求解三维Helmholtz方程的高阶快速数值算法  

A high-order fast algorithm for three-dimensional Helmholtz equation

作　　者：邹静文[1] 李郴良[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2013年第5期420-424,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11161014)

摘　　要：针对三维Helmholtz方程Dirichlet边界问题,提出一种高阶快速数值算法。该算法采用高阶有限差分方法离散化,利用FFT方法将离散方程缩小为规模较小的界面线性方程,可用直接法快速有效地求解。基于该方法可构造出解决三维Helmholtz方程的高阶快速数值算法,数值实验验证了算法的准确性和有效性。Aiming at the Dirichlet boundary problem of 3D Helmholtz equation, a high-order fast numerical algorithm is proposed. The algorithm is discretized by using the high-order finite difference method, and then exploiting the dis- crete Fourier transformation, the discrete system is reduce to a much smaller interface linear system. Direct methods are availed to solve this interface linear system. Numerical results demonstrate the remarkable accuracy and efficiency of the proposed algorithm.

关 键 词：三维Helmholtz方程 紧有限差分方法 FFT 界面线性方程 

分 类 号：O241.82[理学—计算数学]