求解二维Helmholtz外问题的一种快速算法

本基于虚拟边界积分法，通过将虚拟积分曲线选为多(单)条圆形曲线，并在这些圆形积分曲线上将未知源强密度函数用Fourier级数展开，同时借助快速数值Fourier逆变换(IFFT)计算程序，提出了一种求解二维Helmholtz外问题的快速算等。该方法由于不需要将分布在虚拟边界上的未知函数进行单元分散，不仅克服了边界元法或虚拟边界元法中由于单元形函数是由低阶多项式函数构成导致其结果只适用于较低频率范围的不足，而且具有很高的计算精度和效率。中给出的数值算例表明了这种快速算法的计算效率是虚拟边界元法的20-80倍。

Fast Algorithm for 2-D Helmholtz Exterior Problems

In the paper,based on the virtual boundary integral method,by means of selecting the virtual integral boundary as single or multi circular curves and expanding the unknown source density distributed on each virtual circular curve in to Fourier's series,meanwhile combining with the program of inverse fast Fourier transformation(IFFT),a fast algorithm for solving 2_D exterior Helmholtz problems is presented.Because of that the method presented in the paper doesn't need discretize the unknown functions distributed on virtual boundary with finite elements,not only it can effectually overcome the shortcoming of common discretized methods that it can't be still available in higher_frequency range due to the shape functions of elements being composed of lower order polynomial functions,but also good accuracy and efficiency can be achieved.Numerical results show that the calculation efficiency of the fast algorithm proposed in the paper is 20-80 times higher than the virtual boundary element method.