基于多重网格的Helmholtz方程解算及简单地质模型的大地电磁正演模拟

Solution of Helmholtz equation based on multigrid and magnetotelluric modeling based on simple model

为了提高大地电磁正演模拟的计算效率,开展了基于多重网格算法的Helmholtz方程解算研究;对比Gauss-Seidel、Richardson迭代算法的收敛性,在达到同样的误差限值下,多重网格算法仅需十余次套迭代即可满足误差精度要求,而GaussSeidel和Richardson算法分别需要近500次和5000次迭代;多重网格算法的收敛速度极快,多重网格算法的收敛速度比一般数值算法快近3个数量级;由于其是一种基于套迭代技术,该方法完成一次循环的迭代效率明显比一般数值算法低;多重网格算法极快的收敛速度为将其用于提高大地电磁正演模拟效率提供了可能.

In order to improve computational efficiency for magnetotelluric forward simulation, solving helmholtz equation based on multigrid is studied. Comparing to iterative algorithm such as Gauss-Seidel、Richardson, reached the same error limit,multigrid algorithm need more than ten times,and Gauss-Seidel、Richardson algorithm need 500 times and 600 times respectively.The convergence rate of multigrid is very fast—an order of magnitude upper than the other algorithm. Because the multigrid is a nested iteration,the iteration efficiency is not high than the other numerical algorithm. The fast convergence rate of makes it possible to improve magnetotelluric forward simulation by multigrid.