This paper deals with a new multigrid method with reduced phase error for solving 2D damped Helmholtz equations. The method is obtained by taking the high-effective, reduced phase error 5-point finite difference (FD) scheme as a coarse grid operator and the regular 5-point FD scheme as a fine grid operator. It is found that the proposed method gives a faster convergent rate than the regular multigrid method. A local mode Fourier analysis confirms the validity of our proposed method. Finally, some numerical results demonstrate the efficiency of the method.

中文翻译：

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二维阻尼亥姆霍兹方程减少相位误差的多重网格方法

本文讨论了一种新的多重网格方法，该方法可以减少相位误差，用于求解二维阻尼亥姆霍兹方程。该方法是将高效、减少相位误差的5点有限差分(FD)方案作为粗网格算子，将常规5点FD方案作为细网格算子得到的。发现所提出的方法比常规多重网格方法给出更快的收敛速度。局部模式傅里叶分析证实了我们提出的方法的有效性。最后，一些数值结果证明了该方法的有效性。