| With the development of large-scale magnetotelluric(MT)exploration,it is necessary to carry out an efficient solver for large-scale3 D MT forward modeling.However,as the grid size increases,the convergence speed of Krylov subspace iterative methods will slow down,limiting its use in large-scale exploration.In this paper,the multigrid(MG)method whose convergence rate is independent of the size of the problems is introduced as an efficient solver for 3D MT forward modeling.The fast convergence rate of multigrid solver based on classical Gauss-Seidel(GS)breaks for the nontrivial rich null space of the curl-curl operator.We propose a red-yellow Plane GS smoother for 3D MT modeling to obtain a stable MG solver.The smoother combines the electric field components of all nodes on a plane into an independent plane system.The calculation of the system composed of two non-adjacent faces is independent of each other,and the algorithm has good parallelism.At the same time,the red-yellow Plane GS smoother can remove high-frequency error components quickly because it satisfies the local electric field component divergence to zero and enhances the coupling relationship of electrical parameters between nodes on the plane.Based on the coarsening and the semi-coarsening,the air-earth coupling coarsening is proposed,which avoids the air layer unit and the earth unit with a significant resistivity difference from being coarsened into one coarse unit.In this paper,a low-high resistance geoelectric model,two international geoelectric models,and a realistic conductivity model.Based on the multigrid method of red-yellow Plane GS and the multigrid method of GS and BICGSTAB smoother,as well as Krylov subspace iterative methods,the efficiency and precision of these multigrid solvers are compared and verified.The results show that the modeling results of these multigrid solvers implemented in this paper very well agree with the international public results,which verifies the correctness of the solvers.Compared with the Krylov subspace iteration method,the multigrid solvers can fast convergence about ten iterations.Compared with the multigrid solver based on BICGSTAB smoother,the multigrid solver based on redyellow plane GS smoother is more stable and efficient,and the convergence rate is independent of the grid size and the computing period. |
