| 求解三维Helmholtz方程的高阶快速数值算法 |
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| 引用本文： | 邹静文,李郴良.求解三维Helmholtz方程的高阶快速数值算法[J].桂林电子科技大学学报,2013(5):420-424. |
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| 作者姓名： | 邹静文 李郴良 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院,广西桂林541004 |
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| 基金项目： | 国家自然科学基金（11161014） |
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| 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。
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| 关 键 词： | 三维Helmholtz方程 紧有限差分方法 FFT 界面线性方程 |
A high-order fast algorithm for three-dimensional Helmholtz equation |
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| Zou Jingwen,Li Chenliang.A high-order fast algorithm for three-dimensional Helmholtz equation[J].Journal of Guilin Institute of Electronic Technology,2013(5):420-424. |
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| Authors: | Zou Jingwen Li Chenliang |
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| Affiliation: | (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China) |
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| Abstract: | 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. |
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| Keywords: | three-dimensional Helmholtz equation compact finite difference method FFT interface linear equation |
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