite volume or finite difference methods, it is easy to track the growth of phase boundaries and extensive micro cracking. In this paper the element free Galerkin （EFGM） is introduced. A two-dimensional numerical solution of transient heat transfer problems is obtained by means of element frees Galerkin method （EFGM）. The essential boundary conditions can enforce using penalty function method. The MATLAB codes have been developed to obtain the numerical solution. By applying EFGM, the classical example indicates that, compared with finite--element method （FEM）, EFGM has more computation advantages in such respects as accuracy and post--process, etc. Though the element free Galerkin method has been developed for about 20 years, it is a promising method in many fields.