多小波在一维有限元方法中的应用

有限元方法（FEM）是建立在变分原理基础上的一种频域数值计算方法。其基函数的选取相当重要，既影响到计算结果的精度也影响到计算效率。通常情况下，都是利用拉格朗日线性插值函数作为基函数。文中利用了多尺度函数。由于多尺度函数及它的偏导数的差值特性，可以快速逼近某个函数。同时这个新的基函数的一阶偏导数在相邻节点上是连续的。最后得到的数值结果显示：在保证一定计算效率的基础上，使得精度大幅度提高。因此采用多尺度函数作为基函数具有很多优势。

Applications of Multiwavelets in 1D Finite Element Method

Based on the variational principle,finite element method is a numerical technique in the frequency domain.The choices of basis functions not only influence precision of the solution,but also influence efficiency. Generally,always use the Lagrange linear interpolation functions as the basis functions.In this paper,the multiscalets are employed.Because of the interpolatory properties of the multiscalets and their derivatives,fast convergence in approximating a function is achieved.The first derivatives of the new basis functions are continuous on the connecting nodes.The numerical results demonstrate that this method greatly enhances precision,while a certain extent efficiency is guaranteed.So multiscalets employed as the basis functions have many advantages.