中文摘要：

1引言 许多科学和工程计算问题都可以归结为无界区域上的偏微分方程边值问题．而求解椭圆方程边值问题的常用技术是有限元方法，可是对于无界区域，在用有限元方法求解时，往往遇到困难．最简单的办法显然是直接略去区域的无界部分求解，但这样做或者导致过低的计算精度，或者要付出很高的计算代价．边界归化，即将求解偏微分方程边值问题转化为边界积分方程，是求解某些无界区域问题的强有力的手段．自70年代以来，

英文摘要：

In the present thesis we are mainly concerned with the wavelet method for numerical solution of the boundary value problem of Helmholtz equation which are widely applied in mechanics and engineering. As a result, the stiffness matrix is circulant, symmetry or anti-symmetry where the nonzero entries have finite explicit expression. So that the computational cost is extremely decreased and the accuracy is extremely improved.