计算Helmholtz方程边值问题的一种级数展开法

A series expansion method for solving the boundary value problem connected with the Helmholtz equation

本文主要研究光滑有界域上的Helmholtz方程的边值问题,构造一种级数展开方法给出此问题的近似解,并且使用Tikhonov正则化方法处理带有噪声的数据。利用具体的数值试验,验证了这种数值方法的有效性。

Boundary value problem connected with the Helmholtz equation is studied in a smooth bounded domain.A series expansion method is proposed for obtaining an approximate solution to the problem.Tikhonov regularization is applied to the problem with noisy data.Numerical experiments are presented to show the effectiveness of the proposed method.