二维Helmholtz方程边值问题的虚边界元解法

摘要

针对二维Helmholtz方程边值问题,采用单层位势方式,利用分布在虚边界上的场源函数,建立了二维Helmholtz方程边值问题的虚边界元计算公式.该方法避免了传统边界元算法中奇异积分的计算,具有边界附近精度高的优点.数值算例证明了此方法的可行性和有效性.%Based on the single layer potential, the virtual boundary calculation formula of 2D Helmholtz equation boundary value problem is given with the help of the field source function on the virtual boundary. The method can avoid the singular integral, and it can reach a high accuracy near the boundary. Numerical example demonstrate the feasibility and efficiency of this method.