频域波动方程的多重网格法

针对差分法求解过程中细网格计算所需时间和空间要求高以及在粗网格上计算又达不到所要求的精度等问题，利用粗网格上的残差校正特性消除迭代误差的低频分量，同时利用细网格上的松弛光滑特性消除迭代误差的高频分量，采用不同疏密的网格距消除不同频率范围内的误差分量，将多重网格方法成功应用于频域波动方程的求解，并给出了实际算例。算例中，分别用Gauss-Seidel迭代法和多重网格法求其数值解，并绘出效果图；比较得出多重网格方法具有精度高、收敛速度快和易于实现的特性，更适合于高维波动问题的求解。

A Multigrid Method for the Solution of Wave Equation in the Frequency Domain

During the solution-finding of difference method,using fine grid to calculation need more time and space of the computer,and rough grid can not get the needed precision.Use the residual error correction speciality on rough grid to eliminate the low frequency component of iterative error.At the same time,use the slack smooth speciality on fine grid to eliminate the high frequency component of iterative error.By using different dense grid distant to eliminate the error component in different frequency range,the multigrid method was successful applied to the numerical solution of wave equation in the frequency domain and gave practical experiments. In this example, we separately used the gauss-seidel method and the multi-grid method to solve its numerical solution, and draw the graph. In contrast to them, we conclude that the multi-grid method has quickly convergence, high precision and easy realization. This method is very suitable to high degree problem about wave.