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

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.