A Geometric Multigrid Method for 3D Magnetotelluric Forward Modeling Using Finite-Element Method

The traditional three-dimensional (3D) magnetotelluric (MT) forward modeling using Krylov subspace algorithms has the problem of low modeling efficiency. To improve the computational efficiency of 3D MT forward modeling, we present a novel geometric multigrid algorithm for the finite element method. We use the vector finite element to discretize Maxwell's equations in the frequency domain and apply the Dirichlet boundary conditions to obtain large sparse complex linear equations for the solution of EM responses. To improve the convergence of the solution at low frequencies we use the divergence correction to correct the electric field. Then, we develop a V-cycle geometric multigrid algorithm to solve the linear equations system. To demonstrate the efficiency and effectiveness of our geometric multigrid method, we take three synthetic models (COMMEMI 3D-2 model, Dublin test model 1, modified SEG/EAEG salt dome model) and compare our results with the published ones. Numerical results show that the geometric multigrid algorithm proposed in this paper is much better than the commonly used Krylov subspace algorithms (such as SOR-GMRES, ILU-BICGSTAB, SOR-BICGSTAB) in terms of the iteration number, the solution time, and the stability, and thus is more suitable for large-scale 3D MT forward modeling.

Automated summary

In order to improve the computational efficiency of 3D magnetotelluric (MT) forward modeling, a novel geometric multigrid algorithm for the finite element method is proposed. The algorithm discretizes Maxwell's equations in the frequency domain using vector finite element and applies Dirichlet boundary conditions to obtain complex linear equations for the solution of EM responses. A divergence correction is used to improve the convergence of the solution at low frequencies, and a V-cycle geometric multigrid algorithm is developed to solve the linear equations system. Numerical results show that the proposed algorithm outperforms commonly used Krylov subspace algorithms in terms of iteration number, solution time, and stability, making it more suitable for large-scale 3D MT forward modeling.